A modified particle swarm optimization for multimodal multi-objective optimization

Zhang, XuWei; Liu, Hao; Tu, Liangping

doi:10.1016/j.engappai.2020.103905

Cited by 107 publications

(24 citation statements)

References 31 publications

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“…e particle swarm optimization (PSO) algorithm is a population-based random optimization method developed by Kennedy and Eberhart in 1995 [34], inspired by the social behavior of bird overcrowding and fish farming. Of course, this was just the beginning, and extensive research was conducted to improve this method, which led to stronger versions of this method provided by many authors [35][36][37] that the reader could see a summary of the development, improvement, and applications of this algorithm in [38]. To get a proper understanding of this method, consider a group of birds looking for food in an environment.…”

Section: The Related Work and The Classic Psomentioning

confidence: 99%

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

Yousefikhoshbakht

2021

Complexity

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The traveling salesman problem (TSP) is one of the most important issues in combinatorial optimization problems that are used in many engineering sciences and has attracted the attention of many scientists and researchers. In this issue, a salesman starts to move from a desired node called warehouse and returns to the starting place after meeting n customers provided that each customer is only met once. The aim of this issue is to determine a cycle with a minimum cost for this salesman. One of the major weaknesses of the PSO algorithm in the classical version is that it gets stuck in local optimizations. Therefore, in the proposed algorithm, called MPSO, the best solution in the current iteration is also used in the movement step. In addition, a variety of local search algorithms are provided that are used when better answers are generated than before. Also, a new method for moving the particle towards the best particle is presented, which, in addition to probably increasing the quality of the new answer, prevents the premature convergence of the algorithm due to consideration of the concept of random. The results evaluated with the results of several metaheuristic algorithms in the literature show the efficiency of the MPSO algorithm because it has been able to achieve excellent solutions in most of these instances.

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Section: The Related Work and The Classic Psomentioning

confidence: 99%

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

Yousefikhoshbakht

2021

Complexity

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“…Because PSO is affected by the global best particle or the individual best particle, some scholars generally use the non-dominated solution set to optimize the particle swarm when selecting the optimal particle, such as AMPSO [40], MOPSO [39], SMPSO [41] and NMPSO [42]. There are also some algorithms, such as MO_Ring_PSO_SCD [43], which consider the topological structure of particles.…”

Section: B Multi-objective Particle Swarm Optimizermentioning

confidence: 99%

A Competitive Particle Swarm Algorithm Based on Vector Angles for Multi-Objective Optimization

2021

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Recently, the particle swarm algorithm (PSO) has demonstrated its effectiveness in solving multi-objective optimization problems. However, the performance of most existing multi-objective particle swarm algorithms depends largely on the global or individual best particles. Moreover, due to the rapid convergence of PSO in single objective optimization problems, PSO is prone to poorly distributed indicators when dealing with multi-objective optimization problems. To solve the above problems, we propose a multi-objective competitive particle swarm algorithm based on vector angles (VaCSO). Firstly, in order to remove the influence of global best particles or individual best particles on the algorithm, the competition mechanism is used. Secondly, in order to increase the diversity of solutions while maintaining the convergence of the algorithm, the population is clustered into two populations. Population 1 mainly considers the convergence of the solution in the offspring generation strategy. As a supplement, population 2 adds a new offspring generation strategy to maintain the distribution of the solution, and we innovatively proposed a three-particle competition to improve the distribution and diversity of particle swarms. Finally, based on vector angle information, we consider auxiliary learning to optimize the population gap, so as to improve the distribution of the algorithm. We have established two sets of comparative experiments to test the performance of VaCSO. We compared VaCSO with the currently popular multi-objective particle swarm optimizers and multi-objective evolutionary algorithms. Experimental results show that VaCSO has an excellent performance in convergence and distribution, and has a significant effect in optimizing quality.INDEX TERMS multi-objective optimization, competition particle swarm, competition mechanism, threeparticle competition, vector angle information, auxiliary learning.

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“…Benchmark 1 (see Equation (15)) is a test problem called SYM-PART defined in [47] widely used in the literature [18,20,[48][49][50] for the evaluation of algorithms that characterize nearly optimal or multimodal solutions. Benchmark 1 has the Pareto set located in a single neighborhood, and it also has eight local Pareto set that overlap in the objective space (see Equation (20) and Figure 3).…”

Section: Benchmarkmentioning

confidence: 99%

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

et al. 2021

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In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdatePQ,ϵDxy, Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.

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A modified particle swarm optimization for multimodal multi-objective optimization

Cited by 107 publications

References 31 publications

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

A Competitive Particle Swarm Algorithm Based on Vector Angles for Multi-Objective Optimization

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

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