ED-MOEA: An Event-Driven Multi-Objective Evolutionary Algorithm for Cooperative Planning of Heterogeneous UAV-UGV Systems in Dynamic Post-Disaster Environments

1. Introduction

The April 3, 2024 Hualien earthquake in Taiwan (magnitude 7.2) resulted in 18 fatalities and over 1,100 injured, with numerous buildings collapsed and critical infrastructure damaged. This event highlighted the urgent need for rapid, coordinated rescue operations in challenging post-disaster environments. Traditional rescue operations rely heavily on human responders who face significant risks when traversing unstable structures and hazardous conditions. The integration of Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs) offers a promising solution for improving rescue efficiency while reducing personnel exposure to dangerous environments [1,2,3,4].

UAVs possess superior aerial reconnaissance capabilities, enabling rapid coverage of large areas through onboard sensors and cameras. Their ability to traverse ground-level obstacles makes them ideal for initial damage assessment and survivor detection. However, UAVs are constrained by limited payload capacity (typically <5 kg) and battery endurance (20–40 minutes), restricting their ability to deliver heavy supplies or maintain prolonged operations. Conversely, UGVs offer complementary advantages: higher payload capacity (10–50 kg), extended operational endurance (2–8 hours), and the ability to deliver rescue equipment directly to survivors [7,8,9].

Despite the potential of heterogeneous UAV-UGV systems, existing approaches predominantly adopt a static allocation paradigm—assigning tasks during the planning phase and executing without adjustment [15,17]. This paradigm conflicts with post-disaster dynamics: new survivors may be discovered, aftershocks may create new obstacles, and agent operational states may change unexpectedly. The inability to adapt leads to suboptimal rescue outcomes and potentially dangerous situations where agents attempt to execute outdated plans.

The core challenge addressed in this paper is establishing an effective cooperative sensing-planning closed-loop for real-time adaptation. Specifically, we develop a framework where: (1) UAVs continuously perceive the environment during flight, detecting new task points or obstacles; (2) detected changes trigger an event-driven replanning mechanism; (3) UGVs receive updated plans and dynamically adjust routes.

This paper proposes ED-MOEA (Event-Driven Multi-Objective Evolutionary Algorithm), with three key contributions:

• Event-triggered dynamic replanning: An event detection mechanism that monitors UAV perception outputs, initiating replanning only when significant changes occur (new task discovery or obstacle detection), avoiding unnecessary computational overhead while ensuring timely response.
• Warm-start initialization strategy: When replanning is triggered, the current assignment structure for remaining tasks is preserved and used to seed the initial population, significantly accelerating replanning convergence compared to random initialization while maintaining solution diversity.
• Heterogeneous mobility-aware encoding: A two-segment chromosome encoding that captures the fundamental differences between UAV (direct flight) and UGV (obstacle-avoiding navigation) mobility patterns.

The remainder of this paper is organized as follows: Section 2 reviews related work; Section 3 formulates the problem mathematically; Section 4 details the proposed ED-MOEA framework; Section 5 describes experiments and analyzes results; Section 6 concludes with future directions.

2. Related Work

2.1. Heterogeneous Multi-Robot Task Allocation

The Multi-Robot Task Allocation (MRTA) problem has been extensively studied [14]. Gerkey and Matarić proposed a taxonomy classifying MRTA problems according to robot capabilities, task requirements, and allocation timing. Heterogeneous MRTA requires consideration of task-robot compatibility, adding significant complexity [16,17].

Recent UAV-UGV coordination has shown progress across various domains. Tokekar et al. [10] developed a symbiotic system for precision agriculture. Peterson et al. [11] proposed consensus-based bundle algorithms for distributed allocation. Duan and Luo [12] introduced adaptive collaborative optimization. Robin and Lacroix [13] provided a comprehensive survey of multi-robot target detection. Grocholsky et al. [9] demonstrated early work on cooperative surveillance. However, these approaches primarily focus on static environments and lack mechanisms for real-time adaptation to dynamic changes—a critical limitation for disaster rescue scenarios.

2.2. Dynamic Vehicle Routing Problems

Dynamic Vehicle Routing Problems (DVRP) extend classical VRP by considering time-varying requests and travel times [21,22]. Event-driven strategies have shown good performance in balancing solution quality and computational efficiency [23,24].

Wang et al. [25] proposed rolling horizon optimization for multi-drone delivery. Nunes and Gini [18] developed auctions for task allocation with temporal constraints. Turner et al. [19] addressed distributed task rescheduling. Otte et al. [20] extended auction-based methods to communication-limited environments. While these methods handle dynamic requests, they typically assume homogeneous vehicle fleets and do not address the heterogeneous mobility constraints inherent in UAV-UGV systems.

2.3. Multi-Objective Evolutionary Algorithms

Multi-Objective Evolutionary Algorithms (MOEAs) have proven effective for complex optimization with conflicting objectives [26]. NSGA-II [27] and NSGA-III [28] employ non-dominated sorting for solution selection. MOEA/D [29] decomposes problems into scalar subproblems. RVEA [30] adopts reference vector guided evolution. Li et al. [31] proposed algorithms combining dominance and decomposition. LMEA [32] addresses large-scale optimization through decision variable grouping—although effective for high-dimensional problems, it lacks mechanisms for temporal adaptability required in dynamic environments.

For dynamic environments, Azzouz et al. [33] surveyed dynamic multi-objective optimization. Jiang and Yang [34] developed benchmarks for evolutionary dynamic optimization. Tian et al. [35] developed PlatEMO for multi-objective optimization research.

2.4. Disaster Rescue Robotics

Disaster rescue robotics has received increasing attention [1,3]. The DARPA Subterranean Challenge drove advances in multi-robot exploration [5]. The TRADR project [6] focused on long-term human-robot teaming. Casper and Murphy [4] documented lessons from the World Trade Center response.

Path planning in disaster environments requires handling complex configurations. Dolgov et al. [36] developed methods for autonomous vehicles. Karaman and Frazzoli [37] established foundations for sampling-based planning. LaValle [38] provided comprehensive coverage of planning algorithms.

In the 2024 Hualien earthquake, unmanned systems played important roles [39,40]. However, existing systems mostly adopt pre-planned or teleoperation modes, lacking autonomous adaptation to dynamic changes. This paper addresses this gap through an event-driven cooperative framework.

3. Problem Formulation

3.1. System Model

Consider a heterogeneous multi-robot system comprising $n_a$ UAVs and $n_g$ UGVs operating in a post-disaster environment. The environment is represented as a 2D workspace $\mathcal{W}\subset {\mathbb{R}}^2$ containing obstacle regions $\mathcal{O}\left(t\right)$ that may change over time due to aftershocks or structural collapses.

Let $\mathcal{A}=\{a_1,\dots ,a_{n_a}\}$ denote UAV agents and $\mathcal{G}=\{g_1,\dots ,g_{n_g}\}$ denote UGV agents. Each agent k is characterized by:

• Velocity $v_k$: maximum travel speed (m/s)
• Range $L_k$: maximum operational distance (m)
• Energy coefficient $e_k$: energy consumption per unit distance (J/m)
• Sensing radius $R_k$: perception range for UAVs (m)

Tasks $\mathcal{T}\left(t\right)=\{T_1,\dots ,T_m\}$ represent rescue points requiring service. Each task $T_i$ has location $(x_i,y_i)$, service time $s_i$, and priority $p_i\in \{1,2,3\}$. The task set evolves dynamically: $\mathcal{T}\left(t\right)={\mathcal{T}}_{\mathrm{initial}}\cup {\mathcal{T}}_{\mathrm{discovered}}\left(t\right)$.

3.2. Heterogeneous Mobility Constraints

The fundamental difference between UAVs and UGVs lies in obstacle handling:

$$d_k(p_1,p_2)=\left\{\begin{array}{cc}\parallel p_1-p_2{\parallel }_2\hfill & \mathrm{if}k\in \mathcal{A}(\mathrm{UAV}\text{:}\mathrm{direct}\mathrm{flight})\hfill \\ d_{A^{*}}(p_1,p_2,\mathcal{O}\left(t\right))\hfill & \mathrm{if}k\in \mathcal{G}(\mathrm{UGV}\text{:}\mathrm{path}\mathrm{planning})\hfill \end{array}\right.$$

(1)

where $d_{A^{*}}$ denotes shortest obstacle-free path length computed via A* algorithm [36,38].

3.3. Objective Functions

The problem is formulated as tri-objective optimization:

Objective 1 - Minimize Makespan:

$$F_1=\underset{k\in \mathcal{A}\cup \mathcal{G}}{max}{T}_k^{\mathrm{complete}}$$

(2)

where $T_k^{\mathrm{complete}}$ is the completion time of agent k.

Objective 2 - Minimize Total Energy:

$$F_2=\sum _{k\in \mathcal{A}\cup \mathcal{G}}{e}_k·D_k$$

(3)

where $D_k$ is the total distance traveled by agent k.

Objective 3 - Maximize Task Coverage:

$$F_3={\displaystyle \frac{|{\mathcal{T}}_{\mathrm{covered}}|}{\left|\mathcal{T}\right(t\left)\right|}}$$

(4)

Note: For algorithmic consistency, $F_3$ is converted to minimization form $(1-F_3)$ during optimization, while results are reported as the original maximization metric for interpretability.

3.4. Constraints

$$\begin{array}{cccc}\hfill & D_k\le L_k,\forall k\in \mathcal{A}\cup \mathcal{G}\hfill & \hfill & (\mathrm{Range}\mathrm{constraint})\hfill \end{array}$$

(5)

$$\begin{array}{cccc}\hfill & x_{ij}\in \{0,1\},\forall i,j\hfill & \hfill & (\mathrm{Binary}\mathrm{assignment})\hfill \end{array}$$

(6)

$$\begin{array}{cccc}\hfill & \sum _k{x}_{ik}\le 1,\forall i\in \mathcal{T}\left(t\right)\hfill & \hfill & (\mathrm{Sin}\mathrm{gle}\mathrm{assignment})\hfill \end{array}$$

(7)

4. ED-MOEA Algorithm Framework

4.1. System Architecture

Figure 1 illustrates the ED-MOEA framework comprising three interconnected modules: Perception Module, Event-Trigger Module, and Planning Module.

The Perception Module processes UAV sensor data to detect new task points (survivors) and obstacles (collapsed structures). The Event-Trigger Module evaluates trigger conditions:

$$\mathrm{Trigger}\left(t\right)=\mathbb{I}\left[\right|{\mathcal{T}}_{\mathrm{new}}\left(t\right)|\ge 1]\vee \mathbb{I}\left[\right|{\mathcal{O}}_{\mathrm{new}}\left(t\right)|\ge 1]$$

(8)

When triggered, the Planning Module executes warm-start replanning, updating task allocation and paths for all agents.

4.2. Chromosome Encoding

A two-segment encoding captures both assignment and sequencing:

$$\mathrm{Chromosome}=\left[\underset{\mathrm{Assignment}\mathrm{Segment}}{\underbrace{a_1,a_2,\dots ,a_m}}\right|\underset{\mathrm{Priority}\mathrm{Segment}}{\underbrace{{\pi }_1,{\pi }_2,\dots ,{\pi }_m}}]$$

(9)

The assignment segment $a_i\in \{1,\dots ,n_a+n_g\}$ specifies which agent handles task i. The priority segment ${\pi }_i\in [0,1]$ determines execution order within each agent’s task queue. This encoding naturally handles heterogeneous mobility by allowing the fitness evaluation to compute appropriate distances for each agent type.

4.3. Warm-Start Initialization

The warm-start strategy (Algorithm 1) preserves solution structure during replanning:

Algorithm 1:Warm-Start Initialization

Require:  Current solution S, remaining tasks ${\mathcal{T}}_r$, new tasks ${\mathcal{T}}_n$, population size N Ensure:  Initial population P 1: $P\leftarrow \varnothing$ 2: // Part 1: Solution inheritance (30%) 3: for$i=1$ to $\lfloor 0.3N\rfloor$ do 4:    $\mathrm{ind}\leftarrow$ Copy S with completed tasks removed 5:    Assign ${\mathcal{T}}_n$ to nearest agents based on current positions 6:    $P\leftarrow P\cup \left\{\mathrm{ind}\right\}$ 7: end for 8: // Part 2: Mutation-based (30%) 9: for$i=1$ to $\lfloor 0.3N\rfloor$ do 10:    $\mathrm{ind}\leftarrow$ Mutated copy of S 11:    Randomly reassign 20% tasks, randomly insert ${\mathcal{T}}_n$ 12:    $P\leftarrow P\cup \left\{\mathrm{ind}\right\}$ 13: end for 14: // Part 3: Random exploration (40%) 15: for$i=1$ to remaining do 16:    $\mathrm{ind}\leftarrow$ Random chromosome for ${\mathcal{T}}_r\cup {\mathcal{T}}_n$ 17:    $P\leftarrow P\cup \left\{\mathrm{ind}\right\}$ 18: end for  19: return P

The 30/30/40 ratio balances exploitation (inherited solutions) with exploration (random diversity), achieving optimal convergence-diversity trade-off as validated in sensitivity analysis.

4.4. NSGA-III Integration

ED-MOEA employs NSGA-III [28] as the base optimizer due to its effectiveness on three-objective problems. Key adaptations include:

• Reference points: 91 uniformly distributed points on the 3D objective hyperplane
• Crossover: Order-based crossover preserving assignment validity
• Mutation: Swap mutation for priority segment, random reassignment for assignment segment
• Replanning generations: $G_{\mathrm{replan}}=50$ (vs. $G_{max}=200$ for initial planning)

4.5. Complexity Analysis

The computational complexity per generation is:

$$O(N\times G\times |\mathcal{T}{|}^2\times C_{A^{*}})$$

(10)

where N is population size, G is generation count, and $C_{A^{*}}$ represents average A* pathfinding cost dependent on grid resolution and obstacle density. The warm-start strategy reduces effective G during replanning by approximately 75% (from 200 to 50 generations).

5. Experiments

5.1. Experimental Setup

Benchmark Scenarios: Five synthetic scenarios (S1–S5) with increasing complexity, plus a real-world case based on the 2024 Hualien earthquake (Table 1).

Agent Parameters: Table 2 presents the agent parameter settings used in experiments, based on typical commercial UAV and UGV specifications.

Algorithm Parameters: Population $N=100$, initial generations $G_{max}=200$, replanning generations $G_{\mathrm{replan}}=50$, crossover rate 0.9, mutation rate 0.1.

Baselines: NSGA-III [28], MOEA/D-DE [29], RVEA [30], LMEA [32], and Static (no replanning).

Metrics: Hypervolume (HV), Inverted Generational Distance (IGD), and objective values (makespan, energy, coverage). Results averaged over 30 independent runs with different random seeds.

5.2. Performance Comparison

Table 3 presents results on the S3 scenario (representative medium-scale case).

ED-MOEA achieves the highest hypervolume (4.19$\times {10}^8$), indicating the best overall Pareto front quality considering all three objectives simultaneously. While MOEA/D-DE achieves higher coverage (0.933), this comes at the cost of significantly longer makespan (783.3s vs 670.5s) and higher energy consumption (45.6 kJ vs 34.4 kJ). The Static baseline shows the lowest coverage (0.733), demonstrating the necessity of dynamic replanning—without responding to newly discovered tasks, static approaches fail to achieve adequate mission completion in dynamic environments.

Figure 2 visualizes Pareto fronts on the S3 scenario. ED-MOEA solutions achieve superior trade-offs across the objective space.

Figure 3 shows HV evolution over generations, with replanning events at $t=100$s and $t=250$s. ED-MOEA demonstrates rapid recovery after each replanning through warm-start initialization.

Table 4 summarizes ED-MOEA performance across all scenarios.

ED-MOEA consistently achieves the highest HV across all scenarios, demonstrating robust performance regardless of problem scale. The coverage improvement over Static ranges from -0.8% to +15.7%, with the advantage being most pronounced in smaller scenarios where dynamic events have greater relative impact.

5.3. Ablation Study

To validate individual component contributions, ablation experiments were conducted on a controlled scenario with minimal dynamic events (20 initial tasks, 2 dynamic tasks, 500×500m area, 2 UAVs, 2 UGVs). This configuration isolates component effects under low-dynamism conditions—complementing the benchmark evaluations (S1–S5) that test performance under realistic dynamic frequencies. Table 5 presents the results.

Component Contribution Analysis:

Heterogeneous Coordination: Comparing Full (coverage 0.910) with Only-UAV (0.780) reveals 16.7% improvement in task coverage: $(0.910-0.780)/0.780=16.7\%$. This substantial gain demonstrates the value of combining UAV rapid reconnaissance with UGV high-capacity delivery. The Only-UAV variant achieves lower coverage due to range limitations, while Only-UGV achieves full coverage but requires 1155s—nearly double the heterogeneous system time (603s).

Warm-Start Initialization: Comparing Full with w/o Warm-Start shows 3.6% HV improvement: $(9.78-9.44)/9.44=3.6\%$. More importantly, parameter sensitivity analysis (see Supplementary Materials) demonstrates that warm-start reduces convergence generations from 68 (random initialization) to 42—a 38% reduction. Combined with reduced replanning generations ($G_{\mathrm{replan}}=50$ vs. $G_{max}=200$), the total replanning computation is reduced by over 75%, critical for real-time response.

Event-Trigger Mechanism: The w/o Event-Trigger variant uses fixed 50s replanning intervals instead of event-based triggering. Results show coverage reduction from 0.910 to 0.869 (4.5% decrease) and HV reduction from 9.78 to 9.46. Event-triggering also reduces unnecessary replanning calls by 35% on average, saving computational resources.

Replanning Component: An important observation is that the w/o Replanning variant achieves comparable metrics (HV: 9.82 vs 9.78, Coverage: 0.926 vs 0.910) in this controlled scenario. This result is consistent with the design rationale of event-triggered replanning: the mechanism provides value primarily when dynamic events significantly impact the current plan. In the ablation scenario with only 2 dynamic tasks in a compact 500×500m area, the replanning overhead may not yield proportional benefits. Crucially, the benchmark results (Table 4) demonstrate that as dynamic event frequency and spatial distribution complexity increase, ED-MOEA’s advantage becomes substantial—achieving +4.1% to +15.7% coverage improvement over Static baselines in scenarios S1–S4. This validates that the event-triggered mechanism appropriately activates replanning when beneficial, while avoiding unnecessary computational overhead in stable conditions.

Figure 4 visualizes ablation results across four metrics.

5.4. Hualien Earthquake Case Study

Figure 5 presents results for the Hualien scenario, constructed from April 2024 earthquake data [39,40]. Task points correspond to schools, hospitals, and residential areas requiring urgent rescue.

ED-MOEA achieves HV of $5.38\times {10}^8$ with 0.640 coverage, significantly outperforming all baselines in hypervolume. The visualization shows UAVs flying over collapsed buildings while UGVs navigate ground-level routes.

Figure 6 shows dynamic replanning at $t=100$s and $t=250$s. Replanning times of 1.8s and 1.5s demonstrate real-time capability.

5.5. Scalability Analysis

Figure 7 evaluates scalability from 20 to 100 tasks. Initial planning time grows approximately quadratically, consistent with $O\left(\right|\mathcal{T}{|}^2)$ complexity. Replanning time remains under 6 seconds for up to 70 tasks, meeting real-time requirements.

6. Conclusions

This paper proposed ED-MOEA, an event-driven multi-objective evolutionary algorithm for cooperative sensing-planning of heterogeneous UAV-UGV systems in dynamic post-disaster environments. The core contribution is establishing a closed-loop mechanism where UAV perception directly triggers adaptive replanning for the entire system, enabling real-time response to newly discovered survivors and emerging obstacles.

Experiments on five benchmark scenarios and a real case based on the 2024 Hualien earthquake demonstrate that ED-MOEA achieves the highest hypervolume across all test cases, outperforming existing multi-objective algorithms including NSGA-III, MOEA/D-DE, RVEA, and LMEA. The proposed framework achieves 16.7% coverage improvement through heterogeneous coordination, with task coverage increasing from 0.780 (UAV-only) to 0.910 (heterogeneous fleet). The warm-start initialization strategy significantly accelerates replanning convergence (38% fewer generations in sensitivity analysis), enabling real-time response under 6 seconds for scenarios with up to 70 tasks.

Future research directions include: (1) extending the framework to three-dimensional environments for multi-story building rescue; (2) integrating uncertainty quantification for sensor measurements and dynamic event prediction; (3) incorporating learning-based prediction for proactive planning before events occur; (4) exploring hierarchical path planning or learning-based fast pathfinding methods to address A* algorithm efficiency bottlenecks in large-scale scenarios with dense obstacles; (5) validating the approach on physical robot platforms for real-world deployment.