Dominance-based Objective Reduction For Many-objective Optimization Problems

With the rapid development of economy,the demand of high quality,low cost,high security is higher and higher for many enterprises,and thus more and more objectives are needed to be considered.Therefore,the study of the conflict with more than four and four objectives of the many optimization problem is very important.In some practical applications,there exist some redundant objectives in an MaOPs.Reducing the number of objectives of the optimization problem is one of the effective ways to solve the MaOPs with redundant objectives.In this paper,we propose a new objective reduction algorithm.A criterion based on the number of non-dominated solution paired is presented to measure the conflict degree between objectives,called ? indicator.And we introduce a method to quickly calculate the value of ?.We considering the potential drawbacks of dominance structure,the conflict measure criterion proposed in this paper can give an effective measure of the degree of conflict between objectives.Furthermore,we develop an effective objective reduction algorithm using feature selection technique.The algorithm proposed in this paper has low computational complexity.Finally,we compared the proposed algorithm with the LPCA,NLMVUPCA and -MOSS algorithm in some benchmark problems,and the results show the effectiveness of the proposed algorithm.In this paper,we suggest to view objective reduction as a multi-objective optimization problem with constraints,and then we apply the EMO for solving it.Specifically,the first objective is the size of the objective subset and the second objective is value of ? indicator.Because the solution set of dominance relations should be preserved as far as possible in objective reduction,? indicator of value can't be too big.That is to say,we only focus on local PF of the mult-objective optimization problem.In addition,the optimization problem is a selection of objective set of combinatorial optimization problem,combinatorial optimization problem posed a great challenge to evolutionary algorithm.In view of this,we present a local search to improve the performance of the proposed algorithm.We conduct a comprehensive comparison on the proposed algorithm with -MOSS,k-MOSS,FORA on eleven test instances.Numerical studies show the proposed algorithm can obtain a stable performance without any parameter need to finetune.