Research On Two Stage Multimodal Optimization Algorithms Based On Evolutionary Computation

With the increasing complexity of modern engineering optimization problems,many optimization problems exhibit multimodal characteristics.This leads to a significant increase in the difficulty of solving the problems.In view of this,this paper proposes four evolutionary algorithms for solving different types of multimodal optimization problems from four perspectives,namely,expensive function evaluation,huge dimensionality of decision space,difficulty in balancing the performance of objectives and decision space,and difficulty in multi-objective decision making,respectively.(1)A single-objective expensive multimodal optimization algorithm based on fitness penalty ranking is proposed to address the problem of costly function evaluation.The algorithm is a two-stage surrogate model-assisted evolutionary algorithm.In the first stage,the entire decision space is fully searched for promising subregions using the differential evolution algorithm(DE).In addition,the number of evaluations of the real function is reduced by using surrogate models.To balance the convergence and diversity of individuals,an individual ranking method based on fitness penalty is proposed.In the second stage,the population is first clustered using a clustering algorithm,and the potential optimal solutions in each cluster are fine-tuned using a local search algorithm to further improve the convergence quality of the solution set.Experimental results show that the proposed algorithm is able to obtain multiple highly competitive optimal solutions with a limited number of evaluations.(2)A single-objective two-stage multimodal optimization algorithm based on neural network weight sharing is proposed for the problem of huge search space in the single-objective large-scale multimodal feature selection problem.In order to solve the problem of convergence difficulties in the large-scale multimodal feature selection problem,a two-stage search framework is proposed.In the first stage,the large-scale feature selection problem is modeled as an integer optimization problem.A coarse-grained search is performed in a huge search space to find promising low-dimensional feature subspaces.In the second stage,a combinatorial optimization problem is constructed in the low-dimensional feature subspace to efficiently search for a multimodal feature subset of the problem.In addition,the algorithm uses a neural network weight sharing strategy to achieve fast evaluation of individuals and solve the time-consuming problem of fitness evaluation.Experimental results show that the proposed algorithm not only effectively reduces the size of features,but also has better classification accuracy on the test set.Meanwhile,the algorithm can obtain multiple feature subsets with comparable performance.(3)A two-stage evolutionary strategy algorithm based on double niching is proposed to address the problem that the performance of the objective and decision space is difficult to be balanced.The algorithm can effectively balance the diversity of solution sets in the objective space and decision space,and the convergence of solution sets.The algorithm solves multimodal multi-objective optimization problems in two stages.To prevent the loss of the Pareto optimal solution region,the niching strategy is used in the decision space in the first stage of the algorithm.Considering diversity in the decision space ensures that the algorithm is not prone to the phenomenon of Pareto subset loss.However,it may lead to poor distribution of solution sets in the object space.Therefore,in the second stage of the algorithm,the solution sets searched in the first stage are fine-tuned by employing the double niching strategy.Thus,the good distributivity of the solution sets in both spaces is ensured.The experimental results show that the proposed algorithm can effectively find all the Pareto subsets and Pareto front of the optimization problem.(4)A multi criteria decision making strategy is incorporated into the optimization process of the multi-objective multimodal optimization problem to address the problem of difficult decisions in the multi-objective multimodal optimization problem.Meanwhile,an evolutionary algorithm MMO-Evo Knee based on minimum Manhattan distance(MMD)is proposed.The purpose of this algorithm is not to search the entire Pareto front and Pareto set of the problem,but to search all global knee points of the problem.The algorithm consists of two stages.In the first stage,the multimodal multi-objective optimization problem is modeled as a multi-objective optimization problem.And the global knee solutions and boundary solutions are searched by the multi-objective algorithm.In the second stage,the information of global knee solutions and boundary solutions in the objective space is used to find all the global knee multimodal solutions by using the single-objective multimodal algorithm.In addition,the maximum generating subset selection algorithm is designed to accurately identify the complete number of knee solutions from the final population.The experimental results show that the proposed algorithm is effective in finding all global knee solutions of the problem.This shows that the algorithm can effectively reduce the burden of the user in the decision-making process.