ARTICLE | doi:10.20944/preprints201811.0447.v1
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Perturbed Gerdjikov–Ivanov equation; travelling wave solution; extended auxiliary equation method; complex wave solution
Online: 19 November 2018 (10:28:56 CET)
We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.
ARTICLE | doi:10.20944/preprints202010.0605.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Smart cities; Meta-heuristics; Travelling Salesman Problem; TLBO; Parallelism; GPU
Online: 29 October 2020 (09:34:23 CET)
The development of the smart city concept and the inhabitants’ need to reduce travel time, as well as society’s awareness of the reduction of fuel consumption and respect for the environment, lead to a new approach to the classic problem of the Travelling Salesman Problem (TSP) applied to urban environments. This problem can be formulated as “Given a list of geographic points and the distances between each pair of points, what is the shortest possible route that visits each point and returns to the departure point?” Nowadays, with the development of IoT devices and the high sensoring capabilities, a large amount of data and measurements are available, allowing researchers to model accurately the routes to choose. In this work, the purpose is to give solution to the TSP in smart city environments using a modified version of the metaheuristic optimization algorithm TLBO (Teacher Learner Based Optimization). In addition, to improve performance, the solution is implemented using a parallel GPU architecture, specifically a CUDA implementation.
ARTICLE | doi:10.20944/preprints201905.0187.v1
Subject: Mathematics & Computer Science, Information Technology & Data Management Keywords: dynamic travelling salesman problem; pheromone; discrete particle swarm optimization; heterogeneous; homogeneous
Online: 15 May 2019 (10:41:10 CEST)
This paper presents a discrete particle swarm optimization (DPSO) algorithm with heterogeneous (non-uniform) parameter values for solving the dynamic travelling salesman problem (DTSP). The DTSP can be modelled as a sequence of static sub-problems, each of which is an instance of the TSP. We present a method for automatically setting the values of the DPSO parameters without three parameters, which can be defined based on the size of the problem, the size of the particle swarm, the number of iterations, and the particle neighbourhood size. We show that the diversity of parameter values has a positive effect on the quality of the generated results. We compare the performance of the proposed heterogeneous DPSO with two ant colony optimization (ACO) algorithms. The proposed algorithm outperforms the base DPSO and is competitive with the ACO.
ARTICLE | doi:10.20944/preprints201810.0601.v1
Subject: Engineering, Civil Engineering Keywords: support vector machine; travelling time; intelligent transportation system; artificial fish swarm algorithm; big data
Online: 25 October 2018 (10:48:45 CEST)
Freeway travelling time is affected by many factors including traffic volume, adverse weather, accident, traffic control and so on. We employ the multiple source data-mining method to analyze freeway travelling time. We collected toll data, weather data, traffic accident disposal logs and other historical data of freeway G5513 in Hunan province, China. Using Support Vector Machine (SVM), we proposed the travelling time model based on these databases. The new SVM model can simulate the nonlinear relationship between travelling time and those factors. In order to improve the precision of the SVM model, we applied Artificial Fish Swarm algorithm to optimize the SVM model parameters, which include the kernel parameter σ, non-sensitive loss function parameter ε, and penalty parameter C. We compared the new optimized SVM model with Back Propagation (BP) neural network and common SVM model, using the historical data collected from freeway G5513. The results show that the accuracy of the optimized SVM model is 17.27% and 16.44% higher than those of the BP neural network model and the common SVM model respectively.
ARTICLE | doi:10.20944/preprints202007.0565.v1
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Unsteady Exact analytical solutions; Partial differential equations system; Travelling wave method; Moment method; Boltzmann kinetic equation; Neutral non-homogenous gas; Thermal radiation force; Non-equilibrium irreversible thermodynamics; Internal energy.
Online: 23 July 2020 (12:53:22 CEST)
In the present paper, the effect of the non-linear thermal radiation on the neutral gas mixture in the unsteady state is investigated for the first time. The unsteady BGK technique of the Boltzmann kinetic equations for a neutral non-homogenous gas is solved. The solution of the unsteady case makes the problem more general significance than the stationary one. For this purpose, the moments' method, together with the traveling wave method, is applied. The temperature and concentration are calculated for each gas component and mixture for the first time.Furthermore, the study is held for aboard range of temperatures ratio parameter and a wide range of the molar fraction. The distribution functions are calculated for each gas component and the gas mixture. The significant non-equilibrium irreversible thermodynamic characteristics the entire system is acquired analytically. That technic allows us to investigate the consistency of Boltzmann's H-theorem, Le Chatelier principle, and thermodynamics laws. Moreover, the ratios among the different participation of the internal energy alteration are evaluated via the Gibbs formula of total energy. The final results are utilized to the argon-helium non-homogenous gas at different magnitudes of radiation force strength and molar fraction parameters. 3D-graphics are presented to predict the behavior of the calculated variables, and the obtained results are theoretically discussed.