Research On Improved Evolutionary Algorithms For Solving Constrained Multi-objective Optimization Problems

Constrained multi-objective optimization has been widely used in many fields such as energy,biology,and network communications.Such problems often require simultaneous optimization of multiple conflicting objectives.As the number of objective dimensions increases,the problem becomes more difficult.At the same time,constraints also bring new difficulties to the optimization,the complex and discontinuous feasible region will cause great pressure on the search process.Therefore,the research on constrained multi-objective optimization problems has far-reaching significance and value.Evolutionary computation is a search algorithm based on biological evolutionary mechanisms such as natural selection and natural inheritance.Evolutionary algorithm(EA)can approximately reflect a non-dominated solution that weighs conflicting obj ectives in one run,so it has been considered as the main method for multi-objective optimization problems.However,there are still some problems when using evolutionary algorithms to solve constrained multi-objective optimization problems:(1)The existence of the constraint problem makes the feasible solution preferred,so the information of the infeasible solution is not effectively used in the optimization process.(2)With the increase of the objective dimension and the increase of the search space,the convergence index of the algorithm decreases,and it is easy to fall into a local optimum,so it is difficult to obtain all good feasible solutions.Therefore,in view of the above problems,combined with the existing research of constrained multi-objective optimization problems,this paper proposes two algorithms,and the main contents are as follows:1.When solving a constrained multi-objective optimization problem,the constraint processing mechanism is critical to the performance of the constrained multi-objective optimization algorithm.Therefore,as the first part of this paper,in order to effectively use the information of infeasible solutions,a constrained multi-objective optimization algorithm based on particle swarm optimization is proposed,which is called CMOPSO.There are two main innovations:(1)New crossover operator,which can enhance convergence,guides the population to evolve to feasible region.(2)As for constraint handling mechanism,the proposed algorithm no longer takes feasibility as the first screening criterion.CMOPSO retains some potential infeasible solutions,which aims to increase the diversity of the population.2.With the increase of the objective dimension,in addition to the need for a good constraint mechanism,the difficulty of a constrained multi-objective optimization algorithm lies in how to ensure the diversity of the algorithm.So how to simultaneously handle the optimization of the objective and constraints is a problem needs to be solved.Therefore,as the second part of this paper,in constrained many-objective optimization problems,in order to balance the convergence and feasibility of the algorithm,this paper also designs a constrained objective optimization evolutionary algorithm based on double-index optimization,which is called DS-CMOEA.The proposed algorithm also has technique to ensure that the algorithm does not fall into a local optimum.There are three main innovations:(1)Based on the idea of objective space grouping,combined with the objective values and constraints,new individual selection criteria is formulated,and the elite infeasible solution set is designed to effectively use the information of infeasible solutions.(2)A new manyobjective optimization mechanism that updates the local optimum and global optimum in the crossover operator based on grouped information,which aims to obtain feasible solutions with better objective values.(3)In order to maintain the diversity of the population,the corresponding methods are adapted during the population evolution and environment selection,so the search range is expanded to prevent the algorithm from falling into a local optimum.After simulation tests and comparative analysis with existing algorithms,the algorithms proposed in this paper proved to perform well in solving constrained multi-objective optimization problems.