Research On Multi-population Co-evolution Mechanism Of Multi-modal Optimization Algorithms

There are many multi-modal multi-objective optimization problems in life and engineering applications.This kind of problems often has the characteristic that one Pareto front corresponds to many different branches of Pareto set.In order to provide decision makers with more diversified choices,it is necessary to search the solutions distributed on multiple Pareto sets as completely as possible,that is,the solution sets obtained by the algorithm should have good distribution diversity in the decision space.However,the traditional multi-objective evolutionary algorithms are often designed for the diversity of the objective space,and lacks the corresponding diversity preserving strategy in the decision space,so they cannot meet the requirements of the diversity in the decision space of the multi-modal multi-objective optimization problems.Therefore,this paper designs and implements two multi-modal multi-objective algorithms based on multi-population co-evolution mechanism to better solve multi-modal multi-objective optimization problems.The specific research contents are as follows.1)Based on the cooperative co-evolution mechanism,a multi-modal multi-objective evolutionary algorithm KMMPDE is designed and implemented.The algorithm uses K-means clustering to divide the whole population in the decision space,so as to distinguish the solutions distributed near different PS branches as far as possible,so that the PS branches corresponding to the solutions of each sub-population are less,and the difficulty of the sub-problems faced by each sub-population is reduced,so as to realize the cooperative co-evolution among multiple sub-populations.In addition,the improved DE operator is used as the evolution method to expand the distribution range of the new solutions,and the non-dominated selection based on the crowding distance in the decision space is used to improve the distribution diversity of the solutions in the decision space.The experimental results show that,compared with other multi-modal multi-objective evolutionary algorithms,KMMPDE has better convergence and diversity in the decision space,and its population division strategy can distinguish the solutions near different PS branches to a certain extent,and its cooperative co-evolution strategy is effective.2)Based on the competitive co-evolution mechanism,a multi-modal multi-objective evolutionary algorithm MMOICA is designed and implemented.Each part of the algorithm is redesigned based on the imperialist competitive algorithm to meet the characteristics of multi-modal multi-objective optimization problems.In this algorithm,the empire exploration mechanism is designed to make the newly generated solutions more diverse;the colonial contention mechanism is designed to make the better empires obtain more colonies,and the poorer empires gradually shrink,so that each empire competes in order to occupy a better search area in the decision space;the empire transformation mechanism is designed to make the algorithm adapt to the multi-objective optimization problems and can effectively maintain the diversity in the decision space;the empire annexation mechanism is designed to accelerate the change of empire members,so as to strengthen the competitive pressure and information exchange between empires.The experimental results show that,compared with other multi-modal multi-objective evolutionary algorithms,MMOICA can obtain results with better convergence and diversity in the decision space,and its competitive co-evolution strategy can effectively improve the performance of the algorithm in the decision space.