The Study Of Decomposition-Based Evolutionary Algorithms For Multi-And Many-Objective Optimization

Recently,the study in multi-objective and many-objective optimization evolutionary algorithm(MOEA and Ma OEA)has become a hot topic.The aim of this dissertation is to analyze and explore the features of multi-objective optimization problem(MOP)and many-objective optimization problem(Ma OP),to design modified strategies for MOEA based on decomposition,to improve the performance on MOP and Ma OP.The MOEA based on decomposition(MOEA/D)divides a multi-objective space into a set of optimization subproblems with a collaboration manner.MOEA/D can be formed by a series of components,which include weight vector,decomposition approach,mating strategy,recombination operator and update strategy.The decomposition key is the subproblem,which is formed by the weight vectors and the decomposition approach.Decomposition approach can significantly impact the performance on MOEA/D as it directs the evolutionary search.Many improved MOEA/D variants have designed by various kinds of decomposition approaches,which have shown the promising performance on different kinds of problems.In this paper,we give a survey of decomposition approaches,which are classified into five categories,i.e.,tradition decomposition,modified Tchebycheff decomposition,modified penalty-based boundary intersection decomposition,constrained decomposition,and special cases of decomposition.Moreover,two discussions are further given in this paper to analyze the performance of different decomposition approaches.One is to clarify the difference of Tchebycheff decomposition and Pareto-based domination,and the other is to compare the performance of various decomposition approaches on different benchmark problems.At last,a bi-decomposition evoluationary framework has been designed to combine the advantages of different decomposition approaches.As the decomposition approach,update strategy for population also influences the performance significantly.This paper proposes a decomposition-based multiobjective evolutionary algorithm with a constrained solution update strategy.Different from the existing approaches that assign one solution to each subproblem,our approach allocates the closest solutions to each subproblem and thus the number of solutions in a subproblem may not be one.Regarding the subproblem with no solution,it will be assigned one solution in priority,once offspring are generated and closest to the subproblem.To keep the same population size,the subproblem with the largest number of solutions will remove one solution showing the worst convergence.This improves the diversity of population,while the convergence is not lowered.After a period of evolution,our approach may gradually reach a stable status for solution assignment,i.e.,each subproblem is only assigned with one solution.When compared to six competitive multiobjective evolutionary algorithms based on decomposition,the experiments validated the advantages of our approach on tackling two sets of test problems.For many-objective optimization,it is a challenging work for balancing convergence and diversity during the search process due to the large objective space.Although a number of MOEA/D variants have been designed for the above purpose,some difficulties still hold.As inspired by the existing decomposition approaches,Hybridized Angle-Encouragement-based(HAE)decomposition approach is proposed.Two classes of decomposition approaches,i.e.,the angle-based decomposition(AD)and the proposed encouragement-based boundary intersection decomposition(EBI),are sequentially used in HAE.The first one selects appropriate solutions for association in the feasible region of each subproblem,which is expected to well maintain the diversity of associated solutions;the second one acts as a supplement for the angle-based one under the case that no solution is located in the feasible region of subproblem,which aims to ensure the convergence and explore the population boundaries.By this way,HAE can effectively combine their advantages to balance the convergence and diversity in the evolutionary search.To study the effectiveness of HAE,two series of well-known test benchmarks are used,and the experimental results validate the advantages of HAE by comparing to some decomposition approaches and seven recently proposed many-objective evolutionary algorithms.