Research On Multimodal Multiobjective Evolutionary Algorithm With Species Conservation

Multimodal multiobjective optimization problem is a kind of complex multiobjective optimization problem widely existing in the real world,which has attracted extensive attention in recent years.The difficulty of solving this kind of problem is that it not only needs to maintain the diversity of solutions in the objective space as the general multiobjective optimization problem,but also needs to consider the diversity of solutions in the decision space,that is,to find different Pareto solution sets corresponding to the same Pareto front.At present,most multiobjective evolutionary algorithms with good performance in general multiobjective optimization problems cannot effectively solve multimodal multiobjective optimization problems because they do not consider the diversity of solutions in decision space.Some recent researches have preliminarily shown that introducing niche strategy into multiobjective evolutionary algorithm to maintain the diversity of solutions in decision space is a feasible and effective method.As a classical niche strategy,species conservation can not only preserve the high-quality solutions in each generation,but also protect the inferior solutions that are helpful to search for other different high-quality solutions.This technology is expected to provide a more effective means for multimodal multiobjective optimization problems to maintain the diversity of solutions in decision space.Therefore,this thesis creatively introduces species conservation into multimodal multiobjective optimization problems,and carries out the following two works:(1)Aiming at the multimodal multiobjective optimization problems with only global Pareto front,a multimodal multiobjective differential evolutionary optimization with species conservation(MMDE/SC)is proposed.The algorithm uses species conservation strategy to maintain the diversity of solutions in the decision space and the objective space.A differential evolution mutation algorithm is used to enhance the search ability of the algorithm.Among them,the species conservation strategy can be divided into three sub strategies: species division,seed determination and seed conservation.Species division divides the population into different species in the decision space to maintain the Pareto optimal solution set in different regions.Seed determination selects high-quality solutions from each species as seeds that need to be retained to the next generation.Seed conservation will replace the solutions with seeds in the objective space,which has poor performance,so as to ensure that the algorithm will not lose some known regions that may contain different Pareto optimal solution sets in the evolution process.The experimental results on benchmark test sets and practical problems with several excellent multimodal multiobjective evolutionary algorithms show that the proposed algorithm can more uniformly converge to multiple global Pareto optimal solution sets corresponding to the global Pareto front in most test problems.(2)Aiming at the multimodal multiobjective optimization problems with both global and local Pareto fronts,a multimodal multiobjective evolutionary algorithm with two-stage species conservation(MMEA/TSC)is proposed.The algorithm divides the whole evolution process into two stages: the evolution stage based on diversity trend species conservation and the evolution stage based on convergence trend species conservation.The former regards each species as a different sub population,and uses the gaussian mutation strategy to mutate each sub population in the decision space to produce diverse solutions in the decision space.The latter stratified all species according to the Pareto level,and regarded the species in the same level as a sub population,and then used the crossover mutation strategy to search locally in each sub population,so that the solutions can be evenly distributed in the Pareto front of different levels.The experimental results with several advanced algorithms on the benchmark test set show that the algorithm can more uniformly converge to the corresponding multiple global and local Pareto optimal solution sets on the test problem with both global and local Pareto fronts.This thesis excavates the potential of species protection strategy to solve different multimodal multiobjective optimization problems,enriches the theory and method system of species conservation,and provides a new means for solving multimodal multiobjective optimization problems.Therefore,this thesis has important theoretical significance and application value.