Research On Evolutionary Algorithms For Dynamic Multi-objective Programming Problems

Multi-objective programming problems(MOPs)are problems with two or more conflicting goals.In contrast,Dynamic multi-objective programming problems(DMOPs)are time-varying,that is to say,it will show the characteristics of objective functions,parameters,or constraints changing with the change of time.In real life,many problems have the characteristics of DMOPs,whose Pareto optimal solution set(PS)or Pareto optimal front(PF)may change with time.In order to design an effective algorithm to solve the problem,the algorithm needs to accurately detect whether the environment changes,and quickly respond to changes.The time variability of DMOPs poses a challenge to the design of the algorithm.So far,evolutionary algorithms have made some achievements in solving MOPs problems,but further research is still needed in DMOPs.However,most of the existing environmental detection methods are based on the reassessment of "part" or "whole" population,which is too sensitive to environmental changes and is not easy to set thresholds.In view of the above analysis,this paper studies an evolutionary algorithm of K-S change detection based on the data stream.First,the algorithm combines the data stream with Kolmogorov-Smirnov(K-S)test to detect the environment of DMOPs.This method can well depict the characteristics of PF changes with the environment and accurately detect whether the environment changes.Secondly,the algorithm uses the deviation between the historical population and the current population to describe the intensity of environmental changes,and then determines the initial proportion of the population at the next moment according to the intensity,which can quickly adjust the search direction of the population,and reduce the loss of the diversity of the population,resulting in the optimal situation.Finally,the algorithm combined with NSGA-Ⅱ algorithm can converge rapidly under the constraint of time window.In this paper,five test functions are compared with two mainstream algorithms(DNSGA-Ⅱ-A and DNSGA-Ⅱ-B)through simulation experiments.Experiments show that the proposed algorithm has good performance in the accuracy of environmental changes,convergence and diversity as well as the uniformity of solution distribution,and has certain advantages in solving DMOPs.