Research On Multimodal Multiobjective Optimization Algorithm And Application Based On Swarm Intelligence

As the needs of our daily life diversify and the industrial production environment becomes more and more complicated,obtaining only one solution is not enough any more.Multimodal optimization has become quite popular because it can obtain multiple satisfactory solutions in a single run.However,the current research on multimodal optimization focuses on single objective problems.Few researchers study multimodal multiobjective optimization problems in depth.The existing multiobjective optimization algorithms cannot solve multimodal multiobjective optimization problems because they can only obtain one Pareto set.To solve this problem,this thesis conducts research on multimodal multiobjective optimization in several aspects including characteristic analysis,establishing benchmark test function suite,designing novel multimodal multiobjective optimization algorithms,effectiveness verification,and real-world applications.The main contributions are as follows.1.A multimodal multiobjective benchmark test function suite is established.Since there were only a few multimodal multiobjective optimization test functions and their characters are very simple,this thesis establishes a multimodal multiobjective benchmark test function suite with diverse characters and various difficulties.Two kinds of methods are proposed to design these test functions.The first method is to copy or shift the Pareto set of single modal multiobjective test functions to generate simple multimodal multiobjective test functions.These functions are easy to use and can act as the basis functions in complex test functions.The second method is to design a scalable framework.The difficulties of functions generated by this framework are scalable.The number of objectives and decision variables and the number of Pareto sets can be defined by users.Therefore,the diversity of the test functions are greatly improved.These benchmark test functions have been accepted and used by many researchers.2.A decision space niched multiobjective genetic algorithm is designed to enable the genetic algorithm to obtain multiple Pareto sets.This algorithm divides the decision space into different niches according to the distribution of the population in decision space.The search ability is greatly enhanced by restricting competition between individuals in different niches.Furthermore,the population is sorted based on the nondominated relationship and crowding distance in decision space.The individuals with large crowding distances in top fronts survive in the environmental selection.Therefore,the individuals with large crowding distance in decision space but small crowding distance in objective space are not deleted easily.The convergence and diversity in decision space are improved significantly.3.A multimodal multiobjective particle swarm optimization algorithm using ring topology and considering crowding distance both in decision and objective space is proposed.The proposed algorithm can eliminate the difficulty of niching parameter setting and deal with the challenge of improving diversity in decision and objective space.On one hand,using ring topology won't induce any niching parameter thus avoid the parameter setting difficulty.In addition,ring topology increases the search ability and improve population diversity by restricting information transmission and forming stable niches.On the other hand,considering crowding distance in both decision and objective space allows individuals with similar objective values but large differences in decision variables to survive and evolve.Therefore,the algorithm can find multiple Pareto sets.Experimental results show that ring topology helps to find more Pareto solutions and considering crowding distance in both decision and objective space enables the algorithm to keep individuals with similar objective values but quiet different decision variables.The combination of these two operators helps the proposed algorithm find more Pareto sets and improve their diversity.4.The proposed algorithms are applied to real-world multimodal multiobjective application problems in feature selection and location selection.In feature selection problems,the proposed multimodal multiobjective algorithm finds excellent feature subsets that single modal algorithm misses.These feature subsets are easier to be extracted than those found by single modal optimization algorithms.In the location selection problem,the proposed multimodal multiobjective algorithms find desired areas ignored by the single modal optimization algorithm.These potential excellent solutions provide more feasible solutions for decision-makers and help to find useful information.