A Completely Different and Innovative Bio-Inspired Metaheuristic Approach for Effectively Solving Complex Optimization Problems Across Various Domains

1. Introduction

Many problems in both science and real-world applications present multiple feasible solutions, which makes them complex to solve. These problems are referred to as optimization problems, and the process of identifying the most suitable solution from the set of available options is known as optimization [1]. From a mathematical perspective, optimization problems consist of three main components: decision variables, constraints, and objective functions. The goal of optimization, therefore, is to determine the optimal values for the decision variables while adhering to the constraints so that the objective function achieves its most favorable outcome, either maximum or minimum [2]. Optimization problem-solving methods are broadly classified into two completely different categories: deterministic and stochastic approaches [3]. Deterministic methods, which are further divided into gradient-based and non-gradient-based techniques, are particularly effective in solving linear, convex, continuous, differentiable, and low-dimensional optimization problems [4,5]. However, as the complexity and dimensionality of these problems increase, deterministic methods often fail by getting trapped in suboptimal local solutions [6,7]. This is especially true for problems that are non-linear, non-convex, discontinuous, non-differentiable, and high-dimensional, which are common in scientific and practical applications. Due to these limitations, researchers have developed stochastic approaches to tackle more challenging optimization problems.

Metaheuristic algorithms, which are one of the most widely employed stochastic methods, are highly effective in addressing complex optimization challenges. Metaheuristic algorithms work by utilizing a random search mechanism within the problem space, employing random operators and a trial-and-error process to find suitable solutions. The advantages of metaheuristic algorithms include the simplicity of their concepts, ease of implementation, independence from the specific problem type, and the ability to solve non-linear, non-convex, discontinuous, non-derivative, and high-dimensional optimization problems. Furthermore, they are efficient in exploring unknown, non-linear search spaces, which explains their popularity among researchers [8].

The optimization process in metaheuristic algorithms begins by randomly generating a set of initial candidate solutions that respect the constraints of the problem. In an iterative process, these solutions are progressively refined based on the updating steps defined by the algorithm. The best solution found at each iteration is saved, and ultimately, the best overall solution is presented as the final result [9]. While the random search nature of these algorithms means that they cannot guarantee a global optimum, the solutions they produce are often near-optimal, which are referred to as quasi-optimal solutions. Consequently, when comparing the performance of multiple metaheuristic algorithms, the one that provides a better quasi-optimal solution is considered the most effective one for that particular problem [10].

The search process in metaheuristic algorithms must balance two key concepts: global exploration and local exploitation. Global exploration enables the algorithm to thoroughly scan the problem space, preventing it from getting stuck in local optima and helping to identify the most promising areas in the search space. Local exploitation, on the other hand, allows the algorithm to converge towards a global optimum by intensively searching around promising regions and refining solutions. Striking a balance between exploration and exploitation is crucial for the success of any metaheuristic algorithm in providing effective solutions [11].

A key question in metaheuristics research is whether, given the vast number of algorithms already developed, there is still a need to design completely different metaheuristic algorithms. The No Free Lunch (NFL) theorem provides an answer to this. It states that the success of a metaheuristic algorithm in solving one set of optimization problems does not guarantee its success in solving others [12]. Therefore, no single algorithm is universally optimal for all optimization tasks. This insight encourages ongoing innovation in the field of metaheuristic algorithm design, as the NFL theorem suggests that newer algorithms can offer more effective solutions for specific problem sets.

The novelty of this paper lies in the development of a new metaheuristic algorithm called the Orangutan Optimization Algorithm (OOA), designed to solve a variety of optimization problems in different scientific fields and real-world applications. The key contributions of the paper are as follows:

• OOA is inspired by the natural behavior of orangutans in the wild.
• The algorithm’s core inspiration comes from the foraging strategies and nesting skills of orangutans.
• The steps of OOA are described and mathematically modeled in two phases: exploration and exploitation.
• The performance of OOA is evaluated using twenty-nine benchmark functions from the CEC 2017 test suite.
• A comparative performance analysis is conducted, comparing OOA with twelve other well-known metaheuristic algorithms.
• To assess its effectiveness in real-world applications, OOA is applied to twenty-two optimization problems from the CEC 2011 test suite.

The structure of the paper is as follows: Section 2 provides a literature review. Section 3 introduces and models the Orangutan Optimization Algorithm. Section 4 presents the simulation studies and results. Section 5 investigates the effectiveness of OOA in solving real-world applications. Finally, conclusions and suggestions for future research are discussed in Section 6.

2. Literature Review

Metaheuristic algorithms are systems designed by drawing inspiration from a wide range of completely different sources, including natural phenomena, the lifestyles of animals in nature, biological and genetic sciences, fundamental laws of physics, rules and strategies from games, human interactions, and various other evolutionary processes. Depending on the foundational idea utilized in their development, these algorithms are categorized into four completely different groups: swarm-based approaches, evolutionary-based methods, physics-based models, and human-based approaches. This classification allows for a more organized understanding of the many different algorithmic approaches that have been inspired by both nature and human behavior.

Swarm-based metaheuristic algorithms, for example, are rooted in the collective behavior seen in the nature, such as the swarming activities of birds, animals, insects, aquatic species, and even plants. Completely different animals exhibit unique strategies in their collective movements, which has inspired the creation of algorithms like Ant Colony Optimization (ACO) [13], Particle Swarm Optimization (PSO) [14], and Artificial Bee Colony (ABC) [15]. These particular algorithms mimic the way ants discover the shortest path between their colony and food sources by following chemical pheromones, or how flocks of birds and schools of fish adjust their movement when searching for food. The behavior of honey bees in seeking out food resources has inspired the development of ABC. Other swarm-based metaheuristics take inspiration from foraging, hunting strategies, migration, and even digging behaviors observed in wildlife, leading to the creation of completely different algorithms like Reptile Search Algorithm (RSA) [16], Grey Wolf Optimizer (GWO) [17], Orca Predation Algorithm (OPA) [18], Marine Predator Algorithm (MPA) [19], African Vultures Optimization Algorithm (AVOA) [20], White Shark Optimizer (WSO) [21], Honey Badger Algorithm (HBA) [22], Whale Optimization Algorithm (WOA) [23], Tunicate Swarm Algorithm (TSA) [24], and Golden Jackal Optimization (GJO) [25].

Similarly, evolutionary-based metaheuristic algorithms find their foundation in biological processes such as natural selection, genetics, and Darwin’s theory of evolution. Genetic Algorithm (GA) [26] and Differential Evolution (DE) [27] are two of the most prominent examples of this group, which rely heavily on mechanisms like mutation, crossover, and selection to find optimal solutions. The immune system's ability to fight off diseases has also provided inspiration for completely different algorithms, such as Artificial Immune Systems (AISs) [28]. The adaptability and survival strategies of species have also led to the design of algorithms like Evolution Strategy (ES) [29], Cultural Algorithm (CA) [30], and Genetic programming (GP) [31], which all use evolutionary operators to improve solutions over time.

Physics-based metaheuristic algorithms are inspired by the laws of physics and various natural forces. One of the most famous in this category is Simulated Annealing (SA) [32], which models the annealing process in metallurgy, where materials are heated and slowly cooled to form ideal crystals. Physical forces such as gravity, momentum, and spring tension have influenced the creation of algorithms like Spring Search Algorithm (SSA) [10] inspired by the tensile force of springs, Gravitational Search Algorithm (GSA) [33] inspired by gravitational force, and Momentum Search Algorithm (MSA) [8] inspired by momentum force. The natural water cycle has also led to the Water Cycle Algorithm (WCA) [34]. More examples from this completely different category include: Multi-Verse Optimizer (MVO) [35], Archimedes Optimization Algorithm (AOA) [36], Electro-Magnetism Optimization (EMO) [37], Nuclear Reaction Optimization (NRO) [38], Equilibrium Optimizer (EO) [39], Black Hole Algorithm (BHA) [40], Thermal Exchange Optimization (TEO) [41], Lichtenberg Algorithm (LA) [42], and Henry Gas Optimization (HGO) [43], each inspired by unique physical phenomena.

Human-based metaheuristic algorithms draw from human communication, collaboration, and behavior. Teaching-Learning Based Optimization (TLBO) [44], for instance, models the interaction between teachers and students, while Teamwork Optimization Algorithm (TOA) [45] is based on the collaborative efforts of a team working toward a common goal. Completely different human-based algorithms also take inspiration from various other aspects of human behavior, such as Coronavirus Herd Immunity Optimizer (CHIO) [46], Ali Baba and the Forty Thieves (AFT) [47], War Strategy Optimization (WSO) [48], Gaining Sharing Knowledge based Algorithm (GSK) [49], and Driving Training-Based Optimization (DTBO) [6]. Each of these human-based algorithms taps into social behaviors, cooperation, or learning processes to solve optimization problems in unique ways.

Despite the vast range of inspirations used in metaheuristic algorithm design, no algorithm has been modeled after the natural behavior of orangutans. This is surprising given that orangutans demonstrate intelligent strategies in foraging and nesting, making their behaviors a completely different yet promising source of inspiration for developing a new metaheuristic algorithm. Recognizing this gap, the current paper proposes a new metaheuristic algorithm, based on the mathematical modeling of the intelligent behaviors of orangutans, which will be explored in detail in the following section.

3. Orangutan Optimization Algorithm

In this section, the source of inspiration behind the Orangutan Optimization Algorithm (OOA) is thoroughly explained, followed by a comprehensive description of the theory underlying the approach. Afterwards, the step-by-step implementation of the OOA is carefully modeled using mathematical formulations, ensuring it can be effectively applied to solve completely different types of optimization problems.

3.1. Inspiration of OOA

Orangutans are fascinating great apes that reside in the dense rainforests of Malaysia and Indonesia, with their current populations limited to parts of Sumatra and Borneo. Although their range was once much broader, extending throughout South China and Southeast Asia during the Pleistocene era, these critically endangered creatures now face completely different environmental pressures and challenges. Physically, orangutans exhibit a variety of distinct traits: females generally weigh around 37 kg and reach a height of 115 cm, while the larger males weigh approximately 75 kg and stand at 137 cm tall. One of the most striking features of orangutans is their proportionally long arms, with males having an arm span of around 2 meters, compared to their relatively shorter legs. Their bodies are covered with thick reddish-brown hair that darkens to shades of maroon or chocolate as they age, while their skin color ranges from grey to black [50]. A picture of orangutan is shown in Figure 1.

The diet of orangutans is primarily fruit-based, with about 57 to 80% of their foraging time spent consuming a variety of fruits. In addition to fruits, they spend around 25% of their time eating tree leaves. Other sources of nutrition include small vertebrates, insects, bird eggs, honey, and tree bark. This dietary flexibility highlights their adaptability in foraging within the forest [51]. An equally remarkable aspect of orangutan behavior is their skill in nest-building. Young orangutans learn to build nests by observing their mothers, starting the process as early as six months of age and becoming adept by the time they are three years old. Their nests, built in trees, are highly structured. First, orangutans select suitable branches and weave them together to form a foundation. Then, using smaller, leafy branches, they create a soft mattress. Some nests are further enhanced with additional features such as bunk beds, roofs for protection, and even makeshift blankets and pillows to ensure comfort during rest [52].

These intelligent and intricate natural behaviors—specifically their foraging strategies and nest-building techniques—serve as the foundation for the development of the Orangutan Optimization Algorithm (OOA).

3.2. Algorithm Initialization

The newly introduced Orangutan Optimization Algorithm (OOA) is a bio-inspired metaheuristic algorithm that draws its inspiration from the natural behaviors of orangutans. In this approach, orangutans serve as the population members, and each orangutan represents a potential solution to the given optimization problem. These solutions are completely different from one another, as each orangutan occupies a unique position within the problem's search space. The variables corresponding to each solution are determined by the orangutan’s specific position, which can be mathematically modeled as a vector. As a group, these orangutans form the OOA population, which can be represented using a matrix structure using Equation. This matrix is not static; it evolves as the algorithm progresses. Initially, the position of each orangutan in the search space is randomly determined. This randomness is essential in ensuring that the initial population covers diverse areas of the search space, enhancing the exploration capabilities of the algorithm. The initialization process for the population is mathematically modeled using Equation, where each dimension of the orangutan’s position is calculated based on random values within a predefined range. This allows for a completely different starting point for each orangutan, creating diversity in candidate solutions.

$$X={\left[\begin{array}{c}{X}_1\\ ⋮\\ X_i\\ ⋮\\ X_N\end{array}\right]}_{N\times m}={\left[\begin{array}{ccccc}{x}_{\mathrm{1,1}}& \cdots & x_{1,d}& \cdots & x_{1,m}\\ ⋮& \ddots & ⋮& ⋰& ⋮\\ x_{i,1}& \cdots & x_{i,d}& \cdots & x_{i,m}\\ ⋮& ⋰& ⋮& \ddots & ⋮\\ x_{N,1}& \cdots & x_{N,d}& \cdots & x_{N,m}\end{array}\right]}_{N\times m}$$

(1)

$$x_{i,d}=l{b}_d+r·(u{b}_d-l{b}_d)$$

(2)

Here $X$ is the OOA population matrix, $X_i$ is the $i$th orangutan (candidate solution), $x_{i,d}$ is its $d$th dimension in search space (decision variable), $N$ is the number of orangutans, $m$ is the number of decision variables, $r$ is a random number in the interval $\left[\mathrm{0,1}\right]$, $l{b}_d$, and $u{b}_d$ are a lower bound and an upper bound of the $d$th. decision variable, respectively.

After initialization, each orangutan’s position corresponds to a set of variables, which are evaluated using the objective function of the optimization problem. The objective function assigns a value to each candidate solution, and this set of values can be represented mathematically using a vector, as shown in Equation.

$$F={\left[\begin{array}{c}{F}_1\\ ⋮\\ F_i\\ ⋮\\ F_N\end{array}\right]}_{N\times 1}={\left[\begin{array}{c}F\left(X_1\right)\\ ⋮\\ F\left(X_i\right)\\ ⋮\\ F\left(X_N\right)\end{array}\right]}_{N\times 1}$$

(3)

Here $F$ is the vector of calculated objective function and $F_i$ is the calculated objective function based on the $i$th orangutan.

The calculated values of the objective function serve as a measure of the quality of each solution. Based on these evaluations, the algorithm identifies the best-performing orangutan (i.e., the candidate solution with the most optimal value) as well as the worst-performing one. In each iteration of the algorithm, the positions of the orangutans are updated, which means that their corresponding objective function values also change. As the search progresses, the best solution must be continuously updated to reflect the most optimal orangutan found so far.

This iterative process of updating orangutan positions ensures that the algorithm effectively searches the problem space, gradually moving towards an optimal or near-optimal solution.

3.3. Mathematical Modelling of OOA

In the design of the proposed Orangutan Optimization Algorithm (OOA), the position of orangutans in the search space is updated based on a completely different approach that models the natural behaviors of orangutans in two phases: exploration and exploitation. These phases reflect two key activities in orangutans’ lives, each playing a distinct role in the problem-solving process and being modeled with more words and more sentences to highlight their importance.

3.3.1. Phase 1: Foraging Strategy (Exploration)

Orangutans, in their natural habitat, spend a significant amount of time searching for food such as fruits, tree leaves, and other diet items. This foraging behavior leads to large-scale movements and extensive exploration in their environment, allowing them to discover completely different areas in the search of resources. The simulation of this foraging strategy within OOA enhances the algorithm’s exploration capability, making it more adept at scanning and searching the global space of the problem.

In the first phase of OOA, the position of each orangutan is updated to simulate this foraging behavior. Orangutans with better objective function values are considered to represent better food sources, and each orangutan seeks out these superior positions. Equation mathematically defines the set of available food resources for each orangutan by considering all orangutans with better objective function values. The diversity of food sources allows the orangutans to explore a variety of potential solutions in completely different regions of the search space.

$$F{S}_i=\left\{X_k:F_k<F_i and k\ne i\right\}, \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} i=\mathrm{1,2}, \dots , N \mathrm{a}\mathrm{n}\mathrm{d} k\in \left\{\mathrm{1,2}, \dots , N\right\}$$

(4)

Here $F{S}_i$ is the set of candidate food sources’ locations for the $i$th orangutan, $X_k$ is the is the orangutan with a better objective function value than $i$th orangutan, and $F_k$ is the its objective function value.

To model this movement mathematically, a new position is first calculated for each orangutan using Equation. This movement allows the orangutan to adjust its location in a way that explores completely different regions, potentially leading to a significant improvement in the objective function value. If the objective function improves, the new position is confirmed and updated according to Equation:

$$x_{i,d}^{P1}=x_{i,d}+r·\left(SF{S}_{i,d}-I·x_{i,d}\right), i=\mathrm{1,2}, \dots , N, \mathrm{a}\mathrm{n}\mathrm{d} d=\mathrm{1,2}, \dots ,m$$

(5)

$$X_i=\left\{\begin{array}{c}{X}_i^{P1}, F_i^{P1}<F_i\\ X_i, else\end{array}\right.$$

(6)

Here $X_i^{P1}$ is the new suggested position of the ith orangutan based on the first phase of OOA, $x_{i,d}^{P1}$ is its $d$th dimension, $F_i^{P1}$ is its objective function value, $r$ is a random number with a normal distribution in the range of $\left[\mathrm{0,1}\right]$, $SF{S}_{i,d}$ is the $d$th dimension of the selected food source for the $i$th orangutan, $I$ is a random number from the set $\left\{\mathrm{1,2}\right\}$, $N$ is the number of orangutans, and $m$ is the number of decision variables.

3.3.2. Phase 2: Nesting Skill (Exploitation)

In addition to foraging, orangutans also demonstrate remarkable intelligence through their nesting behavior. Every day, they build nests in trees, selecting branches and leaves near their current location. This activity focuses on a more localized search, optimizing their living space. Simulating the nesting skills of orangutans in OOA enhances the algorithm’s exploitation capabilities, improving the fine-tuning of solutions and allowing for more precise exploration of local regions.

During this second phase of OOA, the orangutan moves towards a nearby tree to nest. In the context of the algorithm, this nesting process is modeled by generating a new position for the orangutan based on its current location. Equation (7) is used to simulate the movement towards the tree, and if the objective function value improves, the new position replaces the previous one, as outlined in Equation (8):

$$x_{i,d}^{P2}=x_{i,d}+\left(1-2r\right)·{\displaystyle \frac{\left(u{b}_d-l{b}_d\right)}{t}}, i=\mathrm{1,2}, \dots , N, d=\mathrm{1,2}, \dots ,m, \mathrm{a}\mathrm{n}\mathrm{d} t=\mathrm{1,2}, \dots , T$$

(7)

$$X_i=\left\{\begin{array}{c}{X}_i^{P2}, F_i^{P2}<F_i\\ X_i, else\end{array}\right.$$

(8)

Here $X_i^{P2}$ is the new suggested position of the $i$th orangutan based on the second phase of OOA, $x_{i,d}^{P2}$ is its $d$th dimension, $F_i^{P2}$ is its objective function value, $t$ is the iteration counter of the algorithm, and $T$ is the maximum number of algorithm iterations.

3.4. Repetition Process, Pseudocode, and Flowchart of OOA

After the positions of all the orangutans are updated in both the exploration and exploitation phases, one iteration of OOA is completed. Based on the new positions and corresponding objective function values, the algorithm enters the next iteration. The position of the best orangutan is updated and stored as the current best solution to the problem. This process is repeated until the algorithm reaches the maximum number of iterations, ensuring that the orangutans explore both globally and locally to find a completely different and quasi-optimal solution.

The steps for the OOA approach are outlined in a flowchart (Figure 2) and further illustrated through a pseudo-code (Algorithm 1). These steps provide a detailed guide for implementing OOA and navigating through the exploration and exploitation phases to find the most suitable solution.

Algorithm 1. Pseudocode of OOA.
Start OOA.
1.	Input problem information: variables, objective function, and constraints.
2.	Set OOA population size (N) and number of iterations (T).
3.	Generate the initial population matrix at random using Equation (2). $x_{i,d}\leftarrow l{b}_d+r·(u{b}_d-l{b}_d)$
4.	Evaluate the objective function.
5.	For $t=1$ to T
6.	For$i=1$ to $N$
7.	Phase 1: foraging strategy (exploration)
8.	Determine the food sources using Equation (4). $F{S}_i\leftarrow \left\{X_{k_i}:F_{k_i}<F_i and k_i\ne i\right\}$
9.	Choose the food source for the ith OOA member at random.
10.	Calculate new position of ith OOA member using Equation (5). $x_{i,d}^{P1}\leftarrow x_{i,d}+r·\left(SF{S}_{i,d}-I·x_{i,d}\right)$
11.	Update ith OOA member using Equation (6). $X_i\leftarrow \left\{\begin{array}{c}{X}_i^{P1}, F_i^{P1}<F_i\\ X_i, else\end{array}\right.$
12.	Phase 2: nesting skill (exploitation)
13.	Calculate new position of ith OOA member using Equation (7). $x_{i,d}^{P2}\leftarrow x_{i,d}+(1-2r)·{\displaystyle \frac{\left(u{b}_d-l{b}_d\right)}{t}}$
14.	Update ith OOA member using Equation (8). $X_i\leftarrow \left\{\begin{array}{c}{X}_i^{P2}, F_i^{P2}<F_i\\ X_i, else\end{array}\right.$
15.	end
16.	Save the best candidate solution so far.
17.	end
18.	Output the best quasi-optimal solution obtained with the OOA.
End OOA.

3.5. Computational Complexity of OOA

In this subsection, the computational complexity of the proposed OOA approach is thoroughly examined in detail. The initial preparation and the complete setup of the OOA, which involves initializing the positions of all the orangutans across the search space, has a computational complexity of O(Nm), where N represents the total number of orangutans involved in the algorithm, and m signifies the number of variables associated with the problem being solved. This initialization stage is essential for creating a completely different starting point for each orangutan, enabling them to explore the search space effectively.

In every iteration of the OOA, the positions of the orangutans are updated through two distinct phases: exploration and exploitation. Both phases contribute to the overall computational complexity of the algorithm. The process of updating the orangutan positions in each iteration incurs a computational complexity of O(2NmT), where T is the maximum number of iterations the algorithm will perform. This dual-phase update mechanism allows the OOA to handle both global exploration and local exploitation in completely different manners, ensuring a comprehensive search.

When all these steps are combined, including the initialization and the repeated updating of positions over multiple iterations, the total computational complexity of the proposed OOA approach is calculated to be O(Nm(1+2T)). This total complexity provides a clear understanding of how the algorithm scales with the number of orangutans, problem variables, and iterations, ensuring that the overall performance remains efficient even as the problem size or the number of iterations increases. More words and more sentences can further elaborate on how these computations differ from other optimization algorithms, offering a completely different approach to solving complex problems.

4. Simulation Studies and Results

In this section, the effectiveness of the proposed OOA approach in addressing optimization tasks is thoroughly evaluated. To perform this evaluation, the OOA is applied to solve the CEC 2017 test suite across multiple dimensions, specifically for dimensions of 10, 30, 50, and 100. This test suite is comprised of thirty benchmark functions, which are categorized into four completely different types: three unimodal functions (C17-F1 to C17-F3), seven multimodal functions (C17-F4 to C17-F10), ten hybrid functions (C17-F11 to C17-F20), and ten composition functions (C17-F21 to C17-F30). The C17-F2 function is excluded from the simulation studies due to its unpredictable and unstable behavior. A complete and detailed description of the CEC 2017 test suite can be found in reference [53]. The optimization results obtained by the proposed OOA approach are compared with the performance of twelve well-established metaheuristic algorithms, including: GA [26], PSO [14], GSA [33], TLBO [44], MVO [35], GWO [17], WOA [23], MPA [19], TSA [24], RSA [16], AVOA [20], and WSO [21]. The control parameters for each of these metaheuristic algorithms are outlined in Table 1 to provide a consistent basis for comparison.

Both the proposed OOA approach and the competing algorithms have been rigorously tested on the CEC 2017 test suite. Simulation results are evaluated using six different performance indicators: mean, best, worst, standard deviation (std), median, and rank. The mean value, in particular, is used as a primary metric for ranking the metaheuristic algorithms across the various benchmark functions, offering a completely different perspective on algorithm performance in handling these optimization tasks.

4.1. Evaluation of the CEC 2017 Test Suite

In this subsection, the performance and scalability of OOA are tested against the CEC 2017 test suite. With scalability in mind, the OOA and the competing algorithms are implemented on benchmark problems with different dimensions: 10, 30, 50, and 100. Detailed results of how each metaheuristic algorithm performed across these dimensions are presented in Table 2 to Table 5. Additionally, boxplot diagrams visualizing the performance of OOA in comparison to competitor algorithms are shown in Figure 3 to Figure 6, offering more clarity and insights into the optimization process.

Table 2. Optimization results for the CEC 2017 test suite (dimension=10).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	4.57E+09	6092047	8.29E+09	56201704	1.42E+09	11323487	6095031	77678220	1.26E+08	6089533	6091479	15707647
	best	100	3.8E+09	379556	7.18E+09	393096.5	3.03E+08	5107850	384388.7	399819.9	53937180	377342.1	377541.5	7436354
	worst	100	5.86E+09	20916097	9.87E+09	2.03E+08	3.08E+09	24727199	20924670	2.81E+08	2.89E+08	20916044	20916624	31674536
	std	0	9.76E+08	10831270	1.33E+09	1.07E+08	1.35E+09	9844980	10834854	1.49E+08	1.19E+08	10832711	10831576	12015321
	median	100	4.31E+09	1536267	8.06E+09	10716402	1.14E+09	7729450	1535532	14652173	79854589	1532373	1535876	11859849
	rank	1	12	4	13	8	11	6	5	9	10	2	3	7
C17-F3	mean	300	7248.184	571.5281	8154.719	2142.586	9415.993	1730.133	570.036	2816.555	915.8546	8649.637	569.9917	12313.31
	best	300	4040.38	414.8698	4757.951	1219.993	3998.354	671.0715	412.0351	1566.271	712.7909	5406.083	412.0105	4066.203
	worst	300	9592.022	783.7548	10642.15	3953.862	13181.16	3032.767	780.5693	5313.887	1205.835	11582.85	780.4684	19216.7
	std	0	2620.36	170.1347	2978.868	1393.199	4229.499	1233.067	169.5981	1926.548	251.1957	2773.823	169.5629	8640.361
	median	300	7680.167	543.744	8609.39	1698.245	10242.23	1608.347	543.7698	2193.031	872.3965	8804.809	543.7439	12985.17
	rank	1	9	4	10	7	12	6	3	8	5	11	2	13
C17-F4	mean	400	835.7551	406.4469	1174.797	410.9103	545.8488	423.0108	405.2963	412.1203	410.0356	406.2858	419.0835	414.5412
	best	400	642.091	402.0343	763.6607	405.3976	464.2377	407.6079	402.3208	406.0623	408.5747	403.9185	402.6623	411.7172
	worst	400	1008.67	410.7245	1575.738	418.5266	642.1531	465.1624	409.2626	425.4072	413.2791	408.487	458.6695	418.0923
	std	0	183.3701	3.881619	378.8062	6.05711	94.72065	30.73053	3.214865	9.887667	2.37778	2.039167	28.95685	3.540612
	median	400	846.1297	406.5143	1179.894	409.8584	538.5022	409.6363	404.8009	408.5058	409.1443	406.3689	407.5011	414.1776
	rank	1	12	4	13	6	11	10	2	7	5	3	9	8
C17-F5	mean	501.2464	557.4474	541.1602	564.7486	516.4128	557.8182	538.638	524.478	515.7273	532.9683	549.2062	527.9241	528.0157
	best	500.9951	544.4366	527.2032	552.1821	511.0034	538.4153	522.1972	511.3503	510.8122	527.2536	545.3728	512.9635	522.0813
	worst	501.9917	568.3431	554.4998	575.955	521.7626	587.2215	571.1876	539.3237	521.8585	536.0193	557.6306	545.415	532.8969
	std	0.542176	11.63739	14.93161	13.61137	4.795212	23.59202	24.83581	12.60054	5.368424	4.501047	6.320925	15.57701	4.868066
	median	500.9993	558.5049	541.4689	565.4287	516.4425	552.8179	530.5836	523.619	515.1193	534.3002	546.9107	526.6589	528.5424
	rank	1	11	9	13	3	12	8	4	2	7	10	5	6
C17-F6	mean	600	628.4323	615.9861	635.2421	602.9869	622.1701	620.8009	603.4957	602.6535	607.3761	615.8922	607.8432	610.1736
	best	600	624.1009	614.3231	633.5008	601.4639	613.0406	606.8255	601.5283	601.4623	604.5468	604.0917	602.8059	606.314
	worst	600	631.6332	619.3806	637.6472	603.8607	634.9719	640.2358	605.1156	603.51	609.9158	632.7783	617.4219	613.5072
	std	0	3.914527	2.505415	2.10038	1.233147	10.16695	15.31819	1.629627	0.969989	2.757746	14.66764	7.432853	3.631607
	median	600	628.9975	615.1204	634.9102	603.3115	620.334	618.0712	603.6695	602.8209	607.5209	613.3493	605.5724	610.4366
	rank	1	12	9	13	3	11	10	4	2	5	8	6	7
C17-F7	mean	711.1267	792.4838	761.5358	793.4886	728.8522	813.3485	758.6748	732.9789	728.9728	750.4158	721.6482	734.5142	737.9155
	best	710.6726	777.7683	745.6061	784.4974	722.3432	782.2373	748.2457	722.2875	720.5478	748.4853	719.4226	729.1924	729.9694
	worst	711.7995	805.0745	783.0164	802.8195	739.7237	846.4048	783.4946	750.7517	745.3064	756.0077	723.6266	742.9379	743.1365
	std	0.558828	12.41764	18.86083	9.326893	8.260929	30.30316	18.29701	13.46041	12.13428	4.067939	2.270454	6.518658	6.222324
	median	711.0174	793.5461	758.7605	793.3187	726.671	812.3759	751.4795	729.4382	725.0186	748.585	721.7717	732.9632	739.278
	rank	1	11	10	12	3	13	9	5	4	8	2	6	7
C17-F8	mean	801.4928	844.2021	829.7982	848.395	816.5082	843.9385	834.1154	813.9036	817.2144	835.2252	820.5241	822.9169	817.9912
	best	800.995	838.3304	820.8383	839.8938	812.6332	831.338	818.3525	809.161	812.7939	828.4194	812.9445	815.9728	813.5942
	worst	801.9912	851.0802	841.7132	852.682	818.5181	859.807	844.9105	817.8161	820.2115	841.7782	826.8949	828.6387	824.3819
	std	0.627256	6.791404	9.484391	6.284814	2.899217	14.21684	12.45678	3.920941	3.490774	7.137574	6.446372	6.815545	4.980234
	median	801.4926	843.6989	828.3206	850.5021	817.4408	842.3044	836.5992	814.3187	817.9261	835.3515	821.1284	823.5281	816.9944
	rank	1	12	8	13	3	11	9	2	4	10	6	7	5
C17-F9	mean	900	1362.646	1169.213	1399.203	939.0946	1327.873	1323.411	932.5228	941.6948	941.6063	931.8625	935.3575	936.0737
	best	900	1225.006	993.6875	1324.862	920.1872	1133.226	1055.871	914.9908	923.1881	920.892	912.4248	914.7052	914.7301
	worst	900	1496.611	1556.222	1509.76	949.8375	1582.904	1572.539	949.4968	956.4534	957.4939	949.426	950.235	956.9054
	std	0	128.8973	288.7439	90.48592	14.90113	209.4773	237.1464	15.71312	16.02944	18.38468	16.83996	17.86093	19.19655
	median	900	1364.483	1063.472	1381.096	943.1769	1297.682	1332.617	932.8018	943.5688	944.0197	932.7997	938.2449	936.3297
	rank	1	12	9	13	6	11	10	3	8	7	2	4	5
C17-F10	mean	1006.179	2227.449	1797.977	2451.386	1697.874	2005.992	1999.789	1800.399	1755.209	2119.765	2206.348	1935.161	1747.259
	best	1000.284	1985.409	1549.167	2283.459	1547.179	1811.2	1501.596	1529.61	1594.299	1792.095	1949.695	1611.905	1473.268
	worst	1012.668	2384.368	2288.639	2752.02	1890.028	2203.035	2457.942	2216.838	2003.11	2385.18	2299.928	2296.763	2100.095
	std	7.26307	192.2674	373.5763	226.1773	155.9687	245.1949	492.187	350.6431	190.3448	274.753	187.0969	309.4367	289.5252
	median	1005.882	2270.009	1677.051	2385.033	1677.145	2004.867	2019.81	1727.575	1711.713	2150.892	2287.885	1915.988	1707.837
	rank	1	12	5	13	2	9	8	6	4	10	11	7	3
C17-F11	mean	1100	3358.268	1148.17	3459.363	1143.911	4661.842	1150.17	1131.057	1153.687	1150.133	1140.582	1144.115	2154.142
	best	1100	2343.658	1123.831	1400.259	1124.906	4539.942	1120.499	1112.501	1126.71	1138.815	1125.947	1133.835	1122.198
	worst	1100	4336.956	1192.047	5491.405	1188.779	4728.577	1167.562	1148.954	1214.565	1168.02	1163.473	1162.932	5084.728
	std	0	977.8091	33.18006	2006.444	33.17878	91.42135	24.04206	19.09685	45.12681	13.66304	17.67179	14.2154	2132.255
	median	1100	3376.229	1138.402	3472.894	1130.979	4689.424	1156.31	1131.388	1136.736	1146.849	1136.454	1139.847	1204.821
	rank	1	11	6	12	4	13	8	2	9	7	3	5	10
C17-F12	mean	1352.959	2.89E+08	1210170	5.77E+08	1121258	1160393	2234500	1151758	1467379	4439816	1144626	317370.9	805181.8
	best	1318.646	65190845	565696.3	1.29E+08	471411.1	884935	250457.7	117321.2	481469.9	1215091	662553.5	112162.7	417973.3
	worst	1438.176	5.05E+08	2075411	1.01E+09	1682499	1316401	3605250	3086023	2224279	7723507	1854541	453149	982890.8
	std	62.51949	2.43E+08	826523.8	4.86E+08	567029.2	214838.2	1711978	1440048	815742.6	3737400	595924.9	170960.4	284657.2
	median	1327.506	2.93E+08	1099787	5.85E+08	1165560	1220119	2541145	701843.7	1581884	4410333	1030705	352085.9	909931.4
	rank	1	12	8	13	4	7	10	6	9	11	5	2	3
C17-F13	mean	1305.324	14052323	16558.56	28094345	8223.942	11986.93	7771.563	7076.661	9994.289	15246.05	9808.202	6988.977	46072.78
	best	1303.114	1173441	3498.21	2333392	5373.75	7874.623	4355.441	2405.713	6374.938	13963.32	6433.66	3217.032	8655.764
	worst	1308.508	46639423	26725.17	93265201	9910.585	17547.95	14691.72	11790.11	13029.65	17202.54	12864.49	15332.66	148398.8
	std	2.479867	23755591	13040.03	47508976	2180.738	4653.011	5252.727	5568.254	2988.214	1624.425	2912.181	6119.022	74481.01
	median	1304.837	4198214	18005.42	8389394	8805.717	11262.57	6019.546	7055.411	10286.28	14909.17	9967.328	4703.11	13618.26
	rank	1	12	10	13	5	8	4	3	7	9	6	2	11
C17-F14	mean	1400.746	3601.599	1988.918	4708.955	2153.36	3105.336	1577.603	1620.854	2254.44	1636.344	4887.758	2785.575	10938.15
	best	1400	2847.896	1696.674	4095.09	1462.54	1484.853	1478.439	1431.824	1462.476	1507.93	4030.832	1444.054	3320.856
	worst	1400.995	4718.681	2581.197	5914.582	3782.979	4839.726	1798.999	2164.606	4594.103	1859.916	6713.016	5864.913	21397.01
	std	0.54281	885.0455	441.2268	910.1586	1205.338	1867.705	164.5463	395.6014	1701.931	167.9463	1373.507	2280.179	8320.773
	median	1400.995	3419.909	1838.9	4413.074	1683.961	3048.382	1516.487	1443.494	1480.59	1588.766	4403.592	1916.667	9517.356
	rank	1	10	5	11	6	9	2	3	7	4	12	8	13
C17-F15	mean	1500.331	9271.728	5195.141	12210.6	5172.109	6589.465	5947.951	2122.52	5617.441	2259.423	20395.81	8221.043	4583.245
	best	1500.001	3242.03	2311.909	3020.886	3761.056	2681.803	2307.773	1864.808	3537.028	1974.326	9843.108	3008.9	2375.386
	worst	1500.5	15403.95	10988.87	25493.99	6650.756	10879.16	12384.16	2643.353	6828.135	2680.072	30102.57	13486.13	7339.984
	std	0.256877	5615.625	4306.626	10760.16	1288.596	3749.994	4822.34	388.0722	1581.045	330.1566	10378.28	4746.181	2552.922
	median	1500.413	9220.466	3739.894	10163.75	5138.312	6398.449	4549.934	1990.96	6052.301	2191.647	20818.78	8194.569	4308.806
	rank	1	11	6	12	5	9	8	2	7	3	13	10	4
C17-F16	mean	1600.76	1982.417	1816.454	1985.627	1745.24	2010.88	1931.699	1821.91	1750.145	1707.946	2032.039	1909.746	1810.549
	best	1600.356	1920.548	1697.212	1842.04	1678.099	1854.852	1769.843	1743.721	1653.185	1678.46	1924.123	1816.75	1759.747
	worst	1601.12	2099.114	1907.054	2199.342	1811.471	2151.582	2041.625	1889.957	1847.048	1769.939	2208.99	2037.857	1833.409
	std	0.344697	86.8275	95.45012	166.5573	59.88601	151.9123	141.7167	65.84902	86.46288	46.09586	142.6368	105.624	37.28496
	median	1600.781	1955.003	1830.774	1950.562	1745.694	2018.544	1957.664	1826.981	1750.174	1691.692	1997.521	1892.19	1824.52
	rank	1	10	6	11	3	12	9	7	4	2	13	8	5
C17-F17	mean	1700.099	1819.629	1764.615	1819.751	1767.447	1806.513	1838.996	1839.717	1778.972	1770.673	1842.983	1765.748	1768.709
	best	1700.02	1801.836	1744.775	1811.427	1738.37	1788.707	1772.867	1778.876	1737.537	1759.735	1759.272	1753.767	1755.889
	worst	1700.332	1837.01	1799.529	1826.193	1842.651	1822.56	1894.563	1944.574	1880.043	1793.131	1963.088	1784.178	1786.741
	std	0.169302	15.8926	28.07609	6.909195	54.91478	15.25006	55.35931	85.10395	73.82753	16.86636	109.5243	15.6774	14.46863
	median	1700.022	1819.835	1757.077	1820.693	1744.384	1807.392	1844.277	1817.71	1749.155	1764.913	1824.787	1762.522	1766.104
	rank	1	9	2	10	4	8	11	12	7	6	13	3	5
C17-F18	mean	1805.36	2335204	13804.56	4652768	17577.58	13969.78	23146.27	21220.33	20371.01	28202.16	12055.37	21978.5	14585.91
	best	1800.003	123557.4	8013.312	234187.2	9060.126	10152.12	6858.01	8695.712	9599.278	24132.94	6812.501	6411.055	6864.236
	worst	1820.451	6762049	19031.49	13501037	26661.37	17848.67	34427.23	33810.4	31465.07	32117.82	14748.25	36160.44	21386.16
	std	10.98033	3354924	4978.57	6707123	9742.101	3744.082	14795.6	12437.89	13500.23	4686.876	3899.459	17140.19	6513.132
	median	1800.492	1227605	14086.72	2437923	17294.4	13939.16	25649.92	21187.6	20209.85	28278.94	13330.38	22671.25	15046.62
	rank	1	12	3	13	6	4	10	8	7	11	2	9	5
C17-F19	mean	1900.445	326246.8	8176.982	576987.9	8123.921	105109.3	31100.32	4265.894	7096.304	6535.656	35683.8	23056.4	7748.04
	best	1900.039	21270.18	4223.297	38220.34	3495.649	2472.429	7091.41	2412.043	3837.089	2597.264	14176.46	2983.403	6426.274
	worst	1901.559	685969.8	15922.87	1236278	14522.72	206802.8	57102.62	6675.377	16383.7	12794.42	48678.22	64976.7	10313.44
	std	0.812462	313076.4	5977.705	589916.7	5583.882	126664.2	22412.42	1937.333	6759.261	4945.329	17070.38	31183.43	1909.097
	median	1900.09	298873.6	6280.879	516726.7	7238.657	105581	30103.63	3988.078	4082.215	5375.468	39940.26	12132.76	7126.224
	rank	1	12	7	13	6	11	9	2	4	3	10	8	5
C17-F20	mean	2000.312	2208.805	2172.512	2215.316	2146.62	2202.551	2201.912	2147.22	2171.986	2092.106	2240.341	2171.222	2074.33
	best	2000.312	2157.756	2056.338	2165.197	2129.282	2115.686	2110.998	2069.267	2147.075	2085.607	2184.168	2149.148	2060.189
	worst	2000.312	2275.808	2283.337	2257.945	2186.408	2304.88	2277.939	2244.941	2231.476	2098.215	2313.71	2206.913	2089.551
	std	0	53.56279	109.7486	53.87584	29.12888	87.30511	85.26482	79.24193	43.66266	5.640705	65.18882	29.90742	13.23554
	median	2000.312	2200.829	2175.187	2219.06	2135.394	2194.82	2209.355	2137.337	2154.696	2092.3	2231.744	2164.413	2073.79
	rank	1	11	8	12	4	10	9	5	7	3	13	6	2
C17-F21	mean	2200	2293.874	2229.15	2272.679	2292.324	2320.069	2307.568	2261.266	2310.373	2299.266	2355.293	2314.868	2298.025
	best	2200	2252.79	2219.413	2242.24	2288.41	2232.782	2230.466	2216.358	2306.087	2225.718	2340.173	2307.436	2238.034
	worst	2200	2314.369	2254.533	2291.866	2297.611	2363.212	2342.797	2308.365	2314.986	2330.001	2367.011	2325.838	2325.459
	std	0	31.14894	18.54513	23.57032	4.723094	64.93348	56.60492	56.20072	4.639321	53.94494	13.36999	9.48029	44.08846
	median	2200	2304.168	2221.327	2278.304	2291.637	2342.141	2328.505	2260.17	2310.21	2320.672	2356.994	2313.098	2314.303
	rank	1	6	2	4	5	12	9	3	10	8	13	11	7
C17-F22	mean	2300.073	2658.071	2308.515	2804.316	2307.256	2639.297	2320.621	2289.556	2308.203	2317.167	2301.18	2312.018	2315.824
	best	2300	2556.605	2306.656	2634.685	2298.448	2419.396	2317.356	2239.902	2298.584	2309.341	2297.549	2298.071	2309.828
	worst	2300.29	2773.729	2310.327	2931.611	2316.359	2811.163	2323.239	2306.538	2321.527	2328.799	2303.218	2338.871	2320.512
	std	0.158302	110.1861	2.263155	136.2506	7.982471	190.4072	3.159466	36.12051	10.75811	9.199088	2.726583	19.92629	4.904607
	median	2300	2650.976	2308.539	2825.484	2307.109	2663.315	2320.943	2305.892	2306.35	2315.264	2301.977	2305.565	2316.477
	rank	2	12	6	13	4	11	10	1	5	9	3	7	8
C17-F23	mean	2600.919	2684.825	2639.826	2687.708	2618.297	2706.393	2645.265	2621.941	2616.604	2640.215	2762.359	2641.641	2651.347
	best	2600.003	2648.81	2629.687	2664.648	2615.182	2631.812	2629.23	2609.537	2612.404	2631.347	2707.433	2636.412	2635.05
	worst	2602.87	2704.636	2654.396	2720.963	2621.911	2743.753	2662.451	2631.445	2622.131	2648.494	2876.628	2652.399	2659.177
	std	1.440643	28.65226	12.77372	29.45997	3.146459	55.12318	19.38158	10.49306	4.992796	7.861448	86.17189	8.070403	12.33314
	median	2600.403	2692.927	2637.611	2682.61	2618.047	2725.004	2644.69	2623.391	2615.94	2640.51	2732.688	2638.876	2655.58
	rank	1	10	5	11	3	12	8	4	2	6	13	7	9
C17-F24	mean	2630.488	2770.389	2762.249	2829.591	2708.993	2680.964	2756.523	2693.263	2746.839	2752.613	2745.765	2760.576	2725.838
	best	2516.677	2714.329	2740.462	2799.532	2679.923	2567.495	2721.397	2530.727	2713.364	2729.079	2550.576	2744.509	2577.537
	worst	2732.32	2841.573	2782.453	2885.682	2720.993	2804.118	2787.482	2761.175	2764.26	2766.999	2871.867	2783.134	2803.368
	std	127.1166	65.211	19.07885	41.91001	21.2623	143.1527	29.56212	118.7769	25.13303	18.2754	150.1475	17.74422	110.3649
	median	2636.477	2762.828	2763.04	2816.575	2717.527	2676.122	2758.607	2740.576	2754.867	2757.187	2780.309	2757.33	2761.224
	rank	1	12	11	13	4	2	9	3	7	8	6	10	5
C17-F25	mean	2932.639	3116.637	2915.062	3212.151	2928.118	3095.075	2910.197	2922.105	2935.676	2931.45	2922.244	2923.114	2946.754
	best	2898.047	3045.65	2894.722	3160.945	2908.305	2913.735	2781.515	2893.096	2909.545	2905.358	2894.419	2907.767	2933.993
	worst	2945.793	3290.136	2949.055	3279.728	2939.089	3529.038	2957.801	2944.703	2946.48	2949.457	2942.376	2946.134	2960.285
	std	25.19385	127.3414	25.68891	55.61337	14.85483	318.0286	93.76283	28.79726	19.14448	23.31279	25.65604	20.25217	12.76888
	median	2943.359	3065.382	2908.236	3203.966	2932.539	2968.763	2950.736	2925.31	2943.339	2935.493	2926.091	2919.278	2946.369
	rank	8	12	2	13	6	11	1	3	9	7	4	5	10
C17-F26	mean	2900	3515.608	3007.385	3642.688	3140.201	3531.802	3173.614	2942.171	3240.953	3192.935	3728.882	2945.372	2939.773
	best	2900	3259.133	2845.795	3402.733	2982.88	3149.328	2989.348	2922.016	3006.153	2939.584	2853.63	2890.991	2791.937
	worst	2900	3704.033	3177.206	3906.141	3536.327	4042.516	3517.445	2967.174	3791.159	3765.449	4152.713	3038.889	3093.388
	std	4.05E-13	231.225	198.9794	235.1629	288.8082	471.0027	260.8804	22.18356	402.1869	419.6982	650.5965	70.42932	161.8943
	median	2900	3549.632	3003.27	3630.939	3020.798	3467.682	3093.832	2939.747	3083.25	3033.353	3954.592	2925.804	2936.883
	rank	1	10	5	12	6	11	7	3	9	8	13	4	2
C17-F27	mean	3089.518	3195.49	3123.158	3214.078	3117.216	3171.862	3184.459	3099.941	3119.973	3119.139	3209.909	3136.308	3155.888
	best	3089.518	3154.798	3101.985	3128.297	3100.891	3107.813	3174.234	3097.683	3101.473	3102.049	3198.905	3103.653	3121.857
	worst	3089.518	3254.568	3175.783	3370.273	3158.655	3205.385	3193.322	3101.618	3172.393	3164.049	3226.783	3177.805	3203.141
	std	2.86E-13	45.92707	38.38335	116.6041	30.24874	49.10097	8.550188	1.969086	38.16412	32.72923	12.96941	34.12506	37.16475
	median	3089.518	3186.296	3107.431	3178.872	3104.659	3187.126	3185.14	3100.231	3103.012	3105.23	3206.974	3131.887	3149.277
	rank	1	11	6	13	3	9	10	2	5	4	12	7	8
C17-F28	mean	3100	3564.236	3248.179	3692.02	3293.876	3534.345	3289.609	3250.32	3337.12	3320.895	3423.588	3305.022	3256.55
	best	3100	3508.735	3156.491	3644.298	3202.862	3377.077	3164.756	3121.905	3202.333	3237.799	3397.497	3219.509	3160.8
	worst	3100	3618.44	3362.217	3725.321	3338.377	3724.854	3394.177	3393.76	3399.659	3393.957	3458.191	3362.392	3494.323
	std	0	51.28969	98.36261	40.7178	67.96787	194.9551	117.0799	160.4997	100.7499	77.04266	27.74621	68.98006	174.7305
	median	3100	3564.884	3237.005	3699.231	3317.132	3517.725	3299.752	3242.807	3373.244	3325.911	3419.332	3319.093	3185.539
	rank	1	12	2	13	6	11	5	3	9	8	10	7	4
C17-F29	mean	3132.241	3319.905	3284.13	3358.325	3248.02	3244.612	3336.794	3217.153	3268.299	3225.3	3334.331	3269.013	3245.428
	best	3130.076	3300.07	3215.258	3291.717	3192.345	3191.768	3244.239	3159.686	3203.63	3186.914	3246.109	3180.47	3210.067
	worst	3134.841	3339.053	3354.8	3413.375	3313.929	3293.738	3461.603	3285.794	3365.352	3247.698	3570.954	3341.366	3277.406
	std	2.70854	19.48662	76.66374	66.83395	59.02525	45.52817	99.31632	57.20916	83.25541	31.52592	172.3924	78.19647	31.84393
	median	3132.023	3320.249	3283.231	3364.105	3242.904	3246.471	3320.668	3211.565	3252.108	3233.294	3260.131	3277.108	3247.12
	rank	1	10	9	13	6	4	12	2	7	3	11	8	5
C17-F30	mean	3418.734	1953229	384127.8	3138741	709801.2	644655.9	952310.9	390768.1	906420.5	193407.2	781676.3	459509.8	1388299
	best	3394.682	1506631	144960	1078058	36146.78	181123.7	70453.51	21849.04	43153.57	39652.19	667033.1	22285.5	517999
	worst	3442.907	2731657	692344.1	4745919	1177267	1074371	3455229	1344617	1507210	467768.9	894054.8	714360.5	2850473
	std	30.30114	588518.1	277107.7	1669828	532265	461029.5	1821378	695269.5	684113	205814.3	109563.7	352376.6	1127637
	median	3418.673	1787315	349603.6	3365493	812895.6	661564.3	141780.3	98303.29	1037659	133103.9	782808.6	550696.7	1092361
	rank	1	12	3	13	7	6	10	4	9	2	8	5	11
Sum rank		37	320	174	351	138	281	237	112	188	189	238	181	193
Mean rank		1.275862	11.03448	6	12.10345	4.758621	9.689655	8.172414	3.862069	6.482759	6.517241	8.206897	6.241379	6.655172
Total rank		1	12	4	13	3	11	9	2	6	7	10	5	8

Table 2. Optimization results for the CEC 2017 test suite (dimension=10).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	4.57E+09	6092047	8.29E+09	56201704	1.42E+09	11323487	6095031	77678220	1.26E+08	6089533	6091479	15707647
	best	100	3.8E+09	379556	7.18E+09	393096.5	3.03E+08	5107850	384388.7	399819.9	53937180	377342.1	377541.5	7436354
	worst	100	5.86E+09	20916097	9.87E+09	2.03E+08	3.08E+09	24727199	20924670	2.81E+08	2.89E+08	20916044	20916624	31674536
	std	0	9.76E+08	10831270	1.33E+09	1.07E+08	1.35E+09	9844980	10834854	1.49E+08	1.19E+08	10832711	10831576	12015321
	median	100	4.31E+09	1536267	8.06E+09	10716402	1.14E+09	7729450	1535532	14652173	79854589	1532373	1535876	11859849
	rank	1	12	4	13	8	11	6	5	9	10	2	3	7
C17-F3	mean	300	7248.184	571.5281	8154.719	2142.586	9415.993	1730.133	570.036	2816.555	915.8546	8649.637	569.9917	12313.31
	best	300	4040.38	414.8698	4757.951	1219.993	3998.354	671.0715	412.0351	1566.271	712.7909	5406.083	412.0105	4066.203
	worst	300	9592.022	783.7548	10642.15	3953.862	13181.16	3032.767	780.5693	5313.887	1205.835	11582.85	780.4684	19216.7
	std	0	2620.36	170.1347	2978.868	1393.199	4229.499	1233.067	169.5981	1926.548	251.1957	2773.823	169.5629	8640.361
	median	300	7680.167	543.744	8609.39	1698.245	10242.23	1608.347	543.7698	2193.031	872.3965	8804.809	543.7439	12985.17
	rank	1	9	4	10	7	12	6	3	8	5	11	2	13
C17-F4	mean	400	835.7551	406.4469	1174.797	410.9103	545.8488	423.0108	405.2963	412.1203	410.0356	406.2858	419.0835	414.5412
	best	400	642.091	402.0343	763.6607	405.3976	464.2377	407.6079	402.3208	406.0623	408.5747	403.9185	402.6623	411.7172
	worst	400	1008.67	410.7245	1575.738	418.5266	642.1531	465.1624	409.2626	425.4072	413.2791	408.487	458.6695	418.0923
	std	0	183.3701	3.881619	378.8062	6.05711	94.72065	30.73053	3.214865	9.887667	2.37778	2.039167	28.95685	3.540612
	median	400	846.1297	406.5143	1179.894	409.8584	538.5022	409.6363	404.8009	408.5058	409.1443	406.3689	407.5011	414.1776
	rank	1	12	4	13	6	11	10	2	7	5	3	9	8
C17-F5	mean	501.2464	557.4474	541.1602	564.7486	516.4128	557.8182	538.638	524.478	515.7273	532.9683	549.2062	527.9241	528.0157
	best	500.9951	544.4366	527.2032	552.1821	511.0034	538.4153	522.1972	511.3503	510.8122	527.2536	545.3728	512.9635	522.0813
	worst	501.9917	568.3431	554.4998	575.955	521.7626	587.2215	571.1876	539.3237	521.8585	536.0193	557.6306	545.415	532.8969
	std	0.542176	11.63739	14.93161	13.61137	4.795212	23.59202	24.83581	12.60054	5.368424	4.501047	6.320925	15.57701	4.868066
	median	500.9993	558.5049	541.4689	565.4287	516.4425	552.8179	530.5836	523.619	515.1193	534.3002	546.9107	526.6589	528.5424
	rank	1	11	9	13	3	12	8	4	2	7	10	5	6
C17-F6	mean	600	628.4323	615.9861	635.2421	602.9869	622.1701	620.8009	603.4957	602.6535	607.3761	615.8922	607.8432	610.1736
	best	600	624.1009	614.3231	633.5008	601.4639	613.0406	606.8255	601.5283	601.4623	604.5468	604.0917	602.8059	606.314
	worst	600	631.6332	619.3806	637.6472	603.8607	634.9719	640.2358	605.1156	603.51	609.9158	632.7783	617.4219	613.5072
	std	0	3.914527	2.505415	2.10038	1.233147	10.16695	15.31819	1.629627	0.969989	2.757746	14.66764	7.432853	3.631607
	median	600	628.9975	615.1204	634.9102	603.3115	620.334	618.0712	603.6695	602.8209	607.5209	613.3493	605.5724	610.4366
	rank	1	12	9	13	3	11	10	4	2	5	8	6	7
C17-F7	mean	711.1267	792.4838	761.5358	793.4886	728.8522	813.3485	758.6748	732.9789	728.9728	750.4158	721.6482	734.5142	737.9155
	best	710.6726	777.7683	745.6061	784.4974	722.3432	782.2373	748.2457	722.2875	720.5478	748.4853	719.4226	729.1924	729.9694
	worst	711.7995	805.0745	783.0164	802.8195	739.7237	846.4048	783.4946	750.7517	745.3064	756.0077	723.6266	742.9379	743.1365
	std	0.558828	12.41764	18.86083	9.326893	8.260929	30.30316	18.29701	13.46041	12.13428	4.067939	2.270454	6.518658	6.222324
	median	711.0174	793.5461	758.7605	793.3187	726.671	812.3759	751.4795	729.4382	725.0186	748.585	721.7717	732.9632	739.278
	rank	1	11	10	12	3	13	9	5	4	8	2	6	7
C17-F8	mean	801.4928	844.2021	829.7982	848.395	816.5082	843.9385	834.1154	813.9036	817.2144	835.2252	820.5241	822.9169	817.9912
	best	800.995	838.3304	820.8383	839.8938	812.6332	831.338	818.3525	809.161	812.7939	828.4194	812.9445	815.9728	813.5942
	worst	801.9912	851.0802	841.7132	852.682	818.5181	859.807	844.9105	817.8161	820.2115	841.7782	826.8949	828.6387	824.3819
	std	0.627256	6.791404	9.484391	6.284814	2.899217	14.21684	12.45678	3.920941	3.490774	7.137574	6.446372	6.815545	4.980234
	median	801.4926	843.6989	828.3206	850.5021	817.4408	842.3044	836.5992	814.3187	817.9261	835.3515	821.1284	823.5281	816.9944
	rank	1	12	8	13	3	11	9	2	4	10	6	7	5
C17-F9	mean	900	1362.646	1169.213	1399.203	939.0946	1327.873	1323.411	932.5228	941.6948	941.6063	931.8625	935.3575	936.0737
	best	900	1225.006	993.6875	1324.862	920.1872	1133.226	1055.871	914.9908	923.1881	920.892	912.4248	914.7052	914.7301
	worst	900	1496.611	1556.222	1509.76	949.8375	1582.904	1572.539	949.4968	956.4534	957.4939	949.426	950.235	956.9054
	std	0	128.8973	288.7439	90.48592	14.90113	209.4773	237.1464	15.71312	16.02944	18.38468	16.83996	17.86093	19.19655
	median	900	1364.483	1063.472	1381.096	943.1769	1297.682	1332.617	932.8018	943.5688	944.0197	932.7997	938.2449	936.3297
	rank	1	12	9	13	6	11	10	3	8	7	2	4	5
C17-F10	mean	1006.179	2227.449	1797.977	2451.386	1697.874	2005.992	1999.789	1800.399	1755.209	2119.765	2206.348	1935.161	1747.259
	best	1000.284	1985.409	1549.167	2283.459	1547.179	1811.2	1501.596	1529.61	1594.299	1792.095	1949.695	1611.905	1473.268
	worst	1012.668	2384.368	2288.639	2752.02	1890.028	2203.035	2457.942	2216.838	2003.11	2385.18	2299.928	2296.763	2100.095
	std	7.26307	192.2674	373.5763	226.1773	155.9687	245.1949	492.187	350.6431	190.3448	274.753	187.0969	309.4367	289.5252
	median	1005.882	2270.009	1677.051	2385.033	1677.145	2004.867	2019.81	1727.575	1711.713	2150.892	2287.885	1915.988	1707.837
	rank	1	12	5	13	2	9	8	6	4	10	11	7	3
C17-F11	mean	1100	3358.268	1148.17	3459.363	1143.911	4661.842	1150.17	1131.057	1153.687	1150.133	1140.582	1144.115	2154.142
	best	1100	2343.658	1123.831	1400.259	1124.906	4539.942	1120.499	1112.501	1126.71	1138.815	1125.947	1133.835	1122.198
	worst	1100	4336.956	1192.047	5491.405	1188.779	4728.577	1167.562	1148.954	1214.565	1168.02	1163.473	1162.932	5084.728
	std	0	977.8091	33.18006	2006.444	33.17878	91.42135	24.04206	19.09685	45.12681	13.66304	17.67179	14.2154	2132.255
	median	1100	3376.229	1138.402	3472.894	1130.979	4689.424	1156.31	1131.388	1136.736	1146.849	1136.454	1139.847	1204.821
	rank	1	11	6	12	4	13	8	2	9	7	3	5	10
C17-F12	mean	1352.959	2.89E+08	1210170	5.77E+08	1121258	1160393	2234500	1151758	1467379	4439816	1144626	317370.9	805181.8
	best	1318.646	65190845	565696.3	1.29E+08	471411.1	884935	250457.7	117321.2	481469.9	1215091	662553.5	112162.7	417973.3
	worst	1438.176	5.05E+08	2075411	1.01E+09	1682499	1316401	3605250	3086023	2224279	7723507	1854541	453149	982890.8
	std	62.51949	2.43E+08	826523.8	4.86E+08	567029.2	214838.2	1711978	1440048	815742.6	3737400	595924.9	170960.4	284657.2
	median	1327.506	2.93E+08	1099787	5.85E+08	1165560	1220119	2541145	701843.7	1581884	4410333	1030705	352085.9	909931.4
	rank	1	12	8	13	4	7	10	6	9	11	5	2	3
C17-F13	mean	1305.324	14052323	16558.56	28094345	8223.942	11986.93	7771.563	7076.661	9994.289	15246.05	9808.202	6988.977	46072.78
	best	1303.114	1173441	3498.21	2333392	5373.75	7874.623	4355.441	2405.713	6374.938	13963.32	6433.66	3217.032	8655.764
	worst	1308.508	46639423	26725.17	93265201	9910.585	17547.95	14691.72	11790.11	13029.65	17202.54	12864.49	15332.66	148398.8
	std	2.479867	23755591	13040.03	47508976	2180.738	4653.011	5252.727	5568.254	2988.214	1624.425	2912.181	6119.022	74481.01
	median	1304.837	4198214	18005.42	8389394	8805.717	11262.57	6019.546	7055.411	10286.28	14909.17	9967.328	4703.11	13618.26
	rank	1	12	10	13	5	8	4	3	7	9	6	2	11
C17-F14	mean	1400.746	3601.599	1988.918	4708.955	2153.36	3105.336	1577.603	1620.854	2254.44	1636.344	4887.758	2785.575	10938.15
	best	1400	2847.896	1696.674	4095.09	1462.54	1484.853	1478.439	1431.824	1462.476	1507.93	4030.832	1444.054	3320.856
	worst	1400.995	4718.681	2581.197	5914.582	3782.979	4839.726	1798.999	2164.606	4594.103	1859.916	6713.016	5864.913	21397.01
	std	0.54281	885.0455	441.2268	910.1586	1205.338	1867.705	164.5463	395.6014	1701.931	167.9463	1373.507	2280.179	8320.773
	median	1400.995	3419.909	1838.9	4413.074	1683.961	3048.382	1516.487	1443.494	1480.59	1588.766	4403.592	1916.667	9517.356
	rank	1	10	5	11	6	9	2	3	7	4	12	8	13
C17-F15	mean	1500.331	9271.728	5195.141	12210.6	5172.109	6589.465	5947.951	2122.52	5617.441	2259.423	20395.81	8221.043	4583.245
	best	1500.001	3242.03	2311.909	3020.886	3761.056	2681.803	2307.773	1864.808	3537.028	1974.326	9843.108	3008.9	2375.386
	worst	1500.5	15403.95	10988.87	25493.99	6650.756	10879.16	12384.16	2643.353	6828.135	2680.072	30102.57	13486.13	7339.984
	std	0.256877	5615.625	4306.626	10760.16	1288.596	3749.994	4822.34	388.0722	1581.045	330.1566	10378.28	4746.181	2552.922
	median	1500.413	9220.466	3739.894	10163.75	5138.312	6398.449	4549.934	1990.96	6052.301	2191.647	20818.78	8194.569	4308.806
	rank	1	11	6	12	5	9	8	2	7	3	13	10	4
C17-F16	mean	1600.76	1982.417	1816.454	1985.627	1745.24	2010.88	1931.699	1821.91	1750.145	1707.946	2032.039	1909.746	1810.549
	best	1600.356	1920.548	1697.212	1842.04	1678.099	1854.852	1769.843	1743.721	1653.185	1678.46	1924.123	1816.75	1759.747
	worst	1601.12	2099.114	1907.054	2199.342	1811.471	2151.582	2041.625	1889.957	1847.048	1769.939	2208.99	2037.857	1833.409
	std	0.344697	86.8275	95.45012	166.5573	59.88601	151.9123	141.7167	65.84902	86.46288	46.09586	142.6368	105.624	37.28496
	median	1600.781	1955.003	1830.774	1950.562	1745.694	2018.544	1957.664	1826.981	1750.174	1691.692	1997.521	1892.19	1824.52
	rank	1	10	6	11	3	12	9	7	4	2	13	8	5
C17-F17	mean	1700.099	1819.629	1764.615	1819.751	1767.447	1806.513	1838.996	1839.717	1778.972	1770.673	1842.983	1765.748	1768.709
	best	1700.02	1801.836	1744.775	1811.427	1738.37	1788.707	1772.867	1778.876	1737.537	1759.735	1759.272	1753.767	1755.889
	worst	1700.332	1837.01	1799.529	1826.193	1842.651	1822.56	1894.563	1944.574	1880.043	1793.131	1963.088	1784.178	1786.741
	std	0.169302	15.8926	28.07609	6.909195	54.91478	15.25006	55.35931	85.10395	73.82753	16.86636	109.5243	15.6774	14.46863
	median	1700.022	1819.835	1757.077	1820.693	1744.384	1807.392	1844.277	1817.71	1749.155	1764.913	1824.787	1762.522	1766.104
	rank	1	9	2	10	4	8	11	12	7	6	13	3	5
C17-F18	mean	1805.36	2335204	13804.56	4652768	17577.58	13969.78	23146.27	21220.33	20371.01	28202.16	12055.37	21978.5	14585.91
	best	1800.003	123557.4	8013.312	234187.2	9060.126	10152.12	6858.01	8695.712	9599.278	24132.94	6812.501	6411.055	6864.236
	worst	1820.451	6762049	19031.49	13501037	26661.37	17848.67	34427.23	33810.4	31465.07	32117.82	14748.25	36160.44	21386.16
	std	10.98033	3354924	4978.57	6707123	9742.101	3744.082	14795.6	12437.89	13500.23	4686.876	3899.459	17140.19	6513.132
	median	1800.492	1227605	14086.72	2437923	17294.4	13939.16	25649.92	21187.6	20209.85	28278.94	13330.38	22671.25	15046.62
	rank	1	12	3	13	6	4	10	8	7	11	2	9	5
C17-F19	mean	1900.445	326246.8	8176.982	576987.9	8123.921	105109.3	31100.32	4265.894	7096.304	6535.656	35683.8	23056.4	7748.04
	best	1900.039	21270.18	4223.297	38220.34	3495.649	2472.429	7091.41	2412.043	3837.089	2597.264	14176.46	2983.403	6426.274
	worst	1901.559	685969.8	15922.87	1236278	14522.72	206802.8	57102.62	6675.377	16383.7	12794.42	48678.22	64976.7	10313.44
	std	0.812462	313076.4	5977.705	589916.7	5583.882	126664.2	22412.42	1937.333	6759.261	4945.329	17070.38	31183.43	1909.097
	median	1900.09	298873.6	6280.879	516726.7	7238.657	105581	30103.63	3988.078	4082.215	5375.468	39940.26	12132.76	7126.224
	rank	1	12	7	13	6	11	9	2	4	3	10	8	5
C17-F20	mean	2000.312	2208.805	2172.512	2215.316	2146.62	2202.551	2201.912	2147.22	2171.986	2092.106	2240.341	2171.222	2074.33
	best	2000.312	2157.756	2056.338	2165.197	2129.282	2115.686	2110.998	2069.267	2147.075	2085.607	2184.168	2149.148	2060.189
	worst	2000.312	2275.808	2283.337	2257.945	2186.408	2304.88	2277.939	2244.941	2231.476	2098.215	2313.71	2206.913	2089.551
	std	0	53.56279	109.7486	53.87584	29.12888	87.30511	85.26482	79.24193	43.66266	5.640705	65.18882	29.90742	13.23554
	median	2000.312	2200.829	2175.187	2219.06	2135.394	2194.82	2209.355	2137.337	2154.696	2092.3	2231.744	2164.413	2073.79
	rank	1	11	8	12	4	10	9	5	7	3	13	6	2
C17-F21	mean	2200	2293.874	2229.15	2272.679	2292.324	2320.069	2307.568	2261.266	2310.373	2299.266	2355.293	2314.868	2298.025
	best	2200	2252.79	2219.413	2242.24	2288.41	2232.782	2230.466	2216.358	2306.087	2225.718	2340.173	2307.436	2238.034
	worst	2200	2314.369	2254.533	2291.866	2297.611	2363.212	2342.797	2308.365	2314.986	2330.001	2367.011	2325.838	2325.459
	std	0	31.14894	18.54513	23.57032	4.723094	64.93348	56.60492	56.20072	4.639321	53.94494	13.36999	9.48029	44.08846
	median	2200	2304.168	2221.327	2278.304	2291.637	2342.141	2328.505	2260.17	2310.21	2320.672	2356.994	2313.098	2314.303
	rank	1	6	2	4	5	12	9	3	10	8	13	11	7
C17-F22	mean	2300.073	2658.071	2308.515	2804.316	2307.256	2639.297	2320.621	2289.556	2308.203	2317.167	2301.18	2312.018	2315.824
	best	2300	2556.605	2306.656	2634.685	2298.448	2419.396	2317.356	2239.902	2298.584	2309.341	2297.549	2298.071	2309.828
	worst	2300.29	2773.729	2310.327	2931.611	2316.359	2811.163	2323.239	2306.538	2321.527	2328.799	2303.218	2338.871	2320.512
	std	0.158302	110.1861	2.263155	136.2506	7.982471	190.4072	3.159466	36.12051	10.75811	9.199088	2.726583	19.92629	4.904607
	median	2300	2650.976	2308.539	2825.484	2307.109	2663.315	2320.943	2305.892	2306.35	2315.264	2301.977	2305.565	2316.477
	rank	2	12	6	13	4	11	10	1	5	9	3	7	8
C17-F23	mean	2600.919	2684.825	2639.826	2687.708	2618.297	2706.393	2645.265	2621.941	2616.604	2640.215	2762.359	2641.641	2651.347
	best	2600.003	2648.81	2629.687	2664.648	2615.182	2631.812	2629.23	2609.537	2612.404	2631.347	2707.433	2636.412	2635.05
	worst	2602.87	2704.636	2654.396	2720.963	2621.911	2743.753	2662.451	2631.445	2622.131	2648.494	2876.628	2652.399	2659.177
	std	1.440643	28.65226	12.77372	29.45997	3.146459	55.12318	19.38158	10.49306	4.992796	7.861448	86.17189	8.070403	12.33314
	median	2600.403	2692.927	2637.611	2682.61	2618.047	2725.004	2644.69	2623.391	2615.94	2640.51	2732.688	2638.876	2655.58
	rank	1	10	5	11	3	12	8	4	2	6	13	7	9
C17-F24	mean	2630.488	2770.389	2762.249	2829.591	2708.993	2680.964	2756.523	2693.263	2746.839	2752.613	2745.765	2760.576	2725.838
	best	2516.677	2714.329	2740.462	2799.532	2679.923	2567.495	2721.397	2530.727	2713.364	2729.079	2550.576	2744.509	2577.537
	worst	2732.32	2841.573	2782.453	2885.682	2720.993	2804.118	2787.482	2761.175	2764.26	2766.999	2871.867	2783.134	2803.368
	std	127.1166	65.211	19.07885	41.91001	21.2623	143.1527	29.56212	118.7769	25.13303	18.2754	150.1475	17.74422	110.3649
	median	2636.477	2762.828	2763.04	2816.575	2717.527	2676.122	2758.607	2740.576	2754.867	2757.187	2780.309	2757.33	2761.224
	rank	1	12	11	13	4	2	9	3	7	8	6	10	5
C17-F25	mean	2932.639	3116.637	2915.062	3212.151	2928.118	3095.075	2910.197	2922.105	2935.676	2931.45	2922.244	2923.114	2946.754
	best	2898.047	3045.65	2894.722	3160.945	2908.305	2913.735	2781.515	2893.096	2909.545	2905.358	2894.419	2907.767	2933.993
	worst	2945.793	3290.136	2949.055	3279.728	2939.089	3529.038	2957.801	2944.703	2946.48	2949.457	2942.376	2946.134	2960.285
	std	25.19385	127.3414	25.68891	55.61337	14.85483	318.0286	93.76283	28.79726	19.14448	23.31279	25.65604	20.25217	12.76888
	median	2943.359	3065.382	2908.236	3203.966	2932.539	2968.763	2950.736	2925.31	2943.339	2935.493	2926.091	2919.278	2946.369
	rank	8	12	2	13	6	11	1	3	9	7	4	5	10
C17-F26	mean	2900	3515.608	3007.385	3642.688	3140.201	3531.802	3173.614	2942.171	3240.953	3192.935	3728.882	2945.372	2939.773
	best	2900	3259.133	2845.795	3402.733	2982.88	3149.328	2989.348	2922.016	3006.153	2939.584	2853.63	2890.991	2791.937
	worst	2900	3704.033	3177.206	3906.141	3536.327	4042.516	3517.445	2967.174	3791.159	3765.449	4152.713	3038.889	3093.388
	std	4.05E-13	231.225	198.9794	235.1629	288.8082	471.0027	260.8804	22.18356	402.1869	419.6982	650.5965	70.42932	161.8943
	median	2900	3549.632	3003.27	3630.939	3020.798	3467.682	3093.832	2939.747	3083.25	3033.353	3954.592	2925.804	2936.883
	rank	1	10	5	12	6	11	7	3	9	8	13	4	2
C17-F27	mean	3089.518	3195.49	3123.158	3214.078	3117.216	3171.862	3184.459	3099.941	3119.973	3119.139	3209.909	3136.308	3155.888
	best	3089.518	3154.798	3101.985	3128.297	3100.891	3107.813	3174.234	3097.683	3101.473	3102.049	3198.905	3103.653	3121.857
	worst	3089.518	3254.568	3175.783	3370.273	3158.655	3205.385	3193.322	3101.618	3172.393	3164.049	3226.783	3177.805	3203.141
	std	2.86E-13	45.92707	38.38335	116.6041	30.24874	49.10097	8.550188	1.969086	38.16412	32.72923	12.96941	34.12506	37.16475
	median	3089.518	3186.296	3107.431	3178.872	3104.659	3187.126	3185.14	3100.231	3103.012	3105.23	3206.974	3131.887	3149.277
	rank	1	11	6	13	3	9	10	2	5	4	12	7	8
C17-F28	mean	3100	3564.236	3248.179	3692.02	3293.876	3534.345	3289.609	3250.32	3337.12	3320.895	3423.588	3305.022	3256.55
	best	3100	3508.735	3156.491	3644.298	3202.862	3377.077	3164.756	3121.905	3202.333	3237.799	3397.497	3219.509	3160.8
	worst	3100	3618.44	3362.217	3725.321	3338.377	3724.854	3394.177	3393.76	3399.659	3393.957	3458.191	3362.392	3494.323
	std	0	51.28969	98.36261	40.7178	67.96787	194.9551	117.0799	160.4997	100.7499	77.04266	27.74621	68.98006	174.7305
	median	3100	3564.884	3237.005	3699.231	3317.132	3517.725	3299.752	3242.807	3373.244	3325.911	3419.332	3319.093	3185.539
	rank	1	12	2	13	6	11	5	3	9	8	10	7	4
C17-F29	mean	3132.241	3319.905	3284.13	3358.325	3248.02	3244.612	3336.794	3217.153	3268.299	3225.3	3334.331	3269.013	3245.428
	best	3130.076	3300.07	3215.258	3291.717	3192.345	3191.768	3244.239	3159.686	3203.63	3186.914	3246.109	3180.47	3210.067
	worst	3134.841	3339.053	3354.8	3413.375	3313.929	3293.738	3461.603	3285.794	3365.352	3247.698	3570.954	3341.366	3277.406
	std	2.70854	19.48662	76.66374	66.83395	59.02525	45.52817	99.31632	57.20916	83.25541	31.52592	172.3924	78.19647	31.84393
	median	3132.023	3320.249	3283.231	3364.105	3242.904	3246.471	3320.668	3211.565	3252.108	3233.294	3260.131	3277.108	3247.12
	rank	1	10	9	13	6	4	12	2	7	3	11	8	5
C17-F30	mean	3418.734	1953229	384127.8	3138741	709801.2	644655.9	952310.9	390768.1	906420.5	193407.2	781676.3	459509.8	1388299
	best	3394.682	1506631	144960	1078058	36146.78	181123.7	70453.51	21849.04	43153.57	39652.19	667033.1	22285.5	517999
	worst	3442.907	2731657	692344.1	4745919	1177267	1074371	3455229	1344617	1507210	467768.9	894054.8	714360.5	2850473
	std	30.30114	588518.1	277107.7	1669828	532265	461029.5	1821378	695269.5	684113	205814.3	109563.7	352376.6	1127637
	median	3418.673	1787315	349603.6	3365493	812895.6	661564.3	141780.3	98303.29	1037659	133103.9	782808.6	550696.7	1092361
	rank	1	12	3	13	7	6	10	4	9	2	8	5	11
Sum rank		37	320	174	351	138	281	237	112	188	189	238	181	193
Mean rank		1.275862	11.03448	6	12.10345	4.758621	9.689655	8.172414	3.862069	6.482759	6.517241	8.206897	6.241379	6.655172
Total rank		1	12	4	13	3	11	9	2	6	7	10	5	8

Table 3. Optimization results for the CEC 2017 test suite (dimension=30).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	2.15E+10	2.16E+08	3.36E+10	2.16E+08	1.47E+10	1.59E+09	2.17E+08	1.57E+09	5.22E+09	2.25E+08	1.36E+09	3.61E+08
	best	100	1.85E+10	1.04E+08	2.98E+10	1.04E+08	9.3E+09	1.19E+09	1.05E+08	3.27E+08	3.34E+09	1.04E+08	1.04E+08	2.31E+08
	worst	100	2.68E+10	4.58E+08	4.11E+10	4.58E+08	1.99E+10	2.17E+09	4.59E+08	4.53E+09	7.56E+09	4.63E+08	4.67E+09	5.84E+08
	std	8.93E-15	4.22E+09	1.79E+08	5.62E+09	1.79E+08	5.49E+09	5.05E+08	1.79E+08	2.16E+09	1.9E+09	1.8E+08	2.41E+09	1.67E+08
	median	100	2.04E+10	1.52E+08	3.16E+10	1.52E+08	1.49E+10	1.51E+09	1.52E+08	7.1E+08	4.99E+09	1.67E+08	3.22E+08	3.15E+08
	rank	1	12	2	13	3	11	9	4	8	10	5	7	6
C17-F3	mean	300	96614.41	53933.49	77366.61	18585.58	55958.1	205718.4	19131.16	51472.71	45809.84	95407.06	43547.71	153272.3
	best	300	88996.04	39548.33	63712.4	16226.86	51683.78	170987.9	16830.62	47478.85	43809.8	82336.48	38319.08	120561.6
	worst	300	106524.6	62295.66	84695.4	20971.61	58288.34	235879.8	21002.04	53477.99	47780.24	103083	48636.89	208250.5
	std	0	9492.196	10861.79	10276.61	2134.522	3185.682	29329.65	1946.304	3005.516	1764.21	10708.3	5738.33	45101.23
	median	300	95468.51	56944.99	80529.33	18571.92	56930.14	208002.9	19345.98	52467.01	45824.67	98104.4	43617.44	142138.6
	rank	1	11	7	9	2	8	13	3	6	5	10	4	12
C17-F4	mean	458.5616	5350.397	539.4145	8089.186	521.9548	3807.993	817.0299	524.9005	585.8032	858.3046	604.3766	628.1991	780.6074
	best	458.5616	3054.705	523.4544	5224.711	515.404	967.5568	760.4125	517.1595	535.2115	686.5093	590.4452	536.4024	740.8788
	worst	458.5616	7206.478	550.2992	11265.61	534.1434	6252.298	889.6414	530.3765	617.9659	1177.365	619.4999	783.7213	796.0334
	std	0	1871.912	13.03211	2727.29	9.092848	2429.097	64.88372	6.079095	38.78506	236.972	17.05345	124.3083	28.86259
	median	458.5616	5570.202	541.9521	7933.213	519.1358	4006.058	809.0328	526.033	595.0176	784.6721	603.7807	596.3364	792.7587
	rank	1	12	4	13	2	11	9	3	5	10	6	7	8
C17-F5	mean	502.4874	816.585	719.5219	848.4325	603.984	775.2252	799.006	633.4036	635.4277	756.0726	717.4144	644.1008	700.8081
	best	500.995	799.1994	688.3874	826.0953	587.9209	750.8395	777.6683	618.6867	599.8995	739.9461	703.0501	621.5861	658.3407
	worst	503.9798	836.1958	764.645	878.4212	620.0451	804.8383	807.6101	664.2009	661.1234	774.8832	737.5871	683.1084	753.5
	std	1.397379	16.5293	37.13723	26.03724	15.10696	28.20919	15.53716	22.59738	32.74051	18.46433	17.95634	29.331	42.83256
	median	502.4874	815.4724	712.5276	844.6068	603.9851	772.6115	805.3727	625.3633	640.344	754.7306	714.5102	635.8544	695.6958
	rank	1	12	8	13	2	10	11	3	4	9	7	5	6
C17-F6	mean	600	671.8645	645.024	674.4263	609.8658	669.551	668.9306	626.9659	616.8448	642.285	652.9594	645.2092	631.6495
	best	600	670.4622	642.8248	671.1038	608.833	656.5433	659.7693	616.8861	610.4155	637.8877	652.2821	636.7136	625.3622
	worst	600	673.3848	647.2092	679.2321	610.5577	677.7928	672.7284	638.6085	623.9538	651.085	653.7211	653.3163	635.0472
	std	7.14E-14	1.433896	2.015521	4.206224	0.808745	10.70667	6.669619	10.99308	6.058066	6.647049	0.73281	8.093386	4.67082
	median	600	671.8056	645.0311	673.6846	610.0362	671.934	671.6123	626.1845	616.505	640.0838	652.9172	645.4035	633.0942
	rank	1	12	7	13	2	11	10	4	3	6	9	8	5
C17-F7	mean	733.478	1245.794	1122.999	1278.85	880.073	1185.844	1253.075	886.0305	911.6808	1065.519	980.9371	905.745	977.9064
	best	732.8186	1207.453	1027.182	1271.948	862.4656	1068.204	1216.101	847.0424	855.0212	992.1556	940.8225	892.8739	950.0423
	worst	734.5199	1272.678	1258.797	1296.025	922.0296	1304.724	1323.112	946.5276	948.7409	1127.53	1038.579	928.3516	1020.577
	std	0.820293	30.5378	111.7555	12.56992	30.57605	110.8795	54.41842	47.39518	43.42062	77.06954	45.57859	17.57207	32.69181
	median	733.2867	1251.522	1103.008	1273.715	867.8984	1185.224	1236.545	875.276	921.4806	1071.196	972.1733	900.8773	970.5031
	rank	1	11	9	13	2	10	12	3	5	8	7	4	6
C17-F8	mean	803.3298	1058.065	948.5071	1088.37	900.689	1037.026	1013.86	902.9144	901.8313	1007.554	958.1218	927.4182	978.136
	best	801.2023	1047.635	927.1619	1069.187	893.6258	1004.164	966.3403	875.2901	893.4635	989.4507	941.5461	915.1568	963.4448
	worst	804.1574	1071.848	967.1707	1111.511	910.5728	1118.871	1051.081	925.5831	909.499	1037.685	978.3326	941.4581	992.1231
	std	1.545701	12.81537	19.36666	21.54123	7.840737	59.7159	39.42715	24.43217	7.139129	22.72103	17.49184	11.84809	15.27864
	median	803.9798	1056.387	949.8478	1086.391	899.2787	1012.534	1019.009	905.3923	902.1813	1001.541	956.3042	926.5289	978.4881
	rank	1	12	6	13	2	11	10	4	3	9	7	5	8
C17-F9	mean	900	10081.46	5101.467	9806.301	2069.207	10506.5	10131.77	5612.936	2874.474	5870.885	4497.761	4066.545	2238.248
	best	900	8674.481	4115.659	9645.45	1830.887	6753.152	8060.012	4599.951	2484.507	4458.616	4087.39	2957.901	2028.884
	worst	900	11351.77	5672.734	9939.413	2218.791	13826.81	11905.03	7988.969	3400.575	8283.113	5220.916	5463.258	2460.82
	std	7.14E-14	1210.428	757.1536	144.6618	192.7325	3180.977	2131.48	1733.811	502.3072	1852.802	575.9914	1154.492	228.836
	median	900	10149.78	5308.739	9820.171	2113.576	10723.02	10281.02	4931.413	2806.408	5370.905	4341.369	3922.511	2231.644
	rank	1	11	7	10	2	13	12	8	4	9	6	5	3
C17-F10	mean	2293.267	6881.855	5445.848	7438.226	4257.329	6346.146	6294.493	4793.373	4906.424	7454.188	4954.637	5110.67	6007.258
	best	1851.756	6503.624	4840.213	6834.203	3957.726	5306.802	5490.274	4555.776	4406.865	7148.075	4746.047	4829.285	5532.538
	worst	2525.027	7058.243	5930.547	7869.142	4716.564	6752.056	7472.411	5100.911	5269.169	7622.178	5209.384	5479.349	6562.458
	std	326.7738	279.2847	566.2276	475.6195	369.0798	756.3273	945.8514	256.6862	395.0874	227.8082	218.5099	294.6064	507.6167
	median	2398.142	6982.777	5506.315	7524.78	4177.514	6662.862	6107.644	4758.402	4974.83	7523.25	4931.559	5067.022	5967.018
	rank	1	11	7	12	2	10	9	3	4	13	5	6	8
C17-F11	mean	1102.987	6822.248	1745.516	7878.094	1673.799	4893.283	7076.081	1791.348	2507.27	2338.765	3078.954	1738.629	8176.406
	best	1100.995	5637.663	1653.643	6443.573	1530.864	3681.247	5287.212	1651.827	1843.898	2013.563	2441.813	1649.955	3374.532
	worst	1105.977	7627.036	1945.118	8774.924	1858.768	6936.913	10315.56	1946.495	4247.063	3124.093	3623.673	1902.104	14911.18
	std	2.341679	1003.287	146.0792	1130.981	153.8407	1614.778	2415.797	136.0006	1265.008	571.6796	550.8356	122.9817	5372.792
	median	1102.487	7012.146	1691.651	8146.939	1652.781	4477.486	6350.775	1783.535	1969.059	2108.702	3125.165	1701.228	7209.959
	rank	1	10	4	12	2	9	11	5	7	6	8	3	13
C17-F12	mean	1744.553	5.73E+09	37041608	8.89E+09	20094778	4.14E+09	2.22E+08	29210711	62823790	2.66E+08	1.82E+08	22162355	26329511
	best	1721.81	4.76E+09	11046828	7.92E+09	8675865	2.16E+09	60182802	12900846	13535696	1.66E+08	40693025	10717920	13974918
	worst	1764.937	7.28E+09	75615075	1.12E+10	34202179	5.42E+09	4.36E+08	39592150	1.18E+08	4.61E+08	5.51E+08	34408383	38512204
	std	21.92397	1.18E+09	30177935	1.69E+09	14150253	1.53E+09	1.89E+08	12440535	46444843	1.45E+08	2.68E+08	13200207	13435001
	median	1745.733	5.45E+09	30752264	8.23E+09	18750534	4.5E+09	1.95E+08	32174923	60019050	2.19E+08	68002949	21761559	26415462
	rank	1	12	6	13	2	11	9	5	7	10	8	3	4
C17-F13	mean	1315.791	4.65E+09	234475	8.58E+09	114340	1.19E+09	848348.1	186778.5	726743.2	71823934	142473.2	139130.8	9802230
	best	1314.587	2.26E+09	112334.1	4.5E+09	43210.96	16088952	388963.5	77625.43	119097.2	49924732	65964.4	57684.87	2673834
	worst	1318.646	6.51E+09	353565.6	1.05E+10	240984	4.13E+09	1327049	273433.4	2144638	1.06E+08	263683.3	250402.8	21081475
	std	2.106458	1.91E+09	129203.1	3E+09	100849.1	2.15E+09	511048.8	108404.7	1046282	26301943	96404.67	89357.48	8585811
	median	1314.967	4.91E+09	236000.2	9.64E+09	86582.59	3.07E+08	838690.1	198027.5	321618.9	65792667	120122.5	124217.8	7726806
	rank	1	12	6	13	2	11	8	5	7	10	4	3	9
C17-F14	mean	1423.017	1718087	399037.4	1962627	179916.4	1132743	1984755	195263.3	611735.3	292356.5	1107748	193985.3	1809212
	best	1422.014	1061406	132561.7	1008748	61125.47	742595.4	89121.17	72899.9	163245.4	167780.5	714968.1	80039.05	371627.1
	worst	1423.993	2389736	679300.5	2758135	442287.5	1459897	5958393	462069.6	1040164	571838.3	1500624	443698.1	2808801
	std	0.879206	636983.5	317464.3	845287.8	191863.2	321641.1	2931780	195299.3	412610.4	205434.1	470262.9	183056.2	1190488
	median	1423.03	1710604	392143.7	2041812	108126.3	1164240	945753.9	123041.7	621766	214903.5	1107700	126101.9	2028210
	rank	1	10	6	12	2	9	13	4	7	5	8	3	11
C17-F15	mean	1503.129	2.48E+08	1375822	4.87E+08	1346736	13013832	5440226	1380151	14192485	5512754	1358466	1349301	2121150
	best	1502.462	2.18E+08	177100.7	4.24E+08	129052.6	7380528	316349.5	155012.3	283640.6	1128907	141037.9	134942.1	408683.1
	worst	1504.265	2.74E+08	4894040	5.36E+08	4868737	27325764	18162803	4887511	52968867	12712041	4879322	4871739	5009793
	std	0.930751	30351327	2551791	60423759	2554602	10424666	9296555	2544111	28133875	5439895	2553789	2554886	2200031
	median	1502.893	2.51E+08	216074.2	4.93E+08	194577.4	8674518	1640875	239039.2	1758716	4105034	206752.9	195262.5	1533061
	rank	1	12	5	13	2	10	8	6	11	9	4	3	7
C17-F16	mean	1663.469	4101.329	3031.898	4635.035	2241.54	3251.904	4041.201	2696.913	2661.031	3408.197	3572.045	2975.076	2990.448
	best	1614.72	3807.969	2737.754	3978.845	2001.553	2908.494	3376.12	2482.418	2539.576	3251.758	3420.823	2753.289	2710.515
	worst	1744.118	4276.32	3407.61	5176.319	2516.773	3411.485	4801.345	2913.154	2829.105	3667.715	3691.182	3153.728	3343.812
	std	67.41864	234.0283	302.0019	676.0589	242.5108	251.8612	637.99	221.8501	145.2831	201.6661	121.8334	209.1785	322.4667
	median	1647.519	4160.513	2991.113	4692.488	2223.917	3343.819	3993.67	2696.04	2637.723	3356.658	3588.088	2996.644	2953.733
	rank	1	12	7	13	2	8	11	4	3	9	10	5	6
C17-F17	mean	1728.099	3204.184	2445.318	3451.547	1948.085	3094.792	2749.862	2125.927	2005.692	2218.34	2485.993	2332.979	2187.25
	best	1718.761	2673.848	2350.034	3100.934	1867.475	2198.674	2318.895	2043.202	1889.97	2056.227	2364.45	2153.82	2156.169
	worst	1733.659	3820.327	2549.322	4023.651	2005.72	5345.294	3024.682	2272.116	2134.369	2470.026	2632.64	2661.365	2267.963
	std	7.297618	528.6384	89.51016	445.1187	71.30712	1636.126	332.5784	109.2024	134.6634	193.1037	131.3193	258.2104	58.77136
	median	1729.987	3161.279	2440.959	3340.802	1959.573	2417.6	2827.936	2094.196	1999.214	2173.554	2473.441	2258.365	2162.433
	rank	1	12	8	13	2	11	10	4	3	6	9	7	5
C17-F18	mean	1825.696	23516152	2597862	26971587	449288.9	29942772	5237635	967163.3	788246.3	1799905	865686.6	559110.2	3406739
	best	1822.524	7042539	626271.2	8972491	157003.2	1237016	1769612	439399.9	219118.9	1025030	440176.2	287596.9	2707382
	worst	1828.42	45599259	4445437	52908094	800715.7	56693727	10685466	1845177	1272191	2261004	1211045	922395.8	4776390
	std	2.939396	18592179	2060642	20284915	288890.8	33335395	4150540	673195	471794.6	590154.2	364166.3	287799.8	1039578
	median	1825.92	20711405	2659870	23002881	419718.5	30920173	4247731	792038.2	830837.5	1956792	905762.4	513224.1	3071591
	rank	1	11	8	12	2	13	10	6	4	7	5	3	9
C17-F19	mean	1910.989	4.73E+08	1296419	7.96E+08	1243037	2.4E+08	12870427	2003950	4515071	5909591	1307840	1277590	2557263
	best	1908.84	3.53E+08	293139.3	5.75E+08	240422.4	3206791	1752074	367290.5	1497855	3643788	308068.3	347028	1960284
	worst	1913.095	6.15E+08	1937459	1.21E+09	1816626	6.64E+08	21895052	3529380	12027809	8450739	1904376	1822176	3191310
	std	2.101811	1.43E+08	764927.9	3.04E+08	750238.1	3.31E+08	9869339	1494110	5493944	2731583	752848.6	698751.5	548249.5
	median	1911.01	4.61E+08	1477540	7.01E+08	1457550	1.47E+08	13917291	2059565	2267309	5771917	1509458	1470577	2538729
	rank	1	12	4	13	2	11	10	6	8	9	5	3	7
C17-F20	mean	2065.787	2852.05	2636.891	2896.093	2261.509	2812.046	2801.946	2611.987	2423.904	2769.729	2942.41	2564.666	2505.922
	best	2029.521	2778.489	2515.082	2751.613	2145.565	2702.619	2646.95	2401.697	2260.383	2708.159	2644.76	2513.556	2445.026
	worst	2161.126	2924.641	2808.219	2965.309	2346.016	2915.11	2958.567	2955.98	2564.83	2871.895	3346.198	2680.918	2543.795
	std	69.24026	65.16107	137.6245	107.6394	91.9837	95.66384	142.0746	260.8481	136.0149	81.18477	320.9119	85.12862	47.3034
	median	2036.25	2852.534	2612.131	2933.724	2277.228	2815.228	2801.134	2545.137	2435.202	2749.43	2889.341	2532.096	2517.433
	rank	1	11	7	12	2	10	9	6	3	8	13	5	4
C17-F21	mean	2308.456	2596.762	2448.231	2643.694	2387.133	2525.165	2586.829	2418.922	2406.48	2492.791	2553.99	2442.966	2490.435
	best	2304.034	2526.449	2257.85	2586.165	2378.506	2346.124	2516.104	2385.646	2370.12	2483.421	2534.95	2423.177	2459.35
	worst	2312.987	2652.414	2581.521	2712.368	2392.814	2639.573	2647.646	2450.321	2422.972	2506.051	2588.127	2461.006	2524.428
	std	4.850941	62.82122	148.2022	62.05312	7.047214	138.4952	70.23165	30.08598	26.60579	10.40937	26.17077	16.9696	29.07732
	median	2308.402	2604.093	2476.777	2638.122	2388.606	2557.482	2591.783	2419.861	2416.414	2490.847	2546.441	2443.841	2488.982
	rank	1	12	6	13	2	9	11	4	3	8	10	5	7
C17-F22	mean	2300	7416.278	5606.15	7217.578	2767.064	8062.805	6943.239	4118.651	3095.301	5534.882	6060.652	4879.829	3093.803
	best	2300	7084.193	2589.959	6320.075	2589.259	7696.453	5982.982	2594.276	2812.261	3057.109	3979.755	3036.958	2959.648
	worst	2300	7992.923	6648.708	8208.241	2909.439	8295.31	7587.508	5936.695	3456.066	8044.654	6842.973	6624.719	3284.397
	std	0	447.0653	2188.073	850.4959	157.5029	294.8451	745.0711	1866.174	293.5383	2998.334	1511.723	1800.442	156.411
	median	2300	7293.999	6592.966	7170.999	2784.779	8129.728	7101.233	3971.816	3056.438	5518.882	6709.94	4928.821	3065.584
	rank	1	12	8	11	2	13	10	5	4	7	9	6	3
C17-F23	mean	2655.081	3134.082	2916.197	3179.248	2684.911	3138.091	3015.153	2760.249	2771.554	2897.243	3608.12	2894.462	2956.074
	best	2653.745	3052.541	2831.729	3137.587	2546.881	3029.414	2858.446	2726.062	2757.65	2880.102	3508.173	2872.493	2937.475
	worst	2657.377	3203.731	3047.601	3249.515	2737.578	3302.897	3099.717	2789.67	2791.69	2940.924	3701.653	2925.754	2997.452
	std	1.798497	76.5529	102.9913	56.02015	100.244	128.9959	117.6717	29.73855	15.77988	31.77993	107.6621	27.71245	30.23767
	median	2654.6	3140.028	2892.728	3164.946	2727.593	3110.026	3051.225	2762.632	2768.439	2883.973	3611.326	2889.802	2944.683
	rank	1	10	7	12	2	11	9	3	4	6	13	5	8
C17-F24	mean	2831.409	3259.418	3140.517	3341.852	2903.733	3231.21	3095.648	2922.053	2934.549	3034.572	3299.789	3107.738	3186.227
	best	2829.992	3230.675	3028.691	3270.724	2893.367	3144.047	3034.507	2874.181	2916.054	3017.56	3271.765	3047.614	3111.252
	worst	2832.366	3316.083	3271.067	3461.734	2911.236	3276.173	3120.213	2943.399	2943.03	3056.434	3334.012	3204.837	3254.053
	std	1.246245	41.79513	114.4207	96.12821	8.854297	64.85565	44.52533	35.0327	13.66786	17.53194	32.2566	73.77764	74.20735
	median	2831.64	3245.457	3131.155	3317.475	2905.165	3252.309	3113.936	2935.316	2939.556	3032.148	3296.688	3089.251	3189.801
	rank	1	11	8	13	2	10	6	3	4	5	12	7	9
C17-F25	mean	2886.698	3774.898	2925.976	4289.841	2911.644	3387.596	3068.493	2926.652	2995.621	3062.61	2997.379	2914.669	3089.732
	best	2886.691	3469.485	2913.557	3796.919	2905.41	3075.541	3037.756	2904.458	2963.601	2967.819	2987.174	2907.939	3073.483
	worst	2886.707	4006.444	2955.788	4952.46	2919.105	3708.48	3088.721	2978.817	3058.703	3175.101	3006.087	2927.24	3098.003
	std	0.008274	243.4626	21.95218	524.1696	7.125738	335.2555	24.65864	38.32121	48.44319	109.0198	9.535606	9.848236	12.04774
	median	2886.698	3811.832	2917.28	4204.993	2911.031	3383.182	3073.748	2911.666	2980.09	3053.759	2998.128	2911.748	3093.722
	rank	1	12	4	13	2	11	9	5	6	8	7	3	10
C17-F26	mean	3578.65	8636.168	7115.835	9119.509	3517.931	8270.307	7976.609	5027.116	4844.627	5961.291	7235.355	5077.571	4704.075
	best	3559.841	8275.362	6021.102	8393.15	3464.287	7862.205	7319.7	4705.307	4471.343	4771.815	6317.544	4143.274	4339.294
	worst	3607.686	9218.724	7874.733	10292.52	3655.212	8561.913	8816.14	5683.615	5485.035	6993.609	7822.497	6314.775	5039.848
	std	24.77834	451.0737	858.1697	927.3888	99.99068	319.7006	674.5303	498.4749	480.4831	1148.169	723.9013	1132.346	312.1846
	median	3573.536	8525.294	7283.752	8896.185	3476.113	8328.554	7885.298	4859.772	4711.065	6039.869	7400.69	4926.117	4718.579
	rank	2	12	8	13	1	11	10	5	4	7	9	6	3
C17-F27	mean	3207.018	3558.17	3348.028	3686.102	3232.057	3445.411	3407.476	3245.891	3261.073	3317.182	4679.337	3284.818	3433.969
	best	3200.749	3513.715	3281.108	3464.475	3222.993	3333.514	3254.965	3217.709	3245.537	3251.877	4312.247	3262.488	3357.583
	worst	3210.656	3639.585	3420.281	3921.549	3247.201	3660.88	3521.243	3277.426	3277.837	3364.238	4948.385	3307.204	3475.831
	std	5.056308	60.6895	81.3752	211.586	11.97255	159.4864	124.2612	26.70273	16.15698	51.60339	334.4175	23.63649	57.41877
	median	3208.335	3539.69	3345.361	3679.193	3229.018	3393.626	3426.849	3244.215	3260.46	3326.307	4728.358	3284.79	3451.232
	rank	1	11	7	12	2	10	8	3	4	6	13	5	9
C17-F28	mean	3100	4549.007	3301.393	5298.552	3258.64	4036.604	3443.746	3293.81	3574.489	3634.18	3512.039	3353.589	3562.747
	best	3100	4348.72	3282.68	5037.445	3236.84	3556.727	3373.986	3244.586	3390.627	3490.735	3433.812	3223.124	3528.7
	worst	3100	4754.485	3322.349	5560.625	3278.027	4536.902	3483.68	3322.828	4006.854	3948.647	3629.929	3518.183	3603.925
	std	2.86E-13	196.7029	18.5019	260.9731	23.02828	488.398	52.19947	38.39117	315.8185	230.9762	91.45297	138.501	34.63276
	median	3100	4546.411	3300.272	5298.07	3259.846	4026.393	3458.66	3303.912	3450.238	3548.67	3492.207	3336.525	3559.181
	rank	1	12	4	13	2	11	6	3	9	10	7	5	8
C17-F29	mean	3353.75	5213.215	4333.038	5394.511	3777.799	5082.723	4955.712	3930.648	3887.445	4480.829	4935.906	4198.769	4296.731
	best	3325.385	4843.563	4044.383	4876.369	3636.029	4637.309	4717.357	3828.26	3803.77	4212.207	4695.177	4043.794	3983.394
	worst	3370.797	5617.331	4512.864	6113.132	3902.207	5823.289	5107.337	4015.974	3989.644	4882.639	5151.589	4403.887	4576.177
	std	21.41933	409.7053	227.4317	667.8421	126.4094	602.7249	181.7118	88.47312	86.709	314.1123	260.227	163.3035	291.7309
	median	3359.41	5195.983	4387.452	5294.272	3786.48	4935.147	4999.077	3939.179	3878.183	4414.234	4948.428	4173.698	4313.676
	rank	1	12	7	13	2	11	10	4	3	8	9	5	6
C17-F30	mean	5007.854	1.17E+09	4313339	2.31E+09	3155580	34515516	35156701	5674036	8355706	34049363	4996171	3371754	3722284
	best	4955.449	8.65E+08	1403518	1.66E+09	998299.1	15004022	7376135	4053519	4080505	19564129	2605235	1027243	1806480
	worst	5086.396	1.29E+09	5543722	2.55E+09	4308484	77589428	55588937	7895164	18339730	65808775	6522255	4307400	5396223
	std	64.15759	2.23E+08	2120726	4.71E+08	1694195	31507516	21961834	1832212	7370893	23257021	1900134	1714722	1705773
	median	4994.785	1.27E+09	5153059	2.51E+09	3657767	22734307	38830866	5373731	5501295	25412274	5428596	4076187	3843216
	rank	1	12	5	13	2	10	11	7	8	9	6	3	4
Sum rank		30	334	182	361	58	305	284	128	151	232	231	139	204
Mean rank		1.034483	11.51724	6.275862	12.44828	2	10.51724	9.793103	4.413793	5.206897	8	7.965517	4.793103	7.034483
Total rank		1	12	6	13	2	11	10	3	5	9	8	4	7

Table 3. Optimization results for the CEC 2017 test suite (dimension=30).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	2.15E+10	2.16E+08	3.36E+10	2.16E+08	1.47E+10	1.59E+09	2.17E+08	1.57E+09	5.22E+09	2.25E+08	1.36E+09	3.61E+08
	best	100	1.85E+10	1.04E+08	2.98E+10	1.04E+08	9.3E+09	1.19E+09	1.05E+08	3.27E+08	3.34E+09	1.04E+08	1.04E+08	2.31E+08
	worst	100	2.68E+10	4.58E+08	4.11E+10	4.58E+08	1.99E+10	2.17E+09	4.59E+08	4.53E+09	7.56E+09	4.63E+08	4.67E+09	5.84E+08
	std	8.93E-15	4.22E+09	1.79E+08	5.62E+09	1.79E+08	5.49E+09	5.05E+08	1.79E+08	2.16E+09	1.9E+09	1.8E+08	2.41E+09	1.67E+08
	median	100	2.04E+10	1.52E+08	3.16E+10	1.52E+08	1.49E+10	1.51E+09	1.52E+08	7.1E+08	4.99E+09	1.67E+08	3.22E+08	3.15E+08
	rank	1	12	2	13	3	11	9	4	8	10	5	7	6
C17-F3	mean	300	96614.41	53933.49	77366.61	18585.58	55958.1	205718.4	19131.16	51472.71	45809.84	95407.06	43547.71	153272.3
	best	300	88996.04	39548.33	63712.4	16226.86	51683.78	170987.9	16830.62	47478.85	43809.8	82336.48	38319.08	120561.6
	worst	300	106524.6	62295.66	84695.4	20971.61	58288.34	235879.8	21002.04	53477.99	47780.24	103083	48636.89	208250.5
	std	0	9492.196	10861.79	10276.61	2134.522	3185.682	29329.65	1946.304	3005.516	1764.21	10708.3	5738.33	45101.23
	median	300	95468.51	56944.99	80529.33	18571.92	56930.14	208002.9	19345.98	52467.01	45824.67	98104.4	43617.44	142138.6
	rank	1	11	7	9	2	8	13	3	6	5	10	4	12
C17-F4	mean	458.5616	5350.397	539.4145	8089.186	521.9548	3807.993	817.0299	524.9005	585.8032	858.3046	604.3766	628.1991	780.6074
	best	458.5616	3054.705	523.4544	5224.711	515.404	967.5568	760.4125	517.1595	535.2115	686.5093	590.4452	536.4024	740.8788
	worst	458.5616	7206.478	550.2992	11265.61	534.1434	6252.298	889.6414	530.3765	617.9659	1177.365	619.4999	783.7213	796.0334
	std	0	1871.912	13.03211	2727.29	9.092848	2429.097	64.88372	6.079095	38.78506	236.972	17.05345	124.3083	28.86259
	median	458.5616	5570.202	541.9521	7933.213	519.1358	4006.058	809.0328	526.033	595.0176	784.6721	603.7807	596.3364	792.7587
	rank	1	12	4	13	2	11	9	3	5	10	6	7	8
C17-F5	mean	502.4874	816.585	719.5219	848.4325	603.984	775.2252	799.006	633.4036	635.4277	756.0726	717.4144	644.1008	700.8081
	best	500.995	799.1994	688.3874	826.0953	587.9209	750.8395	777.6683	618.6867	599.8995	739.9461	703.0501	621.5861	658.3407
	worst	503.9798	836.1958	764.645	878.4212	620.0451	804.8383	807.6101	664.2009	661.1234	774.8832	737.5871	683.1084	753.5
	std	1.397379	16.5293	37.13723	26.03724	15.10696	28.20919	15.53716	22.59738	32.74051	18.46433	17.95634	29.331	42.83256
	median	502.4874	815.4724	712.5276	844.6068	603.9851	772.6115	805.3727	625.3633	640.344	754.7306	714.5102	635.8544	695.6958
	rank	1	12	8	13	2	10	11	3	4	9	7	5	6
C17-F6	mean	600	671.8645	645.024	674.4263	609.8658	669.551	668.9306	626.9659	616.8448	642.285	652.9594	645.2092	631.6495
	best	600	670.4622	642.8248	671.1038	608.833	656.5433	659.7693	616.8861	610.4155	637.8877	652.2821	636.7136	625.3622
	worst	600	673.3848	647.2092	679.2321	610.5577	677.7928	672.7284	638.6085	623.9538	651.085	653.7211	653.3163	635.0472
	std	7.14E-14	1.433896	2.015521	4.206224	0.808745	10.70667	6.669619	10.99308	6.058066	6.647049	0.73281	8.093386	4.67082
	median	600	671.8056	645.0311	673.6846	610.0362	671.934	671.6123	626.1845	616.505	640.0838	652.9172	645.4035	633.0942
	rank	1	12	7	13	2	11	10	4	3	6	9	8	5
C17-F7	mean	733.478	1245.794	1122.999	1278.85	880.073	1185.844	1253.075	886.0305	911.6808	1065.519	980.9371	905.745	977.9064
	best	732.8186	1207.453	1027.182	1271.948	862.4656	1068.204	1216.101	847.0424	855.0212	992.1556	940.8225	892.8739	950.0423
	worst	734.5199	1272.678	1258.797	1296.025	922.0296	1304.724	1323.112	946.5276	948.7409	1127.53	1038.579	928.3516	1020.577
	std	0.820293	30.5378	111.7555	12.56992	30.57605	110.8795	54.41842	47.39518	43.42062	77.06954	45.57859	17.57207	32.69181
	median	733.2867	1251.522	1103.008	1273.715	867.8984	1185.224	1236.545	875.276	921.4806	1071.196	972.1733	900.8773	970.5031
	rank	1	11	9	13	2	10	12	3	5	8	7	4	6
C17-F8	mean	803.3298	1058.065	948.5071	1088.37	900.689	1037.026	1013.86	902.9144	901.8313	1007.554	958.1218	927.4182	978.136
	best	801.2023	1047.635	927.1619	1069.187	893.6258	1004.164	966.3403	875.2901	893.4635	989.4507	941.5461	915.1568	963.4448
	worst	804.1574	1071.848	967.1707	1111.511	910.5728	1118.871	1051.081	925.5831	909.499	1037.685	978.3326	941.4581	992.1231
	std	1.545701	12.81537	19.36666	21.54123	7.840737	59.7159	39.42715	24.43217	7.139129	22.72103	17.49184	11.84809	15.27864
	median	803.9798	1056.387	949.8478	1086.391	899.2787	1012.534	1019.009	905.3923	902.1813	1001.541	956.3042	926.5289	978.4881
	rank	1	12	6	13	2	11	10	4	3	9	7	5	8
C17-F9	mean	900	10081.46	5101.467	9806.301	2069.207	10506.5	10131.77	5612.936	2874.474	5870.885	4497.761	4066.545	2238.248
	best	900	8674.481	4115.659	9645.45	1830.887	6753.152	8060.012	4599.951	2484.507	4458.616	4087.39	2957.901	2028.884
	worst	900	11351.77	5672.734	9939.413	2218.791	13826.81	11905.03	7988.969	3400.575	8283.113	5220.916	5463.258	2460.82
	std	7.14E-14	1210.428	757.1536	144.6618	192.7325	3180.977	2131.48	1733.811	502.3072	1852.802	575.9914	1154.492	228.836
	median	900	10149.78	5308.739	9820.171	2113.576	10723.02	10281.02	4931.413	2806.408	5370.905	4341.369	3922.511	2231.644
	rank	1	11	7	10	2	13	12	8	4	9	6	5	3
C17-F10	mean	2293.267	6881.855	5445.848	7438.226	4257.329	6346.146	6294.493	4793.373	4906.424	7454.188	4954.637	5110.67	6007.258
	best	1851.756	6503.624	4840.213	6834.203	3957.726	5306.802	5490.274	4555.776	4406.865	7148.075	4746.047	4829.285	5532.538
	worst	2525.027	7058.243	5930.547	7869.142	4716.564	6752.056	7472.411	5100.911	5269.169	7622.178	5209.384	5479.349	6562.458
	std	326.7738	279.2847	566.2276	475.6195	369.0798	756.3273	945.8514	256.6862	395.0874	227.8082	218.5099	294.6064	507.6167
	median	2398.142	6982.777	5506.315	7524.78	4177.514	6662.862	6107.644	4758.402	4974.83	7523.25	4931.559	5067.022	5967.018
	rank	1	11	7	12	2	10	9	3	4	13	5	6	8
C17-F11	mean	1102.987	6822.248	1745.516	7878.094	1673.799	4893.283	7076.081	1791.348	2507.27	2338.765	3078.954	1738.629	8176.406
	best	1100.995	5637.663	1653.643	6443.573	1530.864	3681.247	5287.212	1651.827	1843.898	2013.563	2441.813	1649.955	3374.532
	worst	1105.977	7627.036	1945.118	8774.924	1858.768	6936.913	10315.56	1946.495	4247.063	3124.093	3623.673	1902.104	14911.18
	std	2.341679	1003.287	146.0792	1130.981	153.8407	1614.778	2415.797	136.0006	1265.008	571.6796	550.8356	122.9817	5372.792
	median	1102.487	7012.146	1691.651	8146.939	1652.781	4477.486	6350.775	1783.535	1969.059	2108.702	3125.165	1701.228	7209.959
	rank	1	10	4	12	2	9	11	5	7	6	8	3	13
C17-F12	mean	1744.553	5.73E+09	37041608	8.89E+09	20094778	4.14E+09	2.22E+08	29210711	62823790	2.66E+08	1.82E+08	22162355	26329511
	best	1721.81	4.76E+09	11046828	7.92E+09	8675865	2.16E+09	60182802	12900846	13535696	1.66E+08	40693025	10717920	13974918
	worst	1764.937	7.28E+09	75615075	1.12E+10	34202179	5.42E+09	4.36E+08	39592150	1.18E+08	4.61E+08	5.51E+08	34408383	38512204
	std	21.92397	1.18E+09	30177935	1.69E+09	14150253	1.53E+09	1.89E+08	12440535	46444843	1.45E+08	2.68E+08	13200207	13435001
	median	1745.733	5.45E+09	30752264	8.23E+09	18750534	4.5E+09	1.95E+08	32174923	60019050	2.19E+08	68002949	21761559	26415462
	rank	1	12	6	13	2	11	9	5	7	10	8	3	4
C17-F13	mean	1315.791	4.65E+09	234475	8.58E+09	114340	1.19E+09	848348.1	186778.5	726743.2	71823934	142473.2	139130.8	9802230
	best	1314.587	2.26E+09	112334.1	4.5E+09	43210.96	16088952	388963.5	77625.43	119097.2	49924732	65964.4	57684.87	2673834
	worst	1318.646	6.51E+09	353565.6	1.05E+10	240984	4.13E+09	1327049	273433.4	2144638	1.06E+08	263683.3	250402.8	21081475
	std	2.106458	1.91E+09	129203.1	3E+09	100849.1	2.15E+09	511048.8	108404.7	1046282	26301943	96404.67	89357.48	8585811
	median	1314.967	4.91E+09	236000.2	9.64E+09	86582.59	3.07E+08	838690.1	198027.5	321618.9	65792667	120122.5	124217.8	7726806
	rank	1	12	6	13	2	11	8	5	7	10	4	3	9
C17-F14	mean	1423.017	1718087	399037.4	1962627	179916.4	1132743	1984755	195263.3	611735.3	292356.5	1107748	193985.3	1809212
	best	1422.014	1061406	132561.7	1008748	61125.47	742595.4	89121.17	72899.9	163245.4	167780.5	714968.1	80039.05	371627.1
	worst	1423.993	2389736	679300.5	2758135	442287.5	1459897	5958393	462069.6	1040164	571838.3	1500624	443698.1	2808801
	std	0.879206	636983.5	317464.3	845287.8	191863.2	321641.1	2931780	195299.3	412610.4	205434.1	470262.9	183056.2	1190488
	median	1423.03	1710604	392143.7	2041812	108126.3	1164240	945753.9	123041.7	621766	214903.5	1107700	126101.9	2028210
	rank	1	10	6	12	2	9	13	4	7	5	8	3	11
C17-F15	mean	1503.129	2.48E+08	1375822	4.87E+08	1346736	13013832	5440226	1380151	14192485	5512754	1358466	1349301	2121150
	best	1502.462	2.18E+08	177100.7	4.24E+08	129052.6	7380528	316349.5	155012.3	283640.6	1128907	141037.9	134942.1	408683.1
	worst	1504.265	2.74E+08	4894040	5.36E+08	4868737	27325764	18162803	4887511	52968867	12712041	4879322	4871739	5009793
	std	0.930751	30351327	2551791	60423759	2554602	10424666	9296555	2544111	28133875	5439895	2553789	2554886	2200031
	median	1502.893	2.51E+08	216074.2	4.93E+08	194577.4	8674518	1640875	239039.2	1758716	4105034	206752.9	195262.5	1533061
	rank	1	12	5	13	2	10	8	6	11	9	4	3	7
C17-F16	mean	1663.469	4101.329	3031.898	4635.035	2241.54	3251.904	4041.201	2696.913	2661.031	3408.197	3572.045	2975.076	2990.448
	best	1614.72	3807.969	2737.754	3978.845	2001.553	2908.494	3376.12	2482.418	2539.576	3251.758	3420.823	2753.289	2710.515
	worst	1744.118	4276.32	3407.61	5176.319	2516.773	3411.485	4801.345	2913.154	2829.105	3667.715	3691.182	3153.728	3343.812
	std	67.41864	234.0283	302.0019	676.0589	242.5108	251.8612	637.99	221.8501	145.2831	201.6661	121.8334	209.1785	322.4667
	median	1647.519	4160.513	2991.113	4692.488	2223.917	3343.819	3993.67	2696.04	2637.723	3356.658	3588.088	2996.644	2953.733
	rank	1	12	7	13	2	8	11	4	3	9	10	5	6
C17-F17	mean	1728.099	3204.184	2445.318	3451.547	1948.085	3094.792	2749.862	2125.927	2005.692	2218.34	2485.993	2332.979	2187.25
	best	1718.761	2673.848	2350.034	3100.934	1867.475	2198.674	2318.895	2043.202	1889.97	2056.227	2364.45	2153.82	2156.169
	worst	1733.659	3820.327	2549.322	4023.651	2005.72	5345.294	3024.682	2272.116	2134.369	2470.026	2632.64	2661.365	2267.963
	std	7.297618	528.6384	89.51016	445.1187	71.30712	1636.126	332.5784	109.2024	134.6634	193.1037	131.3193	258.2104	58.77136
	median	1729.987	3161.279	2440.959	3340.802	1959.573	2417.6	2827.936	2094.196	1999.214	2173.554	2473.441	2258.365	2162.433
	rank	1	12	8	13	2	11	10	4	3	6	9	7	5
C17-F18	mean	1825.696	23516152	2597862	26971587	449288.9	29942772	5237635	967163.3	788246.3	1799905	865686.6	559110.2	3406739
	best	1822.524	7042539	626271.2	8972491	157003.2	1237016	1769612	439399.9	219118.9	1025030	440176.2	287596.9	2707382
	worst	1828.42	45599259	4445437	52908094	800715.7	56693727	10685466	1845177	1272191	2261004	1211045	922395.8	4776390
	std	2.939396	18592179	2060642	20284915	288890.8	33335395	4150540	673195	471794.6	590154.2	364166.3	287799.8	1039578
	median	1825.92	20711405	2659870	23002881	419718.5	30920173	4247731	792038.2	830837.5	1956792	905762.4	513224.1	3071591
	rank	1	11	8	12	2	13	10	6	4	7	5	3	9
C17-F19	mean	1910.989	4.73E+08	1296419	7.96E+08	1243037	2.4E+08	12870427	2003950	4515071	5909591	1307840	1277590	2557263
	best	1908.84	3.53E+08	293139.3	5.75E+08	240422.4	3206791	1752074	367290.5	1497855	3643788	308068.3	347028	1960284
	worst	1913.095	6.15E+08	1937459	1.21E+09	1816626	6.64E+08	21895052	3529380	12027809	8450739	1904376	1822176	3191310
	std	2.101811	1.43E+08	764927.9	3.04E+08	750238.1	3.31E+08	9869339	1494110	5493944	2731583	752848.6	698751.5	548249.5
	median	1911.01	4.61E+08	1477540	7.01E+08	1457550	1.47E+08	13917291	2059565	2267309	5771917	1509458	1470577	2538729
	rank	1	12	4	13	2	11	10	6	8	9	5	3	7
C17-F20	mean	2065.787	2852.05	2636.891	2896.093	2261.509	2812.046	2801.946	2611.987	2423.904	2769.729	2942.41	2564.666	2505.922
	best	2029.521	2778.489	2515.082	2751.613	2145.565	2702.619	2646.95	2401.697	2260.383	2708.159	2644.76	2513.556	2445.026
	worst	2161.126	2924.641	2808.219	2965.309	2346.016	2915.11	2958.567	2955.98	2564.83	2871.895	3346.198	2680.918	2543.795
	std	69.24026	65.16107	137.6245	107.6394	91.9837	95.66384	142.0746	260.8481	136.0149	81.18477	320.9119	85.12862	47.3034
	median	2036.25	2852.534	2612.131	2933.724	2277.228	2815.228	2801.134	2545.137	2435.202	2749.43	2889.341	2532.096	2517.433
	rank	1	11	7	12	2	10	9	6	3	8	13	5	4
C17-F21	mean	2308.456	2596.762	2448.231	2643.694	2387.133	2525.165	2586.829	2418.922	2406.48	2492.791	2553.99	2442.966	2490.435
	best	2304.034	2526.449	2257.85	2586.165	2378.506	2346.124	2516.104	2385.646	2370.12	2483.421	2534.95	2423.177	2459.35
	worst	2312.987	2652.414	2581.521	2712.368	2392.814	2639.573	2647.646	2450.321	2422.972	2506.051	2588.127	2461.006	2524.428
	std	4.850941	62.82122	148.2022	62.05312	7.047214	138.4952	70.23165	30.08598	26.60579	10.40937	26.17077	16.9696	29.07732
	median	2308.402	2604.093	2476.777	2638.122	2388.606	2557.482	2591.783	2419.861	2416.414	2490.847	2546.441	2443.841	2488.982
	rank	1	12	6	13	2	9	11	4	3	8	10	5	7
C17-F22	mean	2300	7416.278	5606.15	7217.578	2767.064	8062.805	6943.239	4118.651	3095.301	5534.882	6060.652	4879.829	3093.803
	best	2300	7084.193	2589.959	6320.075	2589.259	7696.453	5982.982	2594.276	2812.261	3057.109	3979.755	3036.958	2959.648
	worst	2300	7992.923	6648.708	8208.241	2909.439	8295.31	7587.508	5936.695	3456.066	8044.654	6842.973	6624.719	3284.397
	std	0	447.0653	2188.073	850.4959	157.5029	294.8451	745.0711	1866.174	293.5383	2998.334	1511.723	1800.442	156.411
	median	2300	7293.999	6592.966	7170.999	2784.779	8129.728	7101.233	3971.816	3056.438	5518.882	6709.94	4928.821	3065.584
	rank	1	12	8	11	2	13	10	5	4	7	9	6	3
C17-F23	mean	2655.081	3134.082	2916.197	3179.248	2684.911	3138.091	3015.153	2760.249	2771.554	2897.243	3608.12	2894.462	2956.074
	best	2653.745	3052.541	2831.729	3137.587	2546.881	3029.414	2858.446	2726.062	2757.65	2880.102	3508.173	2872.493	2937.475
	worst	2657.377	3203.731	3047.601	3249.515	2737.578	3302.897	3099.717	2789.67	2791.69	2940.924	3701.653	2925.754	2997.452
	std	1.798497	76.5529	102.9913	56.02015	100.244	128.9959	117.6717	29.73855	15.77988	31.77993	107.6621	27.71245	30.23767
	median	2654.6	3140.028	2892.728	3164.946	2727.593	3110.026	3051.225	2762.632	2768.439	2883.973	3611.326	2889.802	2944.683
	rank	1	10	7	12	2	11	9	3	4	6	13	5	8
C17-F24	mean	2831.409	3259.418	3140.517	3341.852	2903.733	3231.21	3095.648	2922.053	2934.549	3034.572	3299.789	3107.738	3186.227
	best	2829.992	3230.675	3028.691	3270.724	2893.367	3144.047	3034.507	2874.181	2916.054	3017.56	3271.765	3047.614	3111.252
	worst	2832.366	3316.083	3271.067	3461.734	2911.236	3276.173	3120.213	2943.399	2943.03	3056.434	3334.012	3204.837	3254.053
	std	1.246245	41.79513	114.4207	96.12821	8.854297	64.85565	44.52533	35.0327	13.66786	17.53194	32.2566	73.77764	74.20735
	median	2831.64	3245.457	3131.155	3317.475	2905.165	3252.309	3113.936	2935.316	2939.556	3032.148	3296.688	3089.251	3189.801
	rank	1	11	8	13	2	10	6	3	4	5	12	7	9
C17-F25	mean	2886.698	3774.898	2925.976	4289.841	2911.644	3387.596	3068.493	2926.652	2995.621	3062.61	2997.379	2914.669	3089.732
	best	2886.691	3469.485	2913.557	3796.919	2905.41	3075.541	3037.756	2904.458	2963.601	2967.819	2987.174	2907.939	3073.483
	worst	2886.707	4006.444	2955.788	4952.46	2919.105	3708.48	3088.721	2978.817	3058.703	3175.101	3006.087	2927.24	3098.003
	std	0.008274	243.4626	21.95218	524.1696	7.125738	335.2555	24.65864	38.32121	48.44319	109.0198	9.535606	9.848236	12.04774
	median	2886.698	3811.832	2917.28	4204.993	2911.031	3383.182	3073.748	2911.666	2980.09	3053.759	2998.128	2911.748	3093.722
	rank	1	12	4	13	2	11	9	5	6	8	7	3	10
C17-F26	mean	3578.65	8636.168	7115.835	9119.509	3517.931	8270.307	7976.609	5027.116	4844.627	5961.291	7235.355	5077.571	4704.075
	best	3559.841	8275.362	6021.102	8393.15	3464.287	7862.205	7319.7	4705.307	4471.343	4771.815	6317.544	4143.274	4339.294
	worst	3607.686	9218.724	7874.733	10292.52	3655.212	8561.913	8816.14	5683.615	5485.035	6993.609	7822.497	6314.775	5039.848
	std	24.77834	451.0737	858.1697	927.3888	99.99068	319.7006	674.5303	498.4749	480.4831	1148.169	723.9013	1132.346	312.1846
	median	3573.536	8525.294	7283.752	8896.185	3476.113	8328.554	7885.298	4859.772	4711.065	6039.869	7400.69	4926.117	4718.579
	rank	2	12	8	13	1	11	10	5	4	7	9	6	3
C17-F27	mean	3207.018	3558.17	3348.028	3686.102	3232.057	3445.411	3407.476	3245.891	3261.073	3317.182	4679.337	3284.818	3433.969
	best	3200.749	3513.715	3281.108	3464.475	3222.993	3333.514	3254.965	3217.709	3245.537	3251.877	4312.247	3262.488	3357.583
	worst	3210.656	3639.585	3420.281	3921.549	3247.201	3660.88	3521.243	3277.426	3277.837	3364.238	4948.385	3307.204	3475.831
	std	5.056308	60.6895	81.3752	211.586	11.97255	159.4864	124.2612	26.70273	16.15698	51.60339	334.4175	23.63649	57.41877
	median	3208.335	3539.69	3345.361	3679.193	3229.018	3393.626	3426.849	3244.215	3260.46	3326.307	4728.358	3284.79	3451.232
	rank	1	11	7	12	2	10	8	3	4	6	13	5	9
C17-F28	mean	3100	4549.007	3301.393	5298.552	3258.64	4036.604	3443.746	3293.81	3574.489	3634.18	3512.039	3353.589	3562.747
	best	3100	4348.72	3282.68	5037.445	3236.84	3556.727	3373.986	3244.586	3390.627	3490.735	3433.812	3223.124	3528.7
	worst	3100	4754.485	3322.349	5560.625	3278.027	4536.902	3483.68	3322.828	4006.854	3948.647	3629.929	3518.183	3603.925
	std	2.86E-13	196.7029	18.5019	260.9731	23.02828	488.398	52.19947	38.39117	315.8185	230.9762	91.45297	138.501	34.63276
	median	3100	4546.411	3300.272	5298.07	3259.846	4026.393	3458.66	3303.912	3450.238	3548.67	3492.207	3336.525	3559.181
	rank	1	12	4	13	2	11	6	3	9	10	7	5	8
C17-F29	mean	3353.75	5213.215	4333.038	5394.511	3777.799	5082.723	4955.712	3930.648	3887.445	4480.829	4935.906	4198.769	4296.731
	best	3325.385	4843.563	4044.383	4876.369	3636.029	4637.309	4717.357	3828.26	3803.77	4212.207	4695.177	4043.794	3983.394
	worst	3370.797	5617.331	4512.864	6113.132	3902.207	5823.289	5107.337	4015.974	3989.644	4882.639	5151.589	4403.887	4576.177
	std	21.41933	409.7053	227.4317	667.8421	126.4094	602.7249	181.7118	88.47312	86.709	314.1123	260.227	163.3035	291.7309
	median	3359.41	5195.983	4387.452	5294.272	3786.48	4935.147	4999.077	3939.179	3878.183	4414.234	4948.428	4173.698	4313.676
	rank	1	12	7	13	2	11	10	4	3	8	9	5	6
C17-F30	mean	5007.854	1.17E+09	4313339	2.31E+09	3155580	34515516	35156701	5674036	8355706	34049363	4996171	3371754	3722284
	best	4955.449	8.65E+08	1403518	1.66E+09	998299.1	15004022	7376135	4053519	4080505	19564129	2605235	1027243	1806480
	worst	5086.396	1.29E+09	5543722	2.55E+09	4308484	77589428	55588937	7895164	18339730	65808775	6522255	4307400	5396223
	std	64.15759	2.23E+08	2120726	4.71E+08	1694195	31507516	21961834	1832212	7370893	23257021	1900134	1714722	1705773
	median	4994.785	1.27E+09	5153059	2.51E+09	3657767	22734307	38830866	5373731	5501295	25412274	5428596	4076187	3843216
	rank	1	12	5	13	2	10	11	7	8	9	6	3	4
Sum rank		30	334	182	361	58	305	284	128	151	232	231	139	204
Mean rank		1.034483	11.51724	6.275862	12.44828	2	10.51724	9.793103	4.413793	5.206897	8	7.965517	4.793103	7.034483
Total rank		1	12	6	13	2	11	10	3	5	9	8	4	7

Table 4. Optimization results for the CEC 2017 test suite (dimension=50).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	4.95E+10	1.1E+09	7.69E+10	1.1E+09	3.19E+10	7.32E+09	1.1E+09	8.66E+09	1.79E+10	1.5E+10	3.14E+09	9.51E+09
	best	100	4.41E+10	7.44E+08	6.72E+10	7.27E+08	2.99E+10	4.4E+09	7.27E+08	6.18E+09	1.23E+10	1.26E+10	2E+09	8.74E+09
	worst	100	5.34E+10	1.56E+09	8.44E+10	1.57E+09	3.39E+10	1.09E+10	1.56E+09	1.19E+10	2.42E+10	1.75E+10	3.92E+09	1.02E+10
	std	0	4.3E+09	3.84E+08	8.03E+09	3.94E+08	1.81E+09	3.29E+09	3.9E+08	2.6E+09	6.28E+09	2.21E+09	8.91E+08	8.27E+08
	median	100	5.02E+10	1.05E+09	7.8E+10	1.05E+09	3.19E+10	7.01E+09	1.05E+09	8.27E+09	1.75E+10	1.49E+10	3.33E+09	9.53E+09
	rank	1	12	4	13	3	11	6	2	7	10	9	5	8
C17-F3	mean	300	154396	144775.7	153921.7	40780	114495.5	215432.5	63673.5	131350.3	105750.1	170162.6	143305	239250.6
	best	300	130935.1	116840.9	136841.4	35610.86	98555.96	164738.1	50699.94	113358.5	82476.83	150986.5	113745.4	199886.3
	worst	300	183241.2	166548.8	164931.7	53012.54	129952.4	324443.8	82406.44	153841	116468.6	188356.6	174868.7	265767.6
	std	0	24150.2	22863.42	13140.4	8961.981	13976.42	82028.55	14810.16	18310.5	17163.84	22179.7	31567.13	30630.41
	median	300	151703.8	147856.6	156956.9	37248.3	114736.8	186273.9	60793.82	129100.9	112027.6	170653.7	142303	245674.3
	rank	1	10	8	9	2	5	12	3	6	4	11	7	13
C17-F4	mean	470.3679	12184.46	816.0011	19457.87	681.4135	6971.561	1820.302	707.3102	1412.912	2511.357	2728.976	1073.423	1485.133
	best	428.5127	9514.955	781.0024	12922.28	656.2968	5678.306	1207.196	644.4745	1114.656	1528.502	2319.866	803.94	1316.601
	worst	525.7252	13801.19	880.4744	23154.52	694.8483	8926.75	2130.731	812.7542	1716.417	4115.779	2931.851	1762.34	1589.352
	std	53.92841	2102.179	47.95718	5099.299	18.62806	1501.712	459.5216	79.82462	284.7839	1229.91	301.2068	501.5184	139.8851
	median	463.6168	12710.85	801.2638	20877.33	687.2544	6640.594	1971.641	686.0061	1410.286	2200.573	2832.093	863.7063	1517.289
	rank	1	12	4	13	2	11	8	3	6	9	10	5	7
C17-F5	mean	504.7261	1042.95	847.6477	1066.558	749.3764	1080.986	926.8785	751.4539	740.7157	961.5023	805.8724	792.0833	875.1166
	best	503.9798	1013.374	816.5437	1061.377	676.9687	962.7314	893.7665	685.5776	712.1028	921.1337	756.8901	741.5352	844.3322
	worst	505.9698	1069.044	891.1425	1071.499	811.096	1166.444	950.6786	852.7761	773.689	983.4193	841.0368	843.6933	899.9478
	std	1.036324	27.21731	35.00028	5.69125	60.73609	106.8864	28.21668	81.0711	32.96958	30.09048	42.06955	45.51418	26.82066
	median	504.4773	1044.692	841.4523	1066.678	754.7205	1097.383	931.5345	733.731	738.5355	970.7282	812.7815	791.5524	878.0932
	rank	1	11	7	12	3	13	9	4	2	10	6	5	8
C17-F6	mean	600	686.6786	658.5233	688.3462	619.2303	682.4414	688.8653	640.3977	628.4489	661.7716	656.7135	653.2132	649.1582
	best	600	683.956	653.561	686.3068	617.0439	667.7492	684.5972	631.1357	624.1073	650.8752	652.8177	650.715	637.678
	worst	600	689.5874	662.2555	692.3995	621.2137	694.7835	697.1782	661.4298	636.4458	667.6559	659.7741	657.7726	659.3786
	std	0	2.564667	4.113542	3.064662	2.433815	13.36965	6.255548	15.58106	6.01381	8.107078	3.221641	3.400265	10.15461
	median	600	686.5855	659.1383	687.3393	619.3317	683.6164	686.8428	634.5125	626.6213	664.2777	657.1311	652.1827	649.7881
	rank	1	11	8	12	2	10	13	4	3	9	7	6	5
C17-F7	mean	756.7298	1690.859	1588.857	1771.25	1075.378	1602.293	1622.731	1095.607	1105.13	1437.854	1383.321	1212.905	1299.674
	best	754.7543	1670.615	1528.091	1705.897	1030.508	1476.164	1568.636	1067.488	1087.362	1337.764	1248.408	1080.822	1236.369
	worst	758.3522	1717.492	1642.381	1851.318	1114.134	1723.89	1695.087	1120.156	1120.405	1488.694	1487.485	1401.47	1341.989
	std	1.689848	21.74419	52.67291	67.87609	42.83676	124.6629	63.58271	24.65415	15.78024	73.8405	118.2269	149.7953	51.14959
	median	756.9065	1687.665	1592.477	1763.893	1078.435	1604.558	1613.601	1097.392	1106.376	1462.479	1398.695	1184.664	1310.17
	rank	1	12	9	13	2	10	11	3	4	8	7	5	6
C17-F8	mean	805.721	1362.398	1124.105	1384.668	1032.391	1376.424	1285.685	1041.59	1051.264	1283.624	1136.983	1069.467	1231.684
	best	802.9849	1309.251	1084.806	1352.051	1005.624	1294.353	1170.851	1014.615	1021.474	1241.854	1129.802	1033.19	1203.054
	worst	810.9445	1401.525	1167.702	1400.527	1057.147	1488.554	1379.566	1102.659	1075.243	1333.975	1153.925	1115.698	1254.588
	std	3.890137	45.90234	46.06279	23.96893	27.67453	92.5422	93.65706	44.66053	27.00846	42.24419	12.44165	41.79212	23.26472
	median	804.4773	1369.408	1121.956	1393.047	1033.396	1361.394	1296.161	1024.543	1054.169	1279.333	1132.102	1064.49	1234.547
	rank	1	11	6	13	2	12	10	3	4	9	7	5	8
C17-F9	mean	900	32893	14489.41	33048.09	6476.341	34318.2	30367.44	19625.77	9331.297	23147.87	12386.16	12080.08	14096.86
	best	900	32012.24	14052.6	31573.96	5145.79	31605.69	28736.98	12085.61	8284.278	18375.71	11832.99	11289.35	12513.65
	worst	900	35391.89	15481.94	34309.71	7499.48	37659.76	34695.5	24942.59	10395.17	26861.39	12891.38	13421.7	15870.92
	std	1.01E-13	1813.192	724.5416	1351.066	1064.184	2774.951	3152.076	6649.26	999.4261	3827.95	610.4995	1090.988	1965.735
	median	900	32083.93	14211.56	33154.35	6630.047	34003.68	29018.63	20737.44	9322.868	23677.19	12410.14	11804.64	14001.44
	rank	1	11	7	12	2	13	10	8	3	9	5	4	6
C17-F10	mean	4347.157	12297.65	8533.281	13280.88	7089.713	11311.92	11318.18	7996.932	8807.23	13109.85	8753.29	8101.21	11254.8
	best	3555.132	11605.91	8403.143	12767.17	6333.566	10727.15	10020.91	6651.02	6939.843	12249.56	8402.124	7681.211	10764.36
	worst	5099.795	12872.86	8683.367	13570.06	7560.938	12147.75	12217.51	8843.609	13337.62	13918.05	9615.519	8869.181	12175.62
	std	701.4234	575.7262	146.9278	386.58	575.5683	711.9956	1022.132	1107.675	3313.016	821.9168	628.3406	571.2351	683.767
	median	4366.851	12355.92	8523.306	13393.14	7232.173	11186.4	11517.15	8246.549	7475.726	13135.89	8497.759	7927.225	11039.61
	rank	1	11	5	13	2	9	10	3	7	12	6	4	8
C17-F11	mean	1128.435	13254.8	2116.688	17775.28	1833.42	11266.11	4936.627	2086.933	5771.513	4949.467	12290.05	2170.136	20218.83
	best	1121.25	12087.39	1830.939	15713.24	1641.984	10172.69	4393.008	1852.248	3603.077	4503.232	11434.11	1889.802	11967.98
	worst	1133.132	13732.8	2422.918	19153.88	2233.299	13218.48	6347.39	2506.348	9794.399	5791.665	13632.1	2324.625	26693.06
	std	5.92135	849.4603	263.3627	1631.104	301.5769	1486.826	1028.431	319.4048	3105.372	641.2799	1031.46	214.7852	6643.792
	median	1129.678	13599.51	2106.447	18117	1729.199	10836.65	4503.056	1994.568	4844.288	4751.485	12046.99	2233.059	21107.15
	rank	1	11	4	12	2	9	6	3	8	7	10	5	13
C17-F12	mean	2905.102	3.54E+10	2.11E+08	5.78E+10	1.63E+08	2.11E+10	1.22E+09	2.15E+08	9.26E+08	4.24E+09	1.91E+09	1.45E+09	3.17E+08
	best	2527.376	2.98E+10	1.1E+08	4.22E+10	95831759	8.91E+09	9.68E+08	1.51E+08	2.07E+08	2.5E+09	7.26E+08	2.09E+08	2.26E+08
	worst	3168.37	4.24E+10	2.66E+08	7.91E+10	2.11E+08	3.54E+10	1.6E+09	2.53E+08	1.64E+09	8.22E+09	3.24E+09	3.84E+09	3.86E+08
	std	297.7638	6.2E+09	74870996	1.85E+10	53591181	1.19E+10	2.98E+08	51817338	7.64E+08	2.94E+09	1.13E+09	1.85E+09	73242431
	median	2962.331	3.48E+10	2.33E+08	5.49E+10	1.73E+08	2E+10	1.16E+09	2.29E+08	9.3E+08	3.12E+09	1.83E+09	8.76E+08	3.27E+08
	rank	1	12	3	13	2	11	7	4	6	10	9	8	5
C17-F13	mean	1340.1	1.99E+10	29140050	3.49E+10	29032641	8.19E+09	1.06E+08	29214686	3.18E+08	5.03E+08	44018606	4.15E+08	62625395
	best	1333.781	1.15E+10	15082176	1.76E+10	14999822	4.36E+09	72744405	15106499	1.46E+08	4.04E+08	15009940	15025904	36890666
	worst	1343.015	2.72E+10	64128728	5.02E+10	64116553	1.27E+10	1.46E+08	64286770	7.91E+08	6.67E+08	73484293	9.95E+08	1.03E+08
	std	4.658645	7.5E+09	25452500	1.49E+10	25520623	3.84E+09	32892364	25514545	3.43E+08	1.27E+08	33816482	5.06E+08	31425996
	median	1341.801	2.05E+10	18674648	3.59E+10	18507094	7.85E+09	1.02E+08	18732738	1.68E+08	4.7E+08	43790095	3.26E+08	55307580
	rank	1	12	3	13	2	11	7	4	8	10	5	9	6
C17-F14	mean	1429.458	21419208	1382812	39595412	393518.5	2568787	4254329	546854.7	1325055	1093309	12662683	857145.1	9473280
	best	1425.995	7220942	751383.8	12376432	326677.5	927699.9	3772080	450691.6	398040.1	930817.6	3226584	519753.6	4821344
	worst	1431.939	41607808	2712100	79818751	447530.2	3898450	5035760	625505.6	2244600	1255133	20593207	1069999	16073840
	std	2.851678	15781750	977068.1	31202565	67876.67	1342318	593266.1	78710.78	820976.9	196648.1	8552318	256936.7	5172877
	median	1429.95	18424041	1033882	33093232	399933.1	2724500	4104737	555610.7	1328791	1093643	13415470	919413.9	8498968
	rank	1	12	7	13	2	8	9	3	6	5	11	4	10
C17-F15	mean	1530.66	2.11E+09	1057529	3.39E+09	1028580	1.38E+09	9064409	1125076	5846302	58192649	1.61E+08	1035542	7974295
	best	1526.359	1.5E+09	129732.7	2.65E+09	74782.39	4.76E+08	813893.6	219713.3	107340.5	34902841	783143	90330.99	4244923
	worst	1532.953	2.77E+09	1909492	4.02E+09	1886011	3.01E+09	16390082	1924768	14578094	75179730	6.21E+08	1886309	15151372
	std	3.191893	6.5E+08	837170.9	6.59E+08	851654.6	1.28E+09	7569081	814458.4	6721675	18326818	3.34E+08	845990.3	5405843
	median	1531.664	2.09E+09	1095445	3.45E+09	1076763	1.02E+09	9526831	1177912	4349887	61344012	11307332	1082764	6250442
	rank	1	12	4	13	2	11	8	5	6	9	10	3	7
C17-F16	mean	2062.891	5865.586	4302.479	6920.014	3004.84	4535.478	5224.679	3470.57	3468.218	4456.184	3979.612	3481.424	3945.63
	best	1728.6	5246.472	4000.657	5435.58	2856.044	4127.203	4325.669	3337.527	3065.361	4182.74	3763.431	3124.763	3496.144
	worst	2242.663	7192.11	4702.332	9876.553	3131.765	4763.08	5825.538	3649.578	4004.577	4750.92	4288.477	3769.133	4355.434
	std	253.3831	995.1847	351.5548	2208.632	142.48	304.3711	722.4993	169.7208	491.0068	257.8711	261.4972	359.8899	439.383
	median	2140.15	5511.882	4253.462	6183.962	3015.775	4625.815	5373.755	3447.587	3401.466	4445.538	3933.271	3515.9	3965.471
	rank	1	12	8	13	2	10	11	4	3	9	7	5	6
C17-F17	mean	2021.151	6848.083	3556.425	9629.557	2746.348	3879.805	4346.813	3161.055	3078.243	4035.004	3768.66	3388.37	3577.713
	best	1900.43	5301.597	3126.73	7139.453	2620.494	3174.823	3897.119	2645.258	2947.105	3448.757	3433.271	3161.766	3422.149
	worst	2138.267	8279.961	3984.3	12346.15	2826.921	4287.61	4563.699	3597.312	3336.306	4343.917	4016.635	3694.363	3711.093
	std	146.025	1337.246	433.6566	2332.841	96.16517	530.519	333.5717	430.4672	198.7397	441.2389	265.75	274.7319	152.2354
	median	2022.954	6905.386	3557.334	9516.314	2768.989	4028.394	4463.216	3200.825	3014.781	4173.671	3812.368	3348.676	3588.805
	rank	1	12	6	13	2	9	11	4	3	10	8	5	7
C17-F18	mean	1830.62	64809056	5394677	94478124	3461290	31856563	40065124	5580678	8080372	10088485	10257555	4108187	11118482
	best	1822.239	53686283	3034887	46889386	963105.3	3514353	10878963	2221244	1894241	5532501	4183491	1244859	5015440
	worst	1841.673	74629822	8158394	1.27E+08	5983500	87143499	72254917	7349171	13443774	15199380	18698186	6398631	23037213
	std	8.860434	9422472	2461765	43284200	2456575	41161815	32747100	2581672	5815218	4557307	7084462	2492722	8998228
	median	1829.285	65460058	5192714	1.02E+08	3449276	18384199	38563309	6376148	8491736	9811030	9074271	4394628	8210638
	rank	1	12	4	13	2	10	11	5	6	7	8	3	9
C17-F19	mean	1925.185	2.21E+09	1054101	3.11E+09	845238.3	2.17E+09	6390103	4998182	1786352	41942343	1209978	1162654	1647542
	best	1924.437	1.05E+09	738624.6	2.1E+09	479903.4	8519676	1312499	3754874	1053878	35483791	688976.4	480615.3	1335633
	worst	1926.121	3.69E+09	1666936	3.85E+09	1480789	6.33E+09	14551966	5976860	2928702	52668431	2282084	1928568	2108001
	std	0.860892	1.21E+09	452664.5	8.47E+08	486851.6	3.08E+09	6201332	1091078	873486.8	8248080	794827.7	687967.2	368268.7
	median	1925.091	2.05E+09	905421.7	3.25E+09	710130.5	1.17E+09	4847973	5130496	1581415	39808575	934426.5	1120716	1573266
	rank	1	12	3	13	2	11	9	8	7	10	5	4	6
C17-F20	mean	2160.172	3717.027	3260.069	3934.224	2768.725	3397.451	3653.399	3271.387	2739.715	3674.026	3889.794	3278.828	3180.586
	best	2104.423	3399.714	2780.017	3661.976	2495.224	2984.482	3366.909	3075.111	2531.75	3598.109	3661.096	2973.788	3082.251
	worst	2323.891	3876.484	3706.835	4075.833	3025.157	3574.253	4142.691	3678.268	2912.856	3770.385	4143.729	3435.552	3297.711
	std	118.748	236.1103	422.9268	202.4307	240.6307	301.4758	371.4289	305.6783	211.1036	81.05394	215.029	225.3384	96.41896
	median	2106.186	3795.955	3276.712	3999.544	2777.259	3515.536	3551.997	3166.085	2757.128	3663.805	3877.175	3352.986	3171.19
	rank	1	11	5	13	3	8	9	6	2	10	12	7	4
C17-F21	mean	2314.895	2937.035	2744.131	2968.401	2494.788	2908.633	2901.223	2595.904	2553.318	2798.183	2814.628	2665.284	2739.49
	best	2309.045	2907.981	2635.865	2873.81	2470.541	2833.317	2798.883	2564.953	2499.752	2771.335	2768.232	2597.611	2711.195
	worst	2329.683	2965.668	2897.153	3036.496	2518.032	3037.663	2990.677	2638.091	2599.768	2832.034	2844.164	2752.389	2752.7
	std	10.75568	30.30095	119.9531	82.1574	25.9814	97.40959	88.69152	37.28297	45.20868	31.1184	37.98088	74.47153	21.27125
	median	2310.426	2937.246	2721.753	2981.649	2495.29	2881.776	2907.667	2590.287	2556.876	2794.682	2823.058	2655.568	2747.032
	rank	1	12	7	13	2	11	10	4	3	8	9	5	6
C17-F22	mean	3095.169	14196.49	11073.38	15228.71	6365.453	13188.11	13128.51	9326.867	9225.422	14779.99	11310.18	9944.648	9192.805
	best	2300	14033.76	9238.502	15114.45	3957.065	12798.56	12696.98	7576.304	8329.12	14295.42	11127.2	9372.921	5375.858
	worst	5480.678	14422.32	12439.08	15345.02	8916.005	13782.15	13512.81	10456.98	9653.614	15328.41	11476.98	10434.23	13124.4
	std	1730.112	177.7323	1594.41	114.417	3009.992	456.5786	364.2617	1347.328	657.65	520.0407	155.678	485.9433	4619.211
	median	2300	14164.93	11307.97	15227.68	6294.371	13085.86	13152.13	9637.091	9459.477	14748.06	11318.28	9985.72	9135.48
	rank	1	11	7	13	2	10	9	5	4	12	8	6	3
C17-F23	mean	2743.354	3724.426	3291.2	3786.62	2962.218	3661.4	3663.478	3043.413	3068.776	3282.921	4490.356	3361.173	3349.272
	best	2729.988	3651.404	3214.739	3763.304	2950.353	3480.618	3505.094	3003.293	2995.842	3209.205	4323.322	3297.887	3234.048
	worst	2752.657	3820.757	3357.126	3812.399	2977.75	3955.284	3762.599	3095.901	3199.533	3332.588	4647.288	3423.377	3462.453
	std	10.89685	79.31584	78.73805	23.68215	13.81755	243.1923	122.3033	49.32064	97.49427	57.4981	144.2477	66.24321	101.5076
	median	2745.387	3712.771	3296.468	3785.388	2960.385	3604.849	3693.109	3037.229	3039.864	3294.945	4495.408	3361.715	3350.294
	rank	1	11	6	12	2	9	10	3	4	5	13	8	7
C17-F24	mean	2919.043	4072.237	3498.98	4298.729	3131.011	3903.337	3759.355	3188.425	3240.714	3445.651	4213.279	3457.812	3623.196
	best	2909.046	3875.562	3400.823	3910.882	3099.847	3815.82	3660.966	3148.663	3151.149	3374.956	4177.74	3318.947	3583.166
	worst	2924.412	4533.876	3643.691	5273.47	3154.145	4020.03	3816.771	3213.778	3360.872	3486.057	4270.343	3588.304	3696.369
	std	7.423833	336.7661	112.0349	713.2005	29.28155	97.02285	75.51448	33.15498	95.74172	56.75356	47.40451	134.0236	54.55307
	median	2921.358	3939.754	3475.702	4005.282	3135.025	3888.748	3779.842	3195.629	3225.417	3460.796	4202.516	3461.998	3606.624
	rank	1	11	7	13	2	10	9	3	4	5	12	6	8
C17-F25	mean	2983.145	7736.397	3291.959	10470.34	3201.645	5609.915	4091.272	3190.91	3992.635	4270.928	4191.957	3245.437	4004.664
	best	2980.235	6497.419	3272.926	8548.133	3192.781	4694.464	3744.106	3168.794	3826.505	3882.895	3912.58	3196.721	3927.118
	worst	2991.831	8512.499	3340.567	11642.69	3223.01	6474.448	4354.968	3214.121	4148.014	4763.265	4721.396	3292.152	4093.46
	std	6.299384	975.905	35.37121	1587.925	15.55327	831.0924	281.0726	20.53635	182.5845	487.4691	412.5417	53.3023	74.3482
	median	2980.257	7967.836	3277.172	10845.26	3195.394	5635.374	4133.007	3190.361	3998.011	4218.777	4066.927	3246.438	3999.039
	rank	1	12	5	13	3	11	8	2	6	10	9	4	7
C17-F26	mean	3776.432	13205.47	10651.35	14013.71	4370.807	12005.93	12984.15	6393.223	6988.245	9622.975	11120.28	8309.269	9019.51
	best	3748.807	13022.2	10285.51	13559.53	4259.443	10277.96	12142.67	6044.941	6671.316	8969.807	10843.64	7757.049	7493.217
	worst	3793.643	13367.83	11084.66	14807.67	4530.472	12969.02	14457	6623.689	7302.684	10164.01	11506.39	8783.881	10932.4
	std	21.15984	165.6016	362.9509	598.9201	144.6035	1289.455	1101.72	287.1685	367.9791	555.7698	315.598	503.3726	1795.318
	median	3781.639	13215.92	10617.63	13843.83	4346.657	12388.36	12668.47	6452.131	6989.491	9679.043	11065.54	8348.074	8826.211
	rank	1	12	8	13	2	10	11	3	4	7	9	5	6
C17-F27	mean	3251.26	4632.85	3854.307	4788.267	3471.181	4559.232	4354.733	3453.597	3681.731	3838.248	7333.892	3686.23	4342.006
	best	3227.701	4328.511	3773.16	4436.845	3411.396	4002.067	3839.574	3377.73	3601.578	3720.803	7114.652	3426.734	4208.145
	worst	3313.631	4783.274	3949.134	5010.243	3595.186	4938.377	4869.363	3540.929	3764.048	3949.409	7587.147	3859.067	4503.043
	std	45.37533	233.1427	78.9762	290.4065	91.91125	457.6084	529.238	82.49883	89.95059	104.576	249.9642	216.5245	132.2133
	median	3231.854	4709.807	3847.468	4852.99	3439.071	4648.242	4354.998	3447.865	3680.649	3841.39	7316.884	3729.559	4328.418
	rank	1	11	7	12	3	10	9	2	4	6	13	5	8
C17-F28	mean	3258.849	7925.265	3711.316	9933.583	3513.464	6715.312	4719.398	3458.998	4375.884	5070.13	4915.08	3940.269	4898.891
	best	3258.849	7254.886	3587.253	8825.367	3426.931	5606.324	4162.72	3414.919	4097.004	4583.099	4875.165	3702.38	4686.733
	worst	3258.849	9693.952	3792.688	12723.47	3587.135	7876.996	4947.471	3498.231	4692.255	5556.052	4957.328	4360.403	5076.712
	std	0	1288.362	104.4625	2029.42	71.96829	1233.812	406.4701	42.95225	295.6242	432.1752	42.80497	313.9815	183.2972
	median	3258.849	7376.111	3732.663	9092.748	3519.895	6688.964	4883.7	3461.421	4357.138	5070.684	4913.914	3849.147	4916.06
	rank	1	12	4	13	3	11	7	2	6	10	9	5	8
C17-F29	mean	3263.038	12353.01	5686.251	17168.73	4529.902	6833.893	8592.371	5140.407	5171.216	6534.254	7882.215	5143.118	6217.421
	best	3247.132	8563.049	5585.325	9645.742	4033.354	6484.723	5966.858	4791.469	4837.655	5587.564	6811.608	4750.136	5769.616
	worst	3278.787	16324.7	5871.373	26271.47	4737.879	7445.224	11074.86	5640.57	5436.431	7527.257	9978.992	5380.845	6722.844
	std	18.99097	3941.317	143.3559	8087.715	361.9768	459.4859	2287.018	410.6392	320.8973	950.287	1608.105	296.6048	427.0937
	median	3263.116	12262.14	5644.153	16378.85	4674.188	6702.812	8663.883	5064.794	5205.39	6511.097	7369.13	5220.746	6188.612
	rank	1	12	6	13	2	9	11	3	5	8	10	4	7
C17-F30	mean	623575.2	2.68E+09	41437213	4.48E+09	25041630	1.37E+09	1.52E+08	80896757	1.37E+08	2.67E+08	1.73E+08	27601219	71121782
	best	582411.6	2.07E+09	27769756	2.75E+09	18070418	1.96E+08	1.04E+08	74219322	71683636	1.87E+08	1.45E+08	20098612	56637848
	worst	655637.4	3.64E+09	55051138	7.02E+09	32054014	2.75E+09	2.08E+08	85086201	1.98E+08	3.38E+08	2.27E+08	35355967	83831645
	std	35536.86	7.42E+08	15457701	2E+09	8620851	1.43E+09	57672201	5099895	70355384	67902860	40022492	8158633	12419998
	median	628125.9	2.51E+09	41463979	4.07E+09	25021044	1.27E+09	1.49E+08	82140752	1.39E+08	2.72E+08	1.61E+08	27475149	72008818
	rank	1	12	4	13	2	11	8	6	7	10	9	3	5
Sum rank		29	335	166	367	64	294	269	112	144	248	254	150	207
Mean rank		1	11.55172	5.724138	12.65517	2.206897	10.13793	9.275862	3.862069	4.965517	8.551724	8.758621	5.172414	7.137931
Total rank		1	12	6	13	2	11	10	3	4	8	9	5	7

Table 4. Optimization results for the CEC 2017 test suite (dimension=50).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	4.95E+10	1.1E+09	7.69E+10	1.1E+09	3.19E+10	7.32E+09	1.1E+09	8.66E+09	1.79E+10	1.5E+10	3.14E+09	9.51E+09
	best	100	4.41E+10	7.44E+08	6.72E+10	7.27E+08	2.99E+10	4.4E+09	7.27E+08	6.18E+09	1.23E+10	1.26E+10	2E+09	8.74E+09
	worst	100	5.34E+10	1.56E+09	8.44E+10	1.57E+09	3.39E+10	1.09E+10	1.56E+09	1.19E+10	2.42E+10	1.75E+10	3.92E+09	1.02E+10
	std	0	4.3E+09	3.84E+08	8.03E+09	3.94E+08	1.81E+09	3.29E+09	3.9E+08	2.6E+09	6.28E+09	2.21E+09	8.91E+08	8.27E+08
	median	100	5.02E+10	1.05E+09	7.8E+10	1.05E+09	3.19E+10	7.01E+09	1.05E+09	8.27E+09	1.75E+10	1.49E+10	3.33E+09	9.53E+09
	rank	1	12	4	13	3	11	6	2	7	10	9	5	8
C17-F3	mean	300	154396	144775.7	153921.7	40780	114495.5	215432.5	63673.5	131350.3	105750.1	170162.6	143305	239250.6
	best	300	130935.1	116840.9	136841.4	35610.86	98555.96	164738.1	50699.94	113358.5	82476.83	150986.5	113745.4	199886.3
	worst	300	183241.2	166548.8	164931.7	53012.54	129952.4	324443.8	82406.44	153841	116468.6	188356.6	174868.7	265767.6
	std	0	24150.2	22863.42	13140.4	8961.981	13976.42	82028.55	14810.16	18310.5	17163.84	22179.7	31567.13	30630.41
	median	300	151703.8	147856.6	156956.9	37248.3	114736.8	186273.9	60793.82	129100.9	112027.6	170653.7	142303	245674.3
	rank	1	10	8	9	2	5	12	3	6	4	11	7	13
C17-F4	mean	470.3679	12184.46	816.0011	19457.87	681.4135	6971.561	1820.302	707.3102	1412.912	2511.357	2728.976	1073.423	1485.133
	best	428.5127	9514.955	781.0024	12922.28	656.2968	5678.306	1207.196	644.4745	1114.656	1528.502	2319.866	803.94	1316.601
	worst	525.7252	13801.19	880.4744	23154.52	694.8483	8926.75	2130.731	812.7542	1716.417	4115.779	2931.851	1762.34	1589.352
	std	53.92841	2102.179	47.95718	5099.299	18.62806	1501.712	459.5216	79.82462	284.7839	1229.91	301.2068	501.5184	139.8851
	median	463.6168	12710.85	801.2638	20877.33	687.2544	6640.594	1971.641	686.0061	1410.286	2200.573	2832.093	863.7063	1517.289
	rank	1	12	4	13	2	11	8	3	6	9	10	5	7
C17-F5	mean	504.7261	1042.95	847.6477	1066.558	749.3764	1080.986	926.8785	751.4539	740.7157	961.5023	805.8724	792.0833	875.1166
	best	503.9798	1013.374	816.5437	1061.377	676.9687	962.7314	893.7665	685.5776	712.1028	921.1337	756.8901	741.5352	844.3322
	worst	505.9698	1069.044	891.1425	1071.499	811.096	1166.444	950.6786	852.7761	773.689	983.4193	841.0368	843.6933	899.9478
	std	1.036324	27.21731	35.00028	5.69125	60.73609	106.8864	28.21668	81.0711	32.96958	30.09048	42.06955	45.51418	26.82066
	median	504.4773	1044.692	841.4523	1066.678	754.7205	1097.383	931.5345	733.731	738.5355	970.7282	812.7815	791.5524	878.0932
	rank	1	11	7	12	3	13	9	4	2	10	6	5	8
C17-F6	mean	600	686.6786	658.5233	688.3462	619.2303	682.4414	688.8653	640.3977	628.4489	661.7716	656.7135	653.2132	649.1582
	best	600	683.956	653.561	686.3068	617.0439	667.7492	684.5972	631.1357	624.1073	650.8752	652.8177	650.715	637.678
	worst	600	689.5874	662.2555	692.3995	621.2137	694.7835	697.1782	661.4298	636.4458	667.6559	659.7741	657.7726	659.3786
	std	0	2.564667	4.113542	3.064662	2.433815	13.36965	6.255548	15.58106	6.01381	8.107078	3.221641	3.400265	10.15461
	median	600	686.5855	659.1383	687.3393	619.3317	683.6164	686.8428	634.5125	626.6213	664.2777	657.1311	652.1827	649.7881
	rank	1	11	8	12	2	10	13	4	3	9	7	6	5
C17-F7	mean	756.7298	1690.859	1588.857	1771.25	1075.378	1602.293	1622.731	1095.607	1105.13	1437.854	1383.321	1212.905	1299.674
	best	754.7543	1670.615	1528.091	1705.897	1030.508	1476.164	1568.636	1067.488	1087.362	1337.764	1248.408	1080.822	1236.369
	worst	758.3522	1717.492	1642.381	1851.318	1114.134	1723.89	1695.087	1120.156	1120.405	1488.694	1487.485	1401.47	1341.989
	std	1.689848	21.74419	52.67291	67.87609	42.83676	124.6629	63.58271	24.65415	15.78024	73.8405	118.2269	149.7953	51.14959
	median	756.9065	1687.665	1592.477	1763.893	1078.435	1604.558	1613.601	1097.392	1106.376	1462.479	1398.695	1184.664	1310.17
	rank	1	12	9	13	2	10	11	3	4	8	7	5	6
C17-F8	mean	805.721	1362.398	1124.105	1384.668	1032.391	1376.424	1285.685	1041.59	1051.264	1283.624	1136.983	1069.467	1231.684
	best	802.9849	1309.251	1084.806	1352.051	1005.624	1294.353	1170.851	1014.615	1021.474	1241.854	1129.802	1033.19	1203.054
	worst	810.9445	1401.525	1167.702	1400.527	1057.147	1488.554	1379.566	1102.659	1075.243	1333.975	1153.925	1115.698	1254.588
	std	3.890137	45.90234	46.06279	23.96893	27.67453	92.5422	93.65706	44.66053	27.00846	42.24419	12.44165	41.79212	23.26472
	median	804.4773	1369.408	1121.956	1393.047	1033.396	1361.394	1296.161	1024.543	1054.169	1279.333	1132.102	1064.49	1234.547
	rank	1	11	6	13	2	12	10	3	4	9	7	5	8
C17-F9	mean	900	32893	14489.41	33048.09	6476.341	34318.2	30367.44	19625.77	9331.297	23147.87	12386.16	12080.08	14096.86
	best	900	32012.24	14052.6	31573.96	5145.79	31605.69	28736.98	12085.61	8284.278	18375.71	11832.99	11289.35	12513.65
	worst	900	35391.89	15481.94	34309.71	7499.48	37659.76	34695.5	24942.59	10395.17	26861.39	12891.38	13421.7	15870.92
	std	1.01E-13	1813.192	724.5416	1351.066	1064.184	2774.951	3152.076	6649.26	999.4261	3827.95	610.4995	1090.988	1965.735
	median	900	32083.93	14211.56	33154.35	6630.047	34003.68	29018.63	20737.44	9322.868	23677.19	12410.14	11804.64	14001.44
	rank	1	11	7	12	2	13	10	8	3	9	5	4	6
C17-F10	mean	4347.157	12297.65	8533.281	13280.88	7089.713	11311.92	11318.18	7996.932	8807.23	13109.85	8753.29	8101.21	11254.8
	best	3555.132	11605.91	8403.143	12767.17	6333.566	10727.15	10020.91	6651.02	6939.843	12249.56	8402.124	7681.211	10764.36
	worst	5099.795	12872.86	8683.367	13570.06	7560.938	12147.75	12217.51	8843.609	13337.62	13918.05	9615.519	8869.181	12175.62
	std	701.4234	575.7262	146.9278	386.58	575.5683	711.9956	1022.132	1107.675	3313.016	821.9168	628.3406	571.2351	683.767
	median	4366.851	12355.92	8523.306	13393.14	7232.173	11186.4	11517.15	8246.549	7475.726	13135.89	8497.759	7927.225	11039.61
	rank	1	11	5	13	2	9	10	3	7	12	6	4	8
C17-F11	mean	1128.435	13254.8	2116.688	17775.28	1833.42	11266.11	4936.627	2086.933	5771.513	4949.467	12290.05	2170.136	20218.83
	best	1121.25	12087.39	1830.939	15713.24	1641.984	10172.69	4393.008	1852.248	3603.077	4503.232	11434.11	1889.802	11967.98
	worst	1133.132	13732.8	2422.918	19153.88	2233.299	13218.48	6347.39	2506.348	9794.399	5791.665	13632.1	2324.625	26693.06
	std	5.92135	849.4603	263.3627	1631.104	301.5769	1486.826	1028.431	319.4048	3105.372	641.2799	1031.46	214.7852	6643.792
	median	1129.678	13599.51	2106.447	18117	1729.199	10836.65	4503.056	1994.568	4844.288	4751.485	12046.99	2233.059	21107.15
	rank	1	11	4	12	2	9	6	3	8	7	10	5	13
C17-F12	mean	2905.102	3.54E+10	2.11E+08	5.78E+10	1.63E+08	2.11E+10	1.22E+09	2.15E+08	9.26E+08	4.24E+09	1.91E+09	1.45E+09	3.17E+08
	best	2527.376	2.98E+10	1.1E+08	4.22E+10	95831759	8.91E+09	9.68E+08	1.51E+08	2.07E+08	2.5E+09	7.26E+08	2.09E+08	2.26E+08
	worst	3168.37	4.24E+10	2.66E+08	7.91E+10	2.11E+08	3.54E+10	1.6E+09	2.53E+08	1.64E+09	8.22E+09	3.24E+09	3.84E+09	3.86E+08
	std	297.7638	6.2E+09	74870996	1.85E+10	53591181	1.19E+10	2.98E+08	51817338	7.64E+08	2.94E+09	1.13E+09	1.85E+09	73242431
	median	2962.331	3.48E+10	2.33E+08	5.49E+10	1.73E+08	2E+10	1.16E+09	2.29E+08	9.3E+08	3.12E+09	1.83E+09	8.76E+08	3.27E+08
	rank	1	12	3	13	2	11	7	4	6	10	9	8	5
C17-F13	mean	1340.1	1.99E+10	29140050	3.49E+10	29032641	8.19E+09	1.06E+08	29214686	3.18E+08	5.03E+08	44018606	4.15E+08	62625395
	best	1333.781	1.15E+10	15082176	1.76E+10	14999822	4.36E+09	72744405	15106499	1.46E+08	4.04E+08	15009940	15025904	36890666
	worst	1343.015	2.72E+10	64128728	5.02E+10	64116553	1.27E+10	1.46E+08	64286770	7.91E+08	6.67E+08	73484293	9.95E+08	1.03E+08
	std	4.658645	7.5E+09	25452500	1.49E+10	25520623	3.84E+09	32892364	25514545	3.43E+08	1.27E+08	33816482	5.06E+08	31425996
	median	1341.801	2.05E+10	18674648	3.59E+10	18507094	7.85E+09	1.02E+08	18732738	1.68E+08	4.7E+08	43790095	3.26E+08	55307580
	rank	1	12	3	13	2	11	7	4	8	10	5	9	6
C17-F14	mean	1429.458	21419208	1382812	39595412	393518.5	2568787	4254329	546854.7	1325055	1093309	12662683	857145.1	9473280
	best	1425.995	7220942	751383.8	12376432	326677.5	927699.9	3772080	450691.6	398040.1	930817.6	3226584	519753.6	4821344
	worst	1431.939	41607808	2712100	79818751	447530.2	3898450	5035760	625505.6	2244600	1255133	20593207	1069999	16073840
	std	2.851678	15781750	977068.1	31202565	67876.67	1342318	593266.1	78710.78	820976.9	196648.1	8552318	256936.7	5172877
	median	1429.95	18424041	1033882	33093232	399933.1	2724500	4104737	555610.7	1328791	1093643	13415470	919413.9	8498968
	rank	1	12	7	13	2	8	9	3	6	5	11	4	10
C17-F15	mean	1530.66	2.11E+09	1057529	3.39E+09	1028580	1.38E+09	9064409	1125076	5846302	58192649	1.61E+08	1035542	7974295
	best	1526.359	1.5E+09	129732.7	2.65E+09	74782.39	4.76E+08	813893.6	219713.3	107340.5	34902841	783143	90330.99	4244923
	worst	1532.953	2.77E+09	1909492	4.02E+09	1886011	3.01E+09	16390082	1924768	14578094	75179730	6.21E+08	1886309	15151372
	std	3.191893	6.5E+08	837170.9	6.59E+08	851654.6	1.28E+09	7569081	814458.4	6721675	18326818	3.34E+08	845990.3	5405843
	median	1531.664	2.09E+09	1095445	3.45E+09	1076763	1.02E+09	9526831	1177912	4349887	61344012	11307332	1082764	6250442
	rank	1	12	4	13	2	11	8	5	6	9	10	3	7
C17-F16	mean	2062.891	5865.586	4302.479	6920.014	3004.84	4535.478	5224.679	3470.57	3468.218	4456.184	3979.612	3481.424	3945.63
	best	1728.6	5246.472	4000.657	5435.58	2856.044	4127.203	4325.669	3337.527	3065.361	4182.74	3763.431	3124.763	3496.144
	worst	2242.663	7192.11	4702.332	9876.553	3131.765	4763.08	5825.538	3649.578	4004.577	4750.92	4288.477	3769.133	4355.434
	std	253.3831	995.1847	351.5548	2208.632	142.48	304.3711	722.4993	169.7208	491.0068	257.8711	261.4972	359.8899	439.383
	median	2140.15	5511.882	4253.462	6183.962	3015.775	4625.815	5373.755	3447.587	3401.466	4445.538	3933.271	3515.9	3965.471
	rank	1	12	8	13	2	10	11	4	3	9	7	5	6
C17-F17	mean	2021.151	6848.083	3556.425	9629.557	2746.348	3879.805	4346.813	3161.055	3078.243	4035.004	3768.66	3388.37	3577.713
	best	1900.43	5301.597	3126.73	7139.453	2620.494	3174.823	3897.119	2645.258	2947.105	3448.757	3433.271	3161.766	3422.149
	worst	2138.267	8279.961	3984.3	12346.15	2826.921	4287.61	4563.699	3597.312	3336.306	4343.917	4016.635	3694.363	3711.093
	std	146.025	1337.246	433.6566	2332.841	96.16517	530.519	333.5717	430.4672	198.7397	441.2389	265.75	274.7319	152.2354
	median	2022.954	6905.386	3557.334	9516.314	2768.989	4028.394	4463.216	3200.825	3014.781	4173.671	3812.368	3348.676	3588.805
	rank	1	12	6	13	2	9	11	4	3	10	8	5	7
C17-F18	mean	1830.62	64809056	5394677	94478124	3461290	31856563	40065124	5580678	8080372	10088485	10257555	4108187	11118482
	best	1822.239	53686283	3034887	46889386	963105.3	3514353	10878963	2221244	1894241	5532501	4183491	1244859	5015440
	worst	1841.673	74629822	8158394	1.27E+08	5983500	87143499	72254917	7349171	13443774	15199380	18698186	6398631	23037213
	std	8.860434	9422472	2461765	43284200	2456575	41161815	32747100	2581672	5815218	4557307	7084462	2492722	8998228
	median	1829.285	65460058	5192714	1.02E+08	3449276	18384199	38563309	6376148	8491736	9811030	9074271	4394628	8210638
	rank	1	12	4	13	2	10	11	5	6	7	8	3	9
C17-F19	mean	1925.185	2.21E+09	1054101	3.11E+09	845238.3	2.17E+09	6390103	4998182	1786352	41942343	1209978	1162654	1647542
	best	1924.437	1.05E+09	738624.6	2.1E+09	479903.4	8519676	1312499	3754874	1053878	35483791	688976.4	480615.3	1335633
	worst	1926.121	3.69E+09	1666936	3.85E+09	1480789	6.33E+09	14551966	5976860	2928702	52668431	2282084	1928568	2108001
	std	0.860892	1.21E+09	452664.5	8.47E+08	486851.6	3.08E+09	6201332	1091078	873486.8	8248080	794827.7	687967.2	368268.7
	median	1925.091	2.05E+09	905421.7	3.25E+09	710130.5	1.17E+09	4847973	5130496	1581415	39808575	934426.5	1120716	1573266
	rank	1	12	3	13	2	11	9	8	7	10	5	4	6
C17-F20	mean	2160.172	3717.027	3260.069	3934.224	2768.725	3397.451	3653.399	3271.387	2739.715	3674.026	3889.794	3278.828	3180.586
	best	2104.423	3399.714	2780.017	3661.976	2495.224	2984.482	3366.909	3075.111	2531.75	3598.109	3661.096	2973.788	3082.251
	worst	2323.891	3876.484	3706.835	4075.833	3025.157	3574.253	4142.691	3678.268	2912.856	3770.385	4143.729	3435.552	3297.711
	std	118.748	236.1103	422.9268	202.4307	240.6307	301.4758	371.4289	305.6783	211.1036	81.05394	215.029	225.3384	96.41896
	median	2106.186	3795.955	3276.712	3999.544	2777.259	3515.536	3551.997	3166.085	2757.128	3663.805	3877.175	3352.986	3171.19
	rank	1	11	5	13	3	8	9	6	2	10	12	7	4
C17-F21	mean	2314.895	2937.035	2744.131	2968.401	2494.788	2908.633	2901.223	2595.904	2553.318	2798.183	2814.628	2665.284	2739.49
	best	2309.045	2907.981	2635.865	2873.81	2470.541	2833.317	2798.883	2564.953	2499.752	2771.335	2768.232	2597.611	2711.195
	worst	2329.683	2965.668	2897.153	3036.496	2518.032	3037.663	2990.677	2638.091	2599.768	2832.034	2844.164	2752.389	2752.7
	std	10.75568	30.30095	119.9531	82.1574	25.9814	97.40959	88.69152	37.28297	45.20868	31.1184	37.98088	74.47153	21.27125
	median	2310.426	2937.246	2721.753	2981.649	2495.29	2881.776	2907.667	2590.287	2556.876	2794.682	2823.058	2655.568	2747.032
	rank	1	12	7	13	2	11	10	4	3	8	9	5	6
C17-F22	mean	3095.169	14196.49	11073.38	15228.71	6365.453	13188.11	13128.51	9326.867	9225.422	14779.99	11310.18	9944.648	9192.805
	best	2300	14033.76	9238.502	15114.45	3957.065	12798.56	12696.98	7576.304	8329.12	14295.42	11127.2	9372.921	5375.858
	worst	5480.678	14422.32	12439.08	15345.02	8916.005	13782.15	13512.81	10456.98	9653.614	15328.41	11476.98	10434.23	13124.4
	std	1730.112	177.7323	1594.41	114.417	3009.992	456.5786	364.2617	1347.328	657.65	520.0407	155.678	485.9433	4619.211
	median	2300	14164.93	11307.97	15227.68	6294.371	13085.86	13152.13	9637.091	9459.477	14748.06	11318.28	9985.72	9135.48
	rank	1	11	7	13	2	10	9	5	4	12	8	6	3
C17-F23	mean	2743.354	3724.426	3291.2	3786.62	2962.218	3661.4	3663.478	3043.413	3068.776	3282.921	4490.356	3361.173	3349.272
	best	2729.988	3651.404	3214.739	3763.304	2950.353	3480.618	3505.094	3003.293	2995.842	3209.205	4323.322	3297.887	3234.048
	worst	2752.657	3820.757	3357.126	3812.399	2977.75	3955.284	3762.599	3095.901	3199.533	3332.588	4647.288	3423.377	3462.453
	std	10.89685	79.31584	78.73805	23.68215	13.81755	243.1923	122.3033	49.32064	97.49427	57.4981	144.2477	66.24321	101.5076
	median	2745.387	3712.771	3296.468	3785.388	2960.385	3604.849	3693.109	3037.229	3039.864	3294.945	4495.408	3361.715	3350.294
	rank	1	11	6	12	2	9	10	3	4	5	13	8	7
C17-F24	mean	2919.043	4072.237	3498.98	4298.729	3131.011	3903.337	3759.355	3188.425	3240.714	3445.651	4213.279	3457.812	3623.196
	best	2909.046	3875.562	3400.823	3910.882	3099.847	3815.82	3660.966	3148.663	3151.149	3374.956	4177.74	3318.947	3583.166
	worst	2924.412	4533.876	3643.691	5273.47	3154.145	4020.03	3816.771	3213.778	3360.872	3486.057	4270.343	3588.304	3696.369
	std	7.423833	336.7661	112.0349	713.2005	29.28155	97.02285	75.51448	33.15498	95.74172	56.75356	47.40451	134.0236	54.55307
	median	2921.358	3939.754	3475.702	4005.282	3135.025	3888.748	3779.842	3195.629	3225.417	3460.796	4202.516	3461.998	3606.624
	rank	1	11	7	13	2	10	9	3	4	5	12	6	8
C17-F25	mean	2983.145	7736.397	3291.959	10470.34	3201.645	5609.915	4091.272	3190.91	3992.635	4270.928	4191.957	3245.437	4004.664
	best	2980.235	6497.419	3272.926	8548.133	3192.781	4694.464	3744.106	3168.794	3826.505	3882.895	3912.58	3196.721	3927.118
	worst	2991.831	8512.499	3340.567	11642.69	3223.01	6474.448	4354.968	3214.121	4148.014	4763.265	4721.396	3292.152	4093.46
	std	6.299384	975.905	35.37121	1587.925	15.55327	831.0924	281.0726	20.53635	182.5845	487.4691	412.5417	53.3023	74.3482
	median	2980.257	7967.836	3277.172	10845.26	3195.394	5635.374	4133.007	3190.361	3998.011	4218.777	4066.927	3246.438	3999.039
	rank	1	12	5	13	3	11	8	2	6	10	9	4	7
C17-F26	mean	3776.432	13205.47	10651.35	14013.71	4370.807	12005.93	12984.15	6393.223	6988.245	9622.975	11120.28	8309.269	9019.51
	best	3748.807	13022.2	10285.51	13559.53	4259.443	10277.96	12142.67	6044.941	6671.316	8969.807	10843.64	7757.049	7493.217
	worst	3793.643	13367.83	11084.66	14807.67	4530.472	12969.02	14457	6623.689	7302.684	10164.01	11506.39	8783.881	10932.4
	std	21.15984	165.6016	362.9509	598.9201	144.6035	1289.455	1101.72	287.1685	367.9791	555.7698	315.598	503.3726	1795.318
	median	3781.639	13215.92	10617.63	13843.83	4346.657	12388.36	12668.47	6452.131	6989.491	9679.043	11065.54	8348.074	8826.211
	rank	1	12	8	13	2	10	11	3	4	7	9	5	6
C17-F27	mean	3251.26	4632.85	3854.307	4788.267	3471.181	4559.232	4354.733	3453.597	3681.731	3838.248	7333.892	3686.23	4342.006
	best	3227.701	4328.511	3773.16	4436.845	3411.396	4002.067	3839.574	3377.73	3601.578	3720.803	7114.652	3426.734	4208.145
	worst	3313.631	4783.274	3949.134	5010.243	3595.186	4938.377	4869.363	3540.929	3764.048	3949.409	7587.147	3859.067	4503.043
	std	45.37533	233.1427	78.9762	290.4065	91.91125	457.6084	529.238	82.49883	89.95059	104.576	249.9642	216.5245	132.2133
	median	3231.854	4709.807	3847.468	4852.99	3439.071	4648.242	4354.998	3447.865	3680.649	3841.39	7316.884	3729.559	4328.418
	rank	1	11	7	12	3	10	9	2	4	6	13	5	8
C17-F28	mean	3258.849	7925.265	3711.316	9933.583	3513.464	6715.312	4719.398	3458.998	4375.884	5070.13	4915.08	3940.269	4898.891
	best	3258.849	7254.886	3587.253	8825.367	3426.931	5606.324	4162.72	3414.919	4097.004	4583.099	4875.165	3702.38	4686.733
	worst	3258.849	9693.952	3792.688	12723.47	3587.135	7876.996	4947.471	3498.231	4692.255	5556.052	4957.328	4360.403	5076.712
	std	0	1288.362	104.4625	2029.42	71.96829	1233.812	406.4701	42.95225	295.6242	432.1752	42.80497	313.9815	183.2972
	median	3258.849	7376.111	3732.663	9092.748	3519.895	6688.964	4883.7	3461.421	4357.138	5070.684	4913.914	3849.147	4916.06
	rank	1	12	4	13	3	11	7	2	6	10	9	5	8
C17-F29	mean	3263.038	12353.01	5686.251	17168.73	4529.902	6833.893	8592.371	5140.407	5171.216	6534.254	7882.215	5143.118	6217.421
	best	3247.132	8563.049	5585.325	9645.742	4033.354	6484.723	5966.858	4791.469	4837.655	5587.564	6811.608	4750.136	5769.616
	worst	3278.787	16324.7	5871.373	26271.47	4737.879	7445.224	11074.86	5640.57	5436.431	7527.257	9978.992	5380.845	6722.844
	std	18.99097	3941.317	143.3559	8087.715	361.9768	459.4859	2287.018	410.6392	320.8973	950.287	1608.105	296.6048	427.0937
	median	3263.116	12262.14	5644.153	16378.85	4674.188	6702.812	8663.883	5064.794	5205.39	6511.097	7369.13	5220.746	6188.612
	rank	1	12	6	13	2	9	11	3	5	8	10	4	7
C17-F30	mean	623575.2	2.68E+09	41437213	4.48E+09	25041630	1.37E+09	1.52E+08	80896757	1.37E+08	2.67E+08	1.73E+08	27601219	71121782
	best	582411.6	2.07E+09	27769756	2.75E+09	18070418	1.96E+08	1.04E+08	74219322	71683636	1.87E+08	1.45E+08	20098612	56637848
	worst	655637.4	3.64E+09	55051138	7.02E+09	32054014	2.75E+09	2.08E+08	85086201	1.98E+08	3.38E+08	2.27E+08	35355967	83831645
	std	35536.86	7.42E+08	15457701	2E+09	8620851	1.43E+09	57672201	5099895	70355384	67902860	40022492	8158633	12419998
	median	628125.9	2.51E+09	41463979	4.07E+09	25021044	1.27E+09	1.49E+08	82140752	1.39E+08	2.72E+08	1.61E+08	27475149	72008818
	rank	1	12	4	13	2	11	8	6	7	10	9	3	5
Sum rank		29	335	166	367	64	294	269	112	144	248	254	150	207
Mean rank		1	11.55172	5.724138	12.65517	2.206897	10.13793	9.275862	3.862069	4.965517	8.551724	8.758621	5.172414	7.137931
Total rank		1	12	6	13	2	11	10	3	4	8	9	5	7

Table 5. Optimization results for the CEC 2017 test suite (dimension=100).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	1.43E+11	1.08E+10	1.97E+11	8.12E+09	1.1E+11	5.85E+10	7.75E+09	5.4E+10	8.16E+10	1.18E+11	2.39E+10	5.32E+10
	best	100	1.39E+11	9.2E+09	1.93E+11	7.8E+09	9.72E+10	5.6E+10	7.33E+09	4.78E+10	7.83E+10	1.09E+11	1.86E+10	5.07E+10
	worst	100	1.47E+11	1.17E+10	1.98E+11	8.44E+09	1.22E+11	6.46E+10	8.01E+09	6.04E+10	8.93E+10	1.26E+11	3E+10	5.93E+10
	std	1.26E-14	3.33E+09	1.2E+09	2.32E+09	2.95E+08	1.13E+10	4.45E+09	3.29E+08	6.58E+09	5.64E+09	7.69E+09	6.54E+09	4.49E+09
	median	100	1.43E+11	1.11E+10	1.97E+11	8.12E+09	1.1E+11	5.68E+10	7.84E+09	5.39E+10	7.94E+10	1.19E+11	2.36E+10	5.13E+10
	rank	1	12	4	13	3	10	8	2	7	9	11	5	6
C17-F3	mean	300	451046.4	368624.4	365517.8	232072.1	398693.7	743396.8	481715.7	402444.6	344084.1	382345.2	542289.3	571803.4
	best	300	415657.7	356641.4	358496.6	197477.5	335586	659039.2	411984.4	371309.4	334398.3	366869.9	431473.7	548010.5
	worst	300	472183.2	379770.7	375732.1	264148.4	434715.5	849656.6	561323.9	435992.9	353420.3	413817.3	713381.9	592229.4
	std	0	26725.61	11798.75	8201.517	29932.45	47632.7	87812.76	78194.62	37769.45	9748.12	23163.56	140245.3	22448.33
	median	300	458172.3	369042.8	363921.3	233331.1	412236.5	732445.6	476777.3	401238	344258.9	374346.9	512150.8	573486.7
	rank	1	9	5	4	2	7	13	10	8	3	6	11	12
C17-F4	mean	602.1722	37102.42	2294.782	61849.41	1860.959	13996.28	9894.146	1651.801	4652.86	9732.592	28652.08	3038.059	8489.017
	best	592.0676	34057.31	2222.33	55989.75	1747.744	9497.259	8411.188	1489.046	3643.242	9152.241	23151.2	2402.387	8054.664
	worst	612.2769	40612.43	2456.32	68829.08	2111.872	18424.71	10795.7	1796.243	6628.828	10596.27	32270.17	3595.684	9110.992
	std	12.6933	3069.679	118.0367	5770.233	183.6471	3997.274	1120.559	151.4474	1458.355	712.2235	4838.803	559.3681	545.0467
	median	602.1722	36869.97	2250.238	61289.4	1792.109	14031.57	10184.85	1660.957	4169.685	9590.929	29593.49	3077.083	8395.206
	rank	1	12	4	13	3	10	9	2	6	8	11	5	7
C17-F5	mean	512.9345	1849.015	1309.375	1824.647	1238.466	1971.239	1726.6	1246.823	1204.711	1754.424	1326.904	1388.776	1522.935
	best	510.9445	1832.77	1289.071	1803.544	1131.464	1947.724	1643.663	1148.939	1148.666	1721.95	1294.324	1302.797	1395.175
	worst	514.9244	1870.179	1328.839	1841.719	1305.988	1989.255	1864.962	1320.012	1260.571	1772.504	1365.707	1521.331	1592.194
	std	1.976192	16.92763	17.72822	20.77925	86.88884	19.45261	104.9591	81.19712	51.05139	25.62091	40.07086	107.2337	101.0663
	median	512.9345	1846.556	1309.794	1826.662	1258.205	1973.989	1698.887	1259.17	1204.804	1761.622	1323.792	1365.488	1552.185
	rank	1	12	5	11	3	13	9	4	2	10	6	7	8
C17-F6	mean	600	697.5095	662.3688	696.1405	643.0508	701.1107	695.5302	672.4315	645.3117	677.6633	664.0424	662.021	663.3134
	best	600	696.1278	658.7847	693.2983	639.655	692.4216	687.4218	668.1534	641.1509	670.4929	661.6138	657.3741	657.2851
	worst	600	699.3058	665.2544	697.9734	647.9631	707.6217	710.2691	677.0231	651.3684	682.915	668.4325	666.2978	667.3333
	std	0	1.631232	2.911396	2.22489	3.938934	8.091524	11.21622	4.256612	4.847844	6.14604	3.298814	4.844511	5.252931
	median	600	697.3022	662.718	696.6452	642.2925	702.1997	692.2149	672.2748	644.3637	678.6226	663.0617	662.2061	664.3176
	rank	1	12	5	11	2	13	10	8	3	9	7	4	6
C17-F7	mean	811.392	3337.98	2919.302	3429.704	1942.299	3200.316	3315.168	2072.342	2084.564	2932.351	2952.401	2442.358	2519.737
	best	810.0205	3273.163	2799.475	3361.862	1902.705	3052.784	3213.368	1937.963	1941.242	2821.94	2855.288	2225.082	2434.182
	worst	813.1726	3425.951	3019.773	3485.678	2001.302	3341.383	3461.669	2176.892	2199.832	3020.888	3118.909	2541.185	2701.024
	std	1.589565	69.39864	124.7716	60.37223	48.67643	138.8142	121.2854	108.0829	116.4936	90.17365	125.5836	160.9562	133.1111
	median	811.1874	3326.404	2928.979	3435.638	1932.594	3203.548	3292.818	2087.257	2098.591	2943.287	2917.703	2501.582	2471.871
	rank	1	12	7	13	2	10	11	3	4	8	9	5	6
C17-F8	mean	812.437	2252.668	1715.54	2295.784	1474.727	2234.763	2171.736	1493.381	1541.767	2120.39	1785.009	1690.75	1946.815
	best	808.9546	2197.101	1655.867	2260.803	1322.369	2174.674	1995.986	1381.774	1442.764	2078.187	1703.036	1642.296	1889.142
	worst	816.9143	2309.409	1761.054	2321.314	1582.188	2312.968	2316.634	1660.906	1661.656	2146.659	1897.294	1789.432	1996.681
	std	3.697116	57.91902	50.78528	28.75944	119.2271	65.34701	176.6718	129.1747	112.1691	32.29819	97.20606	73.37746	55.76106
	median	811.9395	2252.081	1722.619	2300.51	1497.175	2225.705	2187.161	1465.421	1531.323	2128.358	1769.854	1665.636	1950.719
	rank	1	12	6	13	2	11	10	3	4	9	7	5	8
C17-F9	mean	900	81161.25	31377.83	71098.2	28205.81	104895.4	70717.55	56988.28	38781.24	68886.9	29093.76	36368.58	46627.7
	best	900	72932.37	29130.49	68926.32	26834.05	87246.36	56948.01	49058.87	27898.07	66269.65	28722.56	31733.83	42824.19
	worst	900	93336.1	33573.27	73976.47	29759.44	129436.5	87584.54	64582.54	48245.72	71162.38	29674.14	40523.97	50515.68
	std	1.01E-13	9596.367	1978.602	2384.171	1320.54	19311.19	16529.67	6912.151	10531.96	2224	445.1952	4050.232	3576.52
	median	900	79188.26	31403.77	70745.01	28114.87	101449.4	69168.83	57155.85	39490.59	69057.79	28989.17	36608.26	46585.46
	rank	1	12	4	11	2	13	10	8	6	9	3	5	7
C17-F10	mean	11023.04	27933.01	16622.37	28980.38	14973.69	27214.57	26392.24	17428.73	16007.78	28988.01	17613.36	17493.08	24630.72
	best	9625.608	27652.61	14618.74	28225	14364.8	26729.76	25708.76	16870.74	15072.66	27952.24	16173.88	16144.07	24175.53
	worst	11858.81	28262.62	18379.39	29449.1	15732.57	27910.52	27595.69	17906.53	16426.6	29843	18375.97	18473.24	25158.41
	std	1054.018	288.4128	1802.248	596.7115	630.0595	594.7952	937.4496	490.4926	688.4886	853.3036	1123.417	1062.368	440.9406
	median	11303.87	27908.4	16745.67	29123.71	14898.69	27108.99	26132.26	17468.83	16265.92	29078.4	17951.79	17677.52	24594.46
	rank	1	11	4	12	2	10	9	5	3	13	7	6	8
C17-F11	mean	1162.329	149568	69828.1	182882.2	22716.4	70817.28	184408.9	22555.74	88145.51	75900.56	156108.1	60242.48	129524.6
	best	1139.568	114846.1	59194.46	138888.4	17131.19	50522.8	110432.1	16618.66	70952.41	68433.09	127769.2	32235.93	109653.7
	worst	1220.662	167720.5	77624.56	247784	30456.36	95455.46	293732.2	30619.61	95127.79	86110.74	181252.7	111381.2	173704.3
	std	42.46663	26735.73	9010.771	51903.2	7078.385	20170.86	93192.7	7101.506	12544.43	8046.173	25401.83	38324.65	32735.39
	median	1144.542	157852.8	71246.7	172428.1	21639.03	68645.43	166735.7	21492.35	93250.92	74529.21	157705.3	48676.38	117370.1
	rank	1	10	5	12	3	6	13	2	8	7	11	4	9
C17-F12	mean	5974.805	8.54E+10	2.1E+09	1.38E+11	1.78E+09	4.67E+10	1.21E+10	1.84E+09	1.07E+10	1.9E+10	5.47E+10	9.59E+09	1.14E+10
	best	5383.905	6.1E+10	1.85E+09	1.03E+11	1.61E+09	2.46E+10	9.94E+09	1.61E+09	7.66E+09	1.51E+10	4.77E+10	2.41E+09	1.04E+10
	worst	6570.199	9.51E+10	2.4E+09	1.6E+11	2.06E+09	7.67E+10	1.38E+10	2.1E+09	1.27E+10	2.54E+10	6.43E+10	1.67E+10	1.3E+10
	std	537.9317	1.77E+10	2.75E+08	2.82E+10	2.15E+08	2.37E+10	1.76E+09	2.21E+08	2.32E+09	5.01E+09	7.55E+09	7.1E+09	1.21E+09
	median	5972.559	9.27E+10	2.07E+09	1.44E+11	1.72E+09	4.28E+10	1.22E+10	1.82E+09	1.12E+10	1.77E+10	5.33E+10	9.64E+09	1.11E+10
	rank	1	12	4	13	2	10	8	3	6	9	11	5	7
C17-F13	mean	1407.28	2.22E+10	92705799	3.4E+10	92704726	1.71E+10	5.08E+08	92909190	8.46E+08	2.33E+09	7.03E+09	1.5E+09	2.32E+08
	best	1371.145	1.94E+10	35778021	2.63E+10	35755981	1.23E+10	3.37E+08	35985369	1.15E+08	1.6E+09	4.47E+09	3.52E+08	1.96E+08
	worst	1439.935	2.46E+10	1.98E+08	3.85E+10	1.98E+08	2.04E+10	7.01E+08	1.98E+08	2.19E+09	2.8E+09	8.95E+09	2.57E+09	3.15E+08
	std	37.80433	2.94E+09	79765863	6.11E+09	79848507	3.75E+09	1.91E+08	79806622	1.05E+09	6.28E+08	2.04E+09	1.22E+09	60812858
	median	1409.02	2.25E+10	68676712	3.56E+10	68624578	1.78E+10	4.97E+08	68850376	5.4E+08	2.47E+09	7.36E+09	1.53E+09	2.08E+08
	rank	1	12	3	13	2	11	6	4	7	9	10	8	5
C17-F14	mean	1467.509	37877947	7030862	65154615	1789028	8800333	13302701	4132558	9375532	12792370	10872498	2365705	10080431
	best	1458.803	32644101	4836376	59274295	1451673	4633128	8085077	2137713	6252979	9660718	8670929	1724020	6088320
	worst	1472.733	42717300	10230438	70853221	2449331	15229629	18266273	5754127	13910468	15767450	16160007	2961405	13934641
	std	6.576739	4963041	2644356	6244886	502925	4923552	4527378	1623783	3621921	3171801	3856890	735855.9	3656357
	median	1469.25	38075194	6528317	65245472	1627554	7669288	13429726	4319195	8669341	12870655	9329528	2388697	10149383
	rank	1	12	5	13	2	6	11	4	7	10	9	3	8
C17-F15	mean	1609.893	1.23E+10	36148098	1.88E+10	36125523	9.64E+09	91903589	36181669	4.35E+08	9.85E+08	1.02E+09	3.02E+08	46185681
	best	1551.154	1.14E+10	4620645	1.34E+10	4600463	2.97E+08	35638382	4652118	30734893	3.22E+08	4.01E+08	4596634	11063176
	worst	1652.294	1.38E+10	98030172	2.34E+10	98018720	1.8E+10	1.38E+08	98121965	1.29E+09	2.06E+09	1.31E+09	1.15E+09	1.06E+08
	std	48.04352	1.13E+09	46426465	5.4E+09	46426649	8.37E+09	58260804	46461525	6.35E+08	8.24E+08	4.65E+08	6.13E+08	44890477
	median	1618.063	1.2E+10	20970788	1.92E+10	20941454	1.01E+10	97112930	20976297	2.08E+08	7.81E+08	1.19E+09	27775652	34071994
	rank	1	12	3	13	2	11	6	4	8	9	10	7	5
C17-F16	mean	2711.795	16956.42	7552.816	19908.63	6270.614	13471.55	14803.2	7124.848	6730.714	11026.59	10677.43	7035.656	10268.09
	best	2171.69	16007.51	6709.001	16133.46	5919.695	11490.42	12128.13	6250.449	6032.372	10331.36	9600.774	6791.042	9538.753
	worst	3397.326	17485.94	8251.32	22115.6	6491.927	15887.83	16307.44	7634.981	7341.49	11961.13	12131.25	7278.783	11023.86
	std	554.7769	716.5046	741.4654	2883.213	269.5269	1972.259	2042.204	673.9321	689.516	758.3312	1324.658	243.6691	798.3217
	median	2639.081	17166.11	7625.471	20692.72	6335.418	13253.97	15388.61	7306.98	6774.497	10906.93	10488.85	7036.4	10254.87
	rank	1	12	6	13	2	10	11	5	3	9	8	4	7
C17-F17	mean	2716.564	3365610	6430.282	6619405	5476.521	176124.7	15353.45	5732.037	6159.788	8742.176	38771.89	6632.116	7475.817
	best	2275.021	987545.6	5834.403	1795159	4954.032	9823.899	9680.716	4946.827	5222.365	8212.171	26862.3	6275.044	7169.382
	worst	3429.127	7655924	7244.689	15230014	6446.831	464683.5	25617.31	6831.876	8313.246	9720.505	61502.54	7427.666	8170.364
	std	559.6669	3419822	734.3657	6876178	720.5443	216152.4	7812.729	915.3856	1590.62	727.9721	16885.01	585.2986	513.0574
	median	2581.054	2409486	6321.018	4726223	5252.611	114995.7	13057.88	5574.723	5551.77	8518.013	33361.35	6412.876	7281.761
	rank	1	12	5	13	2	11	9	3	4	8	10	6	7
C17-F18	mean	1903.746	48321455	4006624	83925434	1946085	13642201	11330387	5674461	10499161	14680584	11134106	6893096	6574933
	best	1881.15	22849837	2969936	33647437	1493217	6725159	8873986	4057958	3911427	11373385	6174512	5013791	5644819
	worst	1919.921	85359823	5004943	1.51E+08	2403941	25438717	13611211	8329885	16395523	20018055	21997169	9149896	9243974
	std	21.08244	28950727	1089465	53911503	406115.7	9242429	2391759	2032840	5588730	4133768	8093266	2379436	1936009
	median	1906.955	42538079	4025808	75327659	1943590	11202463	11418175	5155001	10844848	13665447	8182372	6704350	5705468
	rank	1	12	3	13	2	10	9	4	7	11	8	6	5
C17-F19	mean	1972.839	1.02E+10	34605426	1.79E+10	32532429	4.06E+09	1.39E+08	45583318	3.2E+08	5.66E+08	1.29E+09	2.47E+08	42519521
	best	1967.139	9.03E+09	6396950	1.31E+10	5896170	1.82E+09	47932771	13260051	8310619	2.68E+08	2.32E+08	57827018	12977414
	worst	1977.869	1.19E+10	83541290	2.22E+10	81285149	8.08E+09	2.2E+08	1.02E+08	9.46E+08	1.31E+09	2.39E+09	5.47E+08	86450536
	std	4.935585	1.44E+09	38700445	4.09E+09	38678074	3.02E+09	1E+08	45816907	4.77E+08	5.43E+08	1.16E+09	2.52E+08	35326744
	median	1973.174	9.88E+09	24241732	1.81E+10	21474198	3.17E+09	1.44E+08	33367906	1.63E+08	3.44E+08	1.28E+09	1.93E+08	35325068
	rank	1	12	3	13	2	11	6	5	8	9	10	7	4
C17-F20	mean	3192.04	7067.911	6178.745	7270.696	4831.952	6861.097	6871.169	5886.822	6097.235	7035.009	6294.737	5534.794	6255.772
	best	2806.762	6963.225	5892.118	7085.342	4728.794	6409.075	6520.18	5543.496	5010.259	6435.384	5937.328	4965.732	5814.332
	worst	3662.121	7223.823	6433.779	7349.966	4907.249	7493.326	7093.428	6345.297	6851.618	7341.828	6529.328	6242.25	6668.691
	std	477.9749	120.9072	250.015	136.2455	81.48558	504.9362	283.8104	364.0394	986.9628	448.3479	301.3688	582.4701	423.2851
	median	3149.639	7042.298	6194.542	7323.739	4845.883	6770.993	6935.534	5829.248	6263.532	7181.413	6356.147	5465.597	6270.032
	rank	1	12	6	13	2	9	10	4	5	11	8	3	7
C17-F21	mean	2342.155	4107.347	3613.51	4206.109	2948.993	3975.75	4057.837	3271.189	3062.898	3646.286	4448.096	3546.05	3415.095
	best	2338.689	4048.41	3454.946	4155.703	2891.822	3858.2	3795.254	3214.039	2995.281	3527.922	4000.757	3406.32	3384.779
	worst	2346.015	4175.581	3735.804	4230.58	2988.511	4065.745	4255.801	3374.645	3117.728	3772.276	4785.364	3842.932	3433.946
	std	3.664912	63.42392	130.1479	37.98541	44.35334	115.5379	224.8005	79.25473	57.21167	112.4554	358.8079	219.8794	24.2828
	median	2341.959	4102.699	3631.645	4219.077	2957.82	3989.527	4090.147	3248.037	3069.292	3642.474	4503.132	3467.473	3420.827
	rank	1	11	7	12	2	9	10	4	3	8	13	6	5
C17-F22	mean	11739	29898.52	20723.87	31226.03	19479.55	29094.17	27786.26	18352.58	23181.46	31127.91	21446.15	22056.4	27515.54
	best	11119.08	29779.68	19403.39	30624.66	18073.66	28753.28	27172.83	17200.8	19021.39	30932.2	20641.6	20699.52	26594.62
	worst	12601.6	30072.48	22835.22	31555.68	20746.51	29671.42	28448.76	18827.71	32749.7	31322.09	22254.89	23255.43	27954.62
	std	710.0872	137.6461	1642.807	467.8853	1327.767	434.0159	650.6848	838.5643	7057.712	191.0211	717.5738	1310.133	676.3022
	median	11617.67	29870.95	20328.44	31361.88	19549.01	28975.99	27761.73	18690.91	20477.36	31128.68	21444.07	22135.31	27756.46
	rank	1	11	4	13	3	10	9	2	7	12	5	6	8
C17-F23	mean	2877.697	5083.185	4099.507	5084.927	3445.26	5180.355	4933.073	3596.027	3703.763	4180.782	7139.788	4708.375	4222.911
	best	2872.107	4880.681	4031.935	4869.153	3436.297	4562.197	4813.676	3523.051	3678.968	4138.966	6660.243	4287.196	4166.74
	worst	2884.013	5319.135	4165.456	5253.542	3467.429	6012.232	5051.596	3689.202	3738.927	4242.374	7478.419	4936.314	4277.171
	std	5.674312	214.7523	68.13705	173.2897	16.22498	705.6868	124.5086	75.93265	31.57676	47.59334	402.3209	316.4086	66.44188
	median	2877.334	5066.461	4100.319	5108.507	3438.657	5073.495	4933.51	3585.927	3698.579	4170.894	7210.245	4804.994	4223.866
	rank	1	10	5	11	2	12	9	3	4	6	13	8	7
C17-F24	mean	3327.407	7832.289	5280.149	9428.317	3940.217	6330.598	6094.752	4144.531	4408.258	4778.634	9682.62	5755.812	5282.543
	best	3295.518	6318.452	5072.135	6625.419	3871.199	5942.583	5721.691	4099.353	4184.416	4636.807	9162.84	5499.274	5178.783
	worst	3357.991	8916.686	5398.615	11283.6	4042.393	6565.008	6665.087	4204.902	4608.176	4977.78	11047.88	6114.686	5432.351
	std	32.22323	1339.285	161.2017	2472.511	78.98107	298.5116	449.4729	47.99135	244.0951	156.4488	992.5122	315.6741	117.0508
	median	3328.059	8047.008	5324.923	9902.123	3923.637	6407.401	5996.115	4136.935	4420.219	4749.974	9259.878	5704.645	5259.52
	rank	1	11	6	12	2	10	9	3	4	5	13	8	7
C17-F25	mean	3185.232	13441.03	4443.825	18340.92	4076.777	9566.79	7002.676	3852.339	6297.608	8299.907	10017.95	4444.685	7475.466
	best	3137.371	12788.33	4148.351	17065.23	3981.421	9083.304	6454.379	3818.204	6150.753	7347.374	9371.909	4238.015	6853.024
	worst	3261.571	14882.91	4781.288	21161.43	4160.817	9890.5	7363.442	3920.764	6674.264	9619.146	11213.94	4749.399	8116.028
	std	65.17161	1063.367	283.5038	2099.322	84.54413	392.097	441.8134	51.57319	273.7552	1151.349	898.1687	256.0706	702.2793
	median	3170.992	13046.44	4422.831	17568.52	4082.435	9646.678	7096.442	3835.193	6182.708	8116.554	9742.967	4395.662	7466.406
	rank	1	12	4	13	3	10	7	2	6	9	11	5	8
C17-F26	mean	5757.621	35939.59	23924.36	40742.7	13415.09	30933.67	31440.72	13583.9	17645.72	23303.5	31361.56	20750.51	22604.74
	best	5645.905	35548.93	21519.99	38728.13	12678.8	30094.95	28449.35	12535.81	16023.04	19694.71	30412.4	19056.98	21134.85
	worst	5844.642	36256.6	26144.4	41924.66	14210.3	31631.99	34028.09	15434.23	18791.4	27827.19	32752.15	22281.77	23407.49
	std	91.29453	325.3611	2174.656	1641.219	742.9473	694.5191	2975.907	1383.242	1311.335	3658.25	1108.06	1527.681	1120.315
	median	5769.969	35976.42	24016.53	41159	13385.62	31003.87	31642.73	13182.78	17884.23	22846.05	31140.83	20831.64	22938.31
	rank	1	12	8	13	2	9	11	3	4	7	10	5	6
C17-F27	mean	3309.493	8431.434	4245.826	10830.78	3735.776	6225.732	5741.618	3808.567	4180.276	4380.606	12263.89	4174.087	5319.714
	best	3278.01	7287.439	4130.044	8379.161	3696.869	6036.76	5126.757	3737.831	4066.466	4114.816	11941.21	3968.903	5067.482
	worst	3344.5	9603.069	4440.188	13398.73	3788.708	6487.562	6434.152	3851.909	4346.426	4779.704	12543.36	4380.956	5598.337
	std	30.85754	1373.966	153.5838	2948.229	50.38312	211.3833	761.9438	56.95285	148.3301	307.8837	297.9776	213.8605	240.7252
	median	3307.732	8417.614	4206.535	10772.62	3728.764	6189.302	5702.781	3822.264	4154.107	4313.953	12285.49	4173.246	5306.519
	rank	1	11	6	12	2	10	9	3	5	7	13	4	8
C17-F28	mean	3322.242	18427.35	5290.668	24374.42	4531.476	14208.35	9888.159	4277.979	8992.637	10535.78	16722.64	7673.922	10790.4
	best	3318.742	17179.28	5187.751	21860.15	4306.165	11382.88	8533.639	4163.251	7759.643	8466.624	14500.96	5548.003	9922.928
	worst	3327.816	20738.38	5348.282	27509.58	4695.913	16434.78	10751.85	4402.695	10785.38	12427.83	18227.73	10992.5	11860.48
	std	4.767125	1774.959	81.43107	2583.4	180.0406	2558.827	1038.94	128.0624	1399.433	1944.961	1727.46	2645.011	1057.399
	median	3321.205	17895.86	5313.32	24063.98	4561.913	14507.86	10133.57	4272.986	8712.762	10624.33	17080.94	7077.593	10689.1
	rank	1	12	4	13	3	10	7	2	6	8	11	5	9
C17-F29	mean	4450.696	150667.3	9925.685	284879.7	7708.141	17070.72	15531.35	9164.636	8858.751	12194.96	22326.86	9135.355	11715.06
	best	4169.151	86958.94	9107.309	154059.3	6882.332	13623.67	13145.33	8445.7	8560.049	11341.48	18688.33	8732.014	11418.94
	worst	4829.521	204859.3	10389.87	394703.9	8233.202	21287.32	17715.52	9910.691	9331.518	12617.52	28480.41	9708.153	11992.34
	std	307.1569	54599.95	611.7269	111549.6	630.288	3496.398	2416.324	662.3035	360.0082	647.0171	4882.893	491.2947	258.21
	median	4402.056	155425.5	10102.78	295377.8	7858.514	16685.93	15632.28	9151.076	8771.719	12410.43	21069.36	9050.626	11724.48
	rank	1	12	6	13	2	10	9	5	3	8	11	4	7
C17-F30	mean	5407.166	1.89E+10	2.43E+08	3.07E+10	2.24E+08	1.1E+10	1.43E+09	3.03E+08	1.7E+09	3.28E+09	6.16E+09	7.09E+08	7.58E+08
	best	5337.48	1.67E+10	1.49E+08	2.87E+10	1.38E+08	6.83E+09	1.13E+09	2.17E+08	7.43E+08	1.4E+09	4.47E+09	2.53E+08	6.84E+08
	worst	5557.155	2.05E+10	2.86E+08	3.31E+10	2.68E+08	1.37E+10	1.91E+09	3.61E+08	2.19E+09	5.8E+09	7.43E+09	1.78E+09	8.33E+08
	std	110.0477	1.76E+09	68900930	2.04E+09	63226580	3.23E+09	3.63E+08	72223274	7.11E+08	2.43E+09	1.37E+09	7.81E+08	88084792
	median	5367.014	1.93E+10	2.68E+08	3.05E+10	2.45E+08	1.18E+10	1.35E+09	3.18E+08	1.94E+09	2.96E+09	6.36E+09	4.02E+08	7.57E+08
	rank	1	12	3	13	2	11	7	4	8	9	10	5	6
Sum rank		29	336	140	355	65	293	265	114	156	249	272	162	203
Mean rank		1	11.58621	4.827586	12.24138	2.241379	10.10345	9.137931	3.931034	5.37931	8.586207	9.37931	5.586207	7
Total rank		1	12	4	13	2	11	9	3	5	8	10	6	7

Table 5. Optimization results for the CEC 2017 test suite (dimension=100).

		OOA	WSO	AVOA	RSA	MPA	TSA	WOA	MVO	GWO	TLBO	GSA	PSO	GA
C17-F1	mean	100	1.43E+11	1.08E+10	1.97E+11	8.12E+09	1.1E+11	5.85E+10	7.75E+09	5.4E+10	8.16E+10	1.18E+11	2.39E+10	5.32E+10
	best	100	1.39E+11	9.2E+09	1.93E+11	7.8E+09	9.72E+10	5.6E+10	7.33E+09	4.78E+10	7.83E+10	1.09E+11	1.86E+10	5.07E+10
	worst	100	1.47E+11	1.17E+10	1.98E+11	8.44E+09	1.22E+11	6.46E+10	8.01E+09	6.04E+10	8.93E+10	1.26E+11	3E+10	5.93E+10
	std	1.26E-14	3.33E+09	1.2E+09	2.32E+09	2.95E+08	1.13E+10	4.45E+09	3.29E+08	6.58E+09	5.64E+09	7.69E+09	6.54E+09	4.49E+09
	median	100	1.43E+11	1.11E+10	1.97E+11	8.12E+09	1.1E+11	5.68E+10	7.84E+09	5.39E+10	7.94E+10	1.19E+11	2.36E+10	5.13E+10
	rank	1	12	4	13	3	10	8	2	7	9	11	5	6
C17-F3	mean	300	451046.4	368624.4	365517.8	232072.1	398693.7	743396.8	481715.7	402444.6	344084.1	382345.2	542289.3	571803.4
	best	300	415657.7	356641.4	358496.6	197477.5	335586	659039.2	411984.4	371309.4	334398.3	366869.9	431473.7	548010.5
	worst	300	472183.2	379770.7	375732.1	264148.4	434715.5	849656.6	561323.9	435992.9	353420.3	413817.3	713381.9	592229.4
	std	0	26725.61	11798.75	8201.517	29932.45	47632.7	87812.76	78194.62	37769.45	9748.12	23163.56	140245.3	22448.33
	median	300	458172.3	369042.8	363921.3	233331.1	412236.5	732445.6	476777.3	401238	344258.9	374346.9	512150.8	573486.7
	rank	1	9	5	4	2	7	13	10	8	3	6	11	12
C17-F4	mean	602.1722	37102.42	2294.782	61849.41	1860.959	13996.28	9894.146	1651.801	4652.86	9732.592	28652.08	3038.059	8489.017
	best	592.0676	34057.31	2222.33	55989.75	1747.744	9497.259	8411.188	1489.046	3643.242	9152.241	23151.2	2402.387	8054.664
	worst	612.2769	40612.43	2456.32	68829.08	2111.872	18424.71	10795.7	1796.243	6628.828	10596.27	32270.17	3595.684	9110.992
	std	12.6933	3069.679	118.0367	5770.233	183.6471	3997.274	1120.559	151.4474	1458.355	712.2235	4838.803	559.3681	545.0467
	median	602.1722	36869.97	2250.238	61289.4	1792.109	14031.57	10184.85	1660.957	4169.685	9590.929	29593.49	3077.083	8395.206
	rank	1	12	4	13	3	10	9	2	6	8	11	5	7
C17-F5	mean	512.9345	1849.015	1309.375	1824.647	1238.466	1971.239	1726.6	1246.823	1204.711	1754.424	1326.904	1388.776	1522.935
	best	510.9445	1832.77	1289.071	1803.544	1131.464	1947.724	1643.663	1148.939	1148.666	1721.95	1294.324	1302.797	1395.175
	worst	514.9244	1870.179	1328.839	1841.719	1305.988	1989.255	1864.962	1320.012	1260.571	1772.504	1365.707	1521.331	1592.194
	std	1.976192	16.92763	17.72822	20.77925	86.88884	19.45261	104.9591	81.19712	51.05139	25.62091	40.07086	107.2337	101.0663
	median	512.9345	1846.556	1309.794	1826.662	1258.205	1973.989	1698.887	1259.17	1204.804	1761.622	1323.792	1365.488	1552.185
	rank	1	12	5	11	3	13	9	4	2	10	6	7	8
C17-F6	mean	600	697.5095	662.3688	696.1405	643.0508	701.1107	695.5302	672.4315	645.3117	677.6633	664.0424	662.021	663.3134
	best	600	696.1278	658.7847	693.2983	639.655	692.4216	687.4218	668.1534	641.1509	670.4929	661.6138	657.3741	657.2851
	worst	600	699.3058	665.2544	697.9734	647.9631	707.6217	710.2691	677.0231	651.3684	682.915	668.4325	666.2978	667.3333
	std	0	1.631232	2.911396	2.22489	3.938934	8.091524	11.21622	4.256612	4.847844	6.14604	3.298814	4.844511	5.252931
	median	600	697.3022	662.718	696.6452	642.2925	702.1997	692.2149	672.2748	644.3637	678.6226	663.0617	662.2061	664.3176
	rank	1	12	5	11	2	13	10	8	3	9	7	4	6
C17-F7	mean	811.392	3337.98	2919.302	3429.704	1942.299	3200.316	3315.168	2072.342	2084.564	2932.351	2952.401	2442.358	2519.737
	best	810.0205	3273.163	2799.475	3361.862	1902.705	3052.784	3213.368	1937.963	1941.242	2821.94	2855.288	2225.082	2434.182
	worst	813.1726	3425.951	3019.773	3485.678	2001.302	3341.383	3461.669	2176.892	2199.832	3020.888	3118.909	2541.185	2701.024
	std	1.589565	69.39864	124.7716	60.37223	48.67643	138.8142	121.2854	108.0829	116.4936	90.17365	125.5836	160.9562	133.1111
	median	811.1874	3326.404	2928.979	3435.638	1932.594	3203.548	3292.818	2087.257	2098.591	2943.287	2917.703	2501.582	2471.871
	rank	1	12	7	13	2	10	11	3	4	8	9	5	6
C17-F8	mean	812.437	2252.668	1715.54	2295.784	1474.727	2234.763	2171.736	1493.381	1541.767	2120.39	1785.009	1690.75	1946.815
	best	808.9546	2197.101	1655.867	2260.803	1322.369	2174.674	1995.986	1381.774	1442.764	2078.187	1703.036	1642.296	1889.142
	worst	816.9143	2309.409	1761.054	2321.314	1582.188	2312.968	2316.634	1660.906	1661.656	2146.659	1897.294	1789.432	1996.681
	std	3.697116	57.91902	50.78528	28.75944	119.2271	65.34701	176.6718	129.1747	112.1691	32.29819	97.20606	73.37746	55.76106
	median	811.9395	2252.081	1722.619	2300.51	1497.175	2225.705	2187.161	1465.421	1531.323	2128.358	1769.854	1665.636	1950.719
	rank	1	12	6	13	2	11	10	3	4	9	7	5	8
C17-F9	mean	900	81161.25	31377.83	71098.2	28205.81	104895.4	70717.55	56988.28	38781.24	68886.9	29093.76	36368.58	46627.7
	best	900	72932.37	29130.49	68926.32	26834.05	87246.36	56948.01	49058.87	27898.07	66269.65	28722.56	31733.83	42824.19
	worst	900	93336.1	33573.27	73976.47	29759.44	129436.5	87584.54	64582.54	48245.72	71162.38	29674.14	40523.97	50515.68
	std	1.01E-13	9596.367	1978.602	2384.171	1320.54	19311.19	16529.67	6912.151	10531.96	2224	445.1952	4050.232	3576.52
	median	900	79188.26	31403.77	70745.01	28114.87	101449.4	69168.83	57155.85	39490.59	69057.79	28989.17	36608.26	46585.46
	rank	1	12	4	11	2	13	10	8	6	9	3	5	7
C17-F10	mean	11023.04	27933.01	16622.37	28980.38	14973.69	27214.57	26392.24	17428.73	16007.78	28988.01	17613.36	17493.08	24630.72
	best	9625.608	27652.61	14618.74	28225	14364.8	26729.76	25708.76	16870.74	15072.66	27952.24	16173.88	16144.07	24175.53
	worst	11858.81	28262.62	18379.39	29449.1	15732.57	27910.52	27595.69	17906.53	16426.6	29843	18375.97	18473.24	25158.41
	std	1054.018	288.4128	1802.248	596.7115	630.0595	594.7952	937.4496	490.4926	688.4886	853.3036	1123.417	1062.368	440.9406
	median	11303.87	27908.4	16745.67	29123.71	14898.69	27108.99	26132.26	17468.83	16265.92	29078.4	17951.79	17677.52	24594.46
	rank	1	11	4	12	2	10	9	5	3	13	7	6	8
C17-F11	mean	1162.329	149568	69828.1	182882.2	22716.4	70817.28	184408.9	22555.74	88145.51	75900.56	156108.1	60242.48	129524.6
	best	1139.568	114846.1	59194.46	138888.4	17131.19	50522.8	110432.1	16618.66	70952.41	68433.09	127769.2	32235.93	109653.7
	worst	1220.662	167720.5	77624.56	247784	30456.36	95455.46	293732.2	30619.61	95127.79	86110.74	181252.7	111381.2	173704.3
	std	42.46663	26735.73	9010.771	51903.2	7078.385	20170.86	93192.7	7101.506	12544.43	8046.173	25401.83	38324.65	32735.39
	median	1144.542	157852.8	71246.7	172428.1	21639.03	68645.43	166735.7	21492.35	93250.92	74529.21	157705.3	48676.38	117370.1
	rank	1	10	5	12	3	6	13	2	8	7	11	4	9
C17-F12	mean	5974.805	8.54E+10	2.1E+09	1.38E+11	1.78E+09	4.67E+10	1.21E+10	1.84E+09	1.07E+10	1.9E+10	5.47E+10	9.59E+09	1.14E+10
	best	5383.905	6.1E+10	1.85E+09	1.03E+11	1.61E+09	2.46E+10	9.94E+09	1.61E+09	7.66E+09	1.51E+10	4.77E+10	2.41E+09	1.04E+10
	worst	6570.199	9.51E+10	2.4E+09	1.6E+11	2.06E+09	7.67E+10	1.38E+10	2.1E+09	1.27E+10	2.54E+10	6.43E+10	1.67E+10	1.3E+10
	std	537.9317	1.77E+10	2.75E+08	2.82E+10	2.15E+08	2.37E+10	1.76E+09	2.21E+08	2.32E+09	5.01E+09	7.55E+09	7.1E+09	1.21E+09
	median	5972.559	9.27E+10	2.07E+09	1.44E+11	1.72E+09	4.28E+10	1.22E+10	1.82E+09	1.12E+10	1.77E+10	5.33E+10	9.64E+09	1.11E+10
	rank	1	12	4	13	2	10	8	3	6	9	11	5	7
C17-F13	mean	1407.28	2.22E+10	92705799	3.4E+10	92704726	1.71E+10	5.08E+08	92909190	8.46E+08	2.33E+09	7.03E+09	1.5E+09	2.32E+08
	best	1371.145	1.94E+10	35778021	2.63E+10	35755981	1.23E+10	3.37E+08	35985369	1.15E+08	1.6E+09	4.47E+09	3.52E+08	1.96E+08
	worst	1439.935	2.46E+10	1.98E+08	3.85E+10	1.98E+08	2.04E+10	7.01E+08	1.98E+08	2.19E+09	2.8E+09	8.95E+09	2.57E+09	3.15E+08
	std	37.80433	2.94E+09	79765863	6.11E+09	79848507	3.75E+09	1.91E+08	79806622	1.05E+09	6.28E+08	2.04E+09	1.22E+09	60812858
	median	1409.02	2.25E+10	68676712	3.56E+10	68624578	1.78E+10	4.97E+08	68850376	5.4E+08	2.47E+09	7.36E+09	1.53E+09	2.08E+08
	rank	1	12	3	13	2	11	6	4	7	9	10	8	5
C17-F14	mean	1467.509	37877947	7030862	65154615	1789028	8800333	13302701	4132558	9375532	12792370	10872498	2365705	10080431
	best	1458.803	32644101	4836376	59274295	1451673	4633128	8085077	2137713	6252979	9660718	8670929	1724020	6088320
	worst	1472.733	42717300	10230438	70853221	2449331	15229629	18266273	5754127	13910468	15767450	16160007	2961405	13934641
	std	6.576739	4963041	2644356	6244886	502925	4923552	4527378	1623783	3621921	3171801	3856890	735855.9	3656357
	median	1469.25	38075194	6528317	65245472	1627554	7669288	13429726	4319195	8669341	12870655	9329528	2388697	10149383
	rank	1	12	5	13	2	6	11	4	7	10	9	3	8
C17-F15	mean	1609.893	1.23E+10	36148098	1.88E+10	36125523	9.64E+09	91903589	36181669	4.35E+08	9.85E+08	1.02E+09	3.02E+08	46185681
	best	1551.154	1.14E+10	4620645	1.34E+10	4600463	2.97E+08	35638382	4652118	30734893	3.22E+08	4.01E+08	4596634	11063176
	worst	1652.294	1.38E+10	98030172	2.34E+10	98018720	1.8E+10	1.38E+08	98121965	1.29E+09	2.06E+09	1.31E+09	1.15E+09	1.06E+08
	std	48.04352	1.13E+09	46426465	5.4E+09	46426649	8.37E+09	58260804	46461525	6.35E+08	8.24E+08	4.65E+08	6.13E+08	44890477
	median	1618.063	1.2E+10	20970788	1.92E+10	20941454	1.01E+10	97112930	20976297	2.08E+08	7.81E+08	1.19E+09	27775652	34071994
	rank	1	12	3	13	2	11	6	4	8	9	10	7	5
C17-F16	mean	2711.795	16956.42	7552.816	19908.63	6270.614	13471.55	14803.2	7124.848	6730.714	11026.59	10677.43	7035.656	10268.09
	best	2171.69	16007.51	6709.001	16133.46	5919.695	11490.42	12128.13	6250.449	6032.372	10331.36	9600.774	6791.042	9538.753
	worst	3397.326	17485.94	8251.32	22115.6	6491.927	15887.83	16307.44	7634.981	7341.49	11961.13	12131.25	7278.783	11023.86
	std	554.7769	716.5046	741.4654	2883.213	269.5269	1972.259	2042.204	673.9321	689.516	758.3312	1324.658	243.6691	798.3217
	median	2639.081	17166.11	7625.471	20692.72	6335.418	13253.97	15388.61	7306.98	6774.497	10906.93	10488.85	7036.4	10254.87
	rank	1	12	6	13	2	10	11	5	3	9	8	4	7
C17-F17	mean	2716.564	3365610	6430.282	6619405	5476.521	176124.7	15353.45	5732.037	6159.788	8742.176	38771.89	6632.116	7475.817
	best	2275.021	987545.6	5834.403	1795159	4954.032	9823.899	9680.716	4946.827	5222.365	8212.171	26862.3	6275.044	7169.382
	worst	3429.127	7655924	7244.689	15230014	6446.831	464683.5	25617.31	6831.876	8313.246	9720.505	61502.54	7427.666	8170.364
	std	559.6669	3419822	734.3657	6876178	720.5443	216152.4	7812.729	915.3856	1590.62	727.9721	16885.01	585.2986	513.0574
	median	2581.054	2409486	6321.018	4726223	5252.611	114995.7	13057.88	5574.723	5551.77	8518.013	33361.35	6412.876	7281.761
	rank	1	12	5	13	2	11	9	3	4	8	10	6	7
C17-F18	mean	1903.746	48321455	4006624	83925434	1946085	13642201	11330387	5674461	10499161	14680584	11134106	6893096	6574933
	best	1881.15	22849837	2969936	33647437	1493217	6725159	8873986	4057958	3911427	11373385	6174512	5013791	5644819
	worst	1919.921	85359823	5004943	1.51E+08	2403941	25438717	13611211	8329885	16395523	20018055	21997169	9149896	9243974
	std	21.08244	28950727	1089465	53911503	406115.7	9242429	2391759	2032840	5588730	4133768	8093266	2379436	1936009
	median	1906.955	42538079	4025808	75327659	1943590	11202463	11418175	5155001	10844848	13665447	8182372	6704350	5705468
	rank	1	12	3	13	2	10	9	4	7	11	8	6	5
C17-F19	mean	1972.839	1.02E+10	34605426	1.79E+10	32532429	4.06E+09	1.39E+08	45583318	3.2E+08	5.66E+08	1.29E+09	2.47E+08	42519521
	best	1967.139	9.03E+09	6396950	1.31E+10	5896170	1.82E+09	47932771	13260051	8310619	2.68E+08	2.32E+08	57827018	12977414
	worst	1977.869	1.19E+10	83541290	2.22E+10	81285149	8.08E+09	2.2E+08	1.02E+08	9.46E+08	1.31E+09	2.39E+09	5.47E+08	86450536
	std	4.935585	1.44E+09	38700445	4.09E+09	38678074	3.02E+09	1E+08	45816907	4.77E+08	5.43E+08	1.16E+09	2.52E+08	35326744
	median	1973.174	9.88E+09	24241732	1.81E+10	21474198	3.17E+09	1.44E+08	33367906	1.63E+08	3.44E+08	1.28E+09	1.93E+08	35325068
	rank	1	12	3	13	2	11	6	5	8	9	10	7	4
C17-F20	mean	3192.04	7067.911	6178.745	7270.696	4831.952	6861.097	6871.169	5886.822	6097.235	7035.009	6294.737	5534.794	6255.772
	best	2806.762	6963.225	5892.118	7085.342	4728.794	6409.075	6520.18	5543.496	5010.259	6435.384	5937.328	4965.732	5814.332
	worst	3662.121	7223.823	6433.779	7349.966	4907.249	7493.326	7093.428	6345.297	6851.618	7341.828	6529.328	6242.25	6668.691
	std	477.9749	120.9072	250.015	136.2455	81.48558	504.9362	283.8104	364.0394	986.9628	448.3479	301.3688	582.4701	423.2851
	median	3149.639	7042.298	6194.542	7323.739	4845.883	6770.993	6935.534	5829.248	6263.532	7181.413	6356.147	5465.597	6270.032
	rank	1	12	6	13	2	9	10	4	5	11	8	3	7
C17-F21	mean	2342.155	4107.347	3613.51	4206.109	2948.993	3975.75	4057.837	3271.189	3062.898	3646.286	4448.096	3546.05	3415.095
	best	2338.689	4048.41	3454.946	4155.703	2891.822	3858.2	3795.254	3214.039	2995.281	3527.922	4000.757	3406.32	3384.779
	worst	2346.015	4175.581	3735.804	4230.58	2988.511	4065.745	4255.801	3374.645	3117.728	3772.276	4785.364	3842.932	3433.946
	std	3.664912	63.42392	130.1479	37.98541	44.35334	115.5379	224.8005	79.25473	57.21167	112.4554	358.8079	219.8794	24.2828
	median	2341.959	4102.699	3631.645	4219.077	2957.82	3989.527	4090.147	3248.037	3069.292	3642.474	4503.132	3467.473	3420.827
	rank	1	11	7	12	2	9	10	4	3	8	13	6	5
C17-F22	mean	11739	29898.52	20723.87	31226.03	19479.55	29094.17	27786.26	18352.58	23181.46	31127.91	21446.15	22056.4	27515.54
	best	11119.08	29779.68	19403.39	30624.66	18073.66	28753.28	27172.83	17200.8	19021.39	30932.2	20641.6	20699.52	26594.62
	worst	12601.6	30072.48	22835.22	31555.68	20746.51	29671.42	28448.76	18827.71	32749.7	31322.09	22254.89	23255.43	27954.62
	std	710.0872	137.6461	1642.807	467.8853	1327.767	434.0159	650.6848	838.5643	7057.712	191.0211	717.5738	1310.133	676.3022
	median	11617.67	29870.95	20328.44	31361.88	19549.01	28975.99	27761.73	18690.91	20477.36	31128.68	21444.07	22135.31	27756.46
	rank	1	11	4	13	3	10	9	2	7	12	5	6	8
C17-F23	mean	2877.697	5083.185	4099.507	5084.927	3445.26	5180.355	4933.073	3596.027	3703.763	4180.782	7139.788	4708.375	4222.911
	best	2872.107	4880.681	4031.935	4869.153	3436.297	4562.197	4813.676	3523.051	3678.968	4138.966	6660.243	4287.196	4166.74
	worst	2884.013	5319.135	4165.456	5253.542	3467.429	6012.232	5051.596	3689.202	3738.927	4242.374	7478.419	4936.314	4277.171
	std	5.674312	214.7523	68.13705	173.2897	16.22498	705.6868	124.5086	75.93265	31.57676	47.59334	402.3209	316.4086	66.44188
	median	2877.334	5066.461	4100.319	5108.507	3438.657	5073.495	4933.51	3585.927	3698.579	4170.894	7210.245	4804.994	4223.866
	rank	1	10	5	11	2	12	9	3	4	6	13	8	7
C17-F24	mean	3327.407	7832.289	5280.149	9428.317	3940.217	6330.598	6094.752	4144.531	4408.258	4778.634	9682.62	5755.812	5282.543
	best	3295.518	6318.452	5072.135	6625.419	3871.199	5942.583	5721.691	4099.353	4184.416	4636.807	9162.84	5499.274	5178.783
	worst	3357.991	8916.686	5398.615	11283.6	4042.393	6565.008	6665.087	4204.902	4608.176	4977.78	11047.88	6114.686	5432.351
	std	32.22323	1339.285	161.2017	2472.511	78.98107	298.5116	449.4729	47.99135	244.0951	156.4488	992.5122	315.6741	117.0508
	median	3328.059	8047.008	5324.923	9902.123	3923.637	6407.401	5996.115	4136.935	4420.219	4749.974	9259.878	5704.645	5259.52
	rank	1	11	6	12	2	10	9	3	4	5	13	8	7
C17-F25	mean	3185.232	13441.03	4443.825	18340.92	4076.777	9566.79	7002.676	3852.339	6297.608	8299.907	10017.95	4444.685	7475.466
	best	3137.371	12788.33	4148.351	17065.23	3981.421	9083.304	6454.379	3818.204	6150.753	7347.374	9371.909	4238.015	6853.024
	worst	3261.571	14882.91	4781.288	21161.43	4160.817	9890.5	7363.442	3920.764	6674.264	9619.146	11213.94	4749.399	8116.028
	std	65.17161	1063.367	283.5038	2099.322	84.54413	392.097	441.8134	51.57319	273.7552	1151.349	898.1687	256.0706	702.2793
	median	3170.992	13046.44	4422.831	17568.52	4082.435	9646.678	7096.442	3835.193	6182.708	8116.554	9742.967	4395.662	7466.406
	rank	1	12	4	13	3	10	7	2	6	9	11	5	8
C17-F26	mean	5757.621	35939.59	23924.36	40742.7	13415.09	30933.67	31440.72	13583.9	17645.72	23303.5	31361.56	20750.51	22604.74
	best	5645.905	35548.93	21519.99	38728.13	12678.8	30094.95	28449.35	12535.81	16023.04	19694.71	30412.4	19056.98	21134.85
	worst	5844.642	36256.6	26144.4	41924.66	14210.3	31631.99	34028.09	15434.23	18791.4	27827.19	32752.15	22281.77	23407.49
	std	91.29453	325.3611	2174.656	1641.219	742.9473	694.5191	2975.907	1383.242	1311.335	3658.25	1108.06	1527.681	1120.315
	median	5769.969	35976.42	24016.53	41159	13385.62	31003.87	31642.73	13182.78	17884.23	22846.05	31140.83	20831.64	22938.31
	rank	1	12	8	13	2	9	11	3	4	7	10	5	6
C17-F27	mean	3309.493	8431.434	4245.826	10830.78	3735.776	6225.732	5741.618	3808.567	4180.276	4380.606	12263.89	4174.087	5319.714
	best	3278.01	7287.439	4130.044	8379.161	3696.869	6036.76	5126.757	3737.831	4066.466	4114.816	11941.21	3968.903	5067.482
	worst	3344.5	9603.069	4440.188	13398.73	3788.708	6487.562	6434.152	3851.909	4346.426	4779.704	12543.36	4380.956	5598.337
	std	30.85754	1373.966	153.5838	2948.229	50.38312	211.3833	761.9438	56.95285	148.3301	307.8837	297.9776	213.8605	240.7252
	median	3307.732	8417.614	4206.535	10772.62	3728.764	6189.302	5702.781	3822.264	4154.107	4313.953	12285.49	4173.246	5306.519
	rank	1	11	6	12	2	10	9	3	5	7	13	4	8
C17-F28	mean	3322.242	18427.35	5290.668	24374.42	4531.476	14208.35	9888.159	4277.979	8992.637	10535.78	16722.64	7673.922	10790.4
	best	3318.742	17179.28	5187.751	21860.15	4306.165	11382.88	8533.639	4163.251	7759.643	8466.624	14500.96	5548.003	9922.928
	worst	3327.816	20738.38	5348.282	27509.58	4695.913	16434.78	10751.85	4402.695	10785.38	12427.83	18227.73	10992.5	11860.48
	std	4.767125	1774.959	81.43107	2583.4	180.0406	2558.827	1038.94	128.0624	1399.433	1944.961	1727.46	2645.011	1057.399
	median	3321.205	17895.86	5313.32	24063.98	4561.913	14507.86	10133.57	4272.986	8712.762	10624.33	17080.94	7077.593	10689.1
	rank	1	12	4	13	3	10	7	2	6	8	11	5	9
C17-F29	mean	4450.696	150667.3	9925.685	284879.7	7708.141	17070.72	15531.35	9164.636	8858.751	12194.96	22326.86	9135.355	11715.06
	best	4169.151	86958.94	9107.309	154059.3	6882.332	13623.67	13145.33	8445.7	8560.049	11341.48	18688.33	8732.014	11418.94
	worst	4829.521	204859.3	10389.87	394703.9	8233.202	21287.32	17715.52	9910.691	9331.518	12617.52	28480.41	9708.153	11992.34
	std	307.1569	54599.95	611.7269	111549.6	630.288	3496.398	2416.324	662.3035	360.0082	647.0171	4882.893	491.2947	258.21
	median	4402.056	155425.5	10102.78	295377.8	7858.514	16685.93	15632.28	9151.076	8771.719	12410.43	21069.36	9050.626	11724.48
	rank	1	12	6	13	2	10	9	5	3	8	11	4	7
C17-F30	mean	5407.166	1.89E+10	2.43E+08	3.07E+10	2.24E+08	1.1E+10	1.43E+09	3.03E+08	1.7E+09	3.28E+09	6.16E+09	7.09E+08	7.58E+08
	best	5337.48	1.67E+10	1.49E+08	2.87E+10	1.38E+08	6.83E+09	1.13E+09	2.17E+08	7.43E+08	1.4E+09	4.47E+09	2.53E+08	6.84E+08
	worst	5557.155	2.05E+10	2.86E+08	3.31E+10	2.68E+08	1.37E+10	1.91E+09	3.61E+08	2.19E+09	5.8E+09	7.43E+09	1.78E+09	8.33E+08
	std	110.0477	1.76E+09	68900930	2.04E+09	63226580	3.23E+09	3.63E+08	72223274	7.11E+08	2.43E+09	1.37E+09	7.81E+08	88084792
	median	5367.014	1.93E+10	2.68E+08	3.05E+10	2.45E+08	1.18E+10	1.35E+09	3.18E+08	1.94E+09	2.96E+09	6.36E+09	4.02E+08	7.57E+08
	rank	1	12	3	13	2	11	7	4	8	9	10	5	6
Sum rank		29	336	140	355	65	293	265	114	156	249	272	162	203
Mean rank		1	11.58621	4.827586	12.24138	2.241379	10.10345	9.137931	3.931034	5.37931	8.586207	9.37931	5.586207	7
Total rank		1	12	4	13	2	11	9	3	5	8	10	6	7

Figure 3. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=10).

Figure 3. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=10).

Figure 4. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=30).

Figure 4. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=30).

Figure 5. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=50).

Figure 5. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=50).

Figure 6. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=100).

Figure 6. Boxplot diagrams of OOA and the competitor algorithms performances for the CEC 2017 test suite (dimension=100).

The analysis of the simulation results for the dimension equal to 10 demonstrates that the OOA is the best optimizer for the benchmark functions C17-F1, C17-F3 to C17-F24, and C17-F27 to C17-F30. For the dimension equal to 30, OOA emerges as the top optimizer for the functions C17-F1, C17-F3 to C17-F5, C17-F7, C17-F12 to C17-F14, C17-F16 to C17-F18, and C17-F21 to C17-F29. As the dimension increases to 50, OOA remains the best optimizer for the functions C17-F1, C17-F3 to C17-F25, and C17-F27 to C17-F30. Finally, for the dimension equal to 100, OOA excels as the top performer for the functions C17-F1 and C17-F3 to C17-F30.

The simulation results clearly indicate that the OOA approach is capable of providing high-quality solutions for the CEC 2017 test suite. OOA demonstrates a strong ability to explore the search space comprehensively, exploit the best solutions effectively, and strike a completely different balance between exploration and exploitation compared to its competitor algorithms. Additionally, a comparison of the overall performance shows that the OOA outperforms most competing metaheuristic algorithms in solving the CEC 2017 test suite for the various problem dimensions of 10, 30, 50, and 100. This confirms the robustness and scalability of the OOA approach in handling different optimization challenges efficiently.

4.2. Statistical Analysis

To thoroughly assess and compare the performance of various metaheuristic algorithms, statistical indicators such as the mean, best, worst, standard deviation (std), median, and rank are typically utilized. These indicators provide valuable insights into the quality and performance of the algorithms, helping to highlight which approach demonstrates superiority over others. However, relying solely on these indicators may not fully capture the statistical significance of the differences between algorithms. Therefore, it is essential to conduct more detailed statistical analyses to verify whether the observed superiority of the proposed OOA approach is truly significant in comparison to competing algorithms.

In this section, we perform a completely different statistical analysis using the Wilcoxon rank-sum test [54], a non-parametric method specifically designed to evaluate whether there is a significant difference between two data samples. The Wilcoxon rank-sum test is particularly useful when the data does not follow a normal distribution, making it a robust choice for analyzing the performance differences between the OOA and other metaheuristic algorithms. By applying this test, we aim to determine whether the OOA's performance advantages are not just random but statistically significant.

The results of applying the Wilcoxon rank-sum test to compare the OOA with competing algorithms are summarized in Table 6. These results include the p-values for each comparison, and based on statistical convention, a p-value less than 0.05 indicates a significant difference. In the cases when the p-value is below this threshold, it can be concluded that the proposed OOA approach exhibits a statistically significant superiority over the corresponding competitor algorithm. This additional statistical validation offers a completely different and more robust understanding of the OOA's competitive edge, reinforcing the confidence in its optimization capabilities.

In conclusion, using more words and sentences in conjunction with statistical tests like the Wilcoxon rank-sum test provides a comprehensive and reliable evaluation of the OOA's performance. This ensures that the OOA's observed superiority is not just apparent but also statistically validated, offering deeper insights into its effectiveness when compared to other algorithms.

5. OOA for Real-World Applications

In this section, the effectiveness of the proposed OOA approach in addressing optimization challenges in real-world applications is thoroughly examined. To achieve this, the CEC 2011 test suite, which comprises twenty-two constrained optimization problems derived from practical applications, has been employed. A comprehensive description and full details of the CEC 2011 test suite are available in [55]. The results of the OOA implementation, along with competitor algorithms, when applied to the CEC 2011 test suite, are summarized in Table 7. Additionally, the comparative performance of OOA and the other algorithms is illustrated through boxplots in Figure 7.

From a detailed comparison of the simulation results, it becomes clear that the OOA approach consistently outperforms the competitors, emerging as the top optimizer across all the problems ranging from C11-F1 to C11-F22. This clearly highlights OOA's robustness and effectiveness in dealing with real-world optimization problems. Notably, the simulation results indicate that OOA ranks as the best optimizer in the majority of the optimization problems from the CEC 2011 test suite, showcasing its superior performance when compared to the other algorithms.

Moreover, the statistical analysis conducted using the Wilcoxon rank-sum test further reinforces the advantage of the OOA approach. The results demonstrate a significant statistical superiority for OOA over the competing algorithms, confirming its enhanced ability to optimize the CEC 2011 test suite more effectively.

5. Conclusions and Future Works

In this paper, a completely different bio-inspired metaheuristic algorithm called the Orangutan Optimization Algorithm (OOA) was introduced, showcasing its capability in solving optimization problems across a variety of scientific disciplines and real-world applications. This novel approach is inspired by two distinct natural behaviors of orangutans: their foraging strategies for obtaining food and their nesting behavior for resting. These behaviors formed the foundation for the design of OOA, which was mathematically structured into two key phases—exploration and exploitation.

The performance of OOA was rigorously tested on twenty-nine standard benchmark functions from the CEC 2017 test suite, where the results demonstrated that OOA excels in balancing exploration and exploitation throughout the search process. When compared to twelve other widely-recognized metaheuristic algorithms, OOA showed a superior performance, producing better optimization results for most benchmark functions. Additionally, OOA was applied to twenty-two optimization problems from the CEC 2011 test suite, further validating its effectiveness in solving real-world optimization challenges.

Moreover, the introduction of OOA opens several new avenues for future research. One of the most promising directions is the development of binary and multi-objective versions of OOA. Furthermore, expanding the application of OOA to address optimization challenges in completely different scientific fields and a broader range of real-world scenarios provides exciting opportunities for future studies.