Research On Multi-objective Estimation Of Distribution Algorithms Based On Regularity Model Learning

The Pareta-optimality set(PS)in decision space and the Pareto-optimality front(PF)in objective space are continuous segmented(m-1)-dimensional manifolds for continuous multi-objective optimization problems,where m is the number of objective functions.According to the regularity,some scholars proposed the regularity model-based multi-objective estimation of distribution algorithm(RM-MEDA)and the multi-objective evolutionary algorithm using Gaussian Process based inverse modeling(IM-MOEA).RM-MEDA and IM-MOCA are very suitable for solving complex multi-objective optimization problems with variable linkages.However,both algorithms have some shortcomings.Firstly,leaning models of RM-MEDA are established based on overall statistical information of the population,ignoring the local information of some excellent solutions,which leads to weak global search capability and slow convergence rate of the algorithm in solving some complex optimization problems.Secondly,inverse models of IM-MOEA is challenged in solving multi-objective optimization problems with extreme non-smoothness in PS or PF,and for RM-MEDA,new individuals sampled from probabilistic learning models established by the candidate solutions without obvious regularity work poorly,which will affect the search efficiency of the algorithm..Based on the above analysis,the research of this paper mainly has two aspects.(1)For RM-MEDA ignoring the local information of solutions,a modified RM-MEDA(MRM-EDA)is proposed by adding operators of differential evolution(DE)that directly use individual information to RM-MEDA.MRM-MEDA enriches individual reproduction modes by combining modeling and sampling method in estimation of distribution algorithm with cross-mutation method in DE,and uses improved DE/rand-to-pbest/l mutation strategy.And during the evolutionary process,an adaptive strategy is used to select one of the reproduction modes to generate new individuals.The experimental results on 32 test functions show that the search ability of MRM-EDA is superior to RM-MEDA and two other improved RM-MEDA.(2)In view of the shortcomings of learning models of RM-MEDA and inverse models of IM-MOEA,RM-IM-EDA is proposed by combining the learning model with the inverse model.RM-IM-EDA integrates the two models dynamically,which expects to take advantage of sampling advantages of the two probability models to achieve better performance.In addition,a sequence-based deterministic initialization is introduced into RM-IM-EDA,which is easier to identify the location of the optimal solutions than randomized initialization,thus the initial population of RM-IM-EDA is closer to the PS.Compared with RM-MEDA,IM-MOEA and two other improved IM-MOEA on 32 test functions,RM-IM-EDA has better convergence and distribution than the comparing algorithms,and has better performance than MRM-MEDA in solving multimode of irregular Pareto-optimality front optimization problems.In this paper,the research of multi-objective distribution estimation algorithms based on regularity model learning in multi-objective optimization algorithms has been further deepened and expanded.The proposed solutions have been verified at simulation analysis,and will be further discussed at practical application in the future for promotion.