Research On Multi-objective Evolutionary Algorithm Based On Evaluation Indicator

Multi-objective optimization problems generally exist in practical applications,such as engineering design,path planning and radar detection system,etc.,they are all multi-objective optimization problems.With the development of society,the number of objectives involved in the optimization problem is increasing,so it is necessary to study how to solve the multi-objective optimization problem to meet the needs.Pareto dominant selection mechanism can solve multi-objective optimization problems well,but severe performance degradation occurs when processing many-objective optimization problems.The main reason is that as the number of objectives continues to increase,the proportion of non-dominated solutions increases sharply,making selection criteria based on Pareto dominance relations useless,and secondary criteria focusing on diversity guide population evolution.As a result,the solutionis distributed in the target space divergently,and the convergence is sharply reduced.Therefore,the key to solving high-dimensional multi-objective optimization problems lies in designing accurate and efficient indicator to measure solutions.Based on which have described,this paper proposes new indicators for selecting solutions based on the multi-objective evolutionary algorithm based on evaluation indicators.The main research work is as follows:(1)This paper introduces the basic concepts of multi-objective optimization problems and the main difficulties faced by many-objective optimization problems.The algorithm framework of multi-objective optimization problems based on evaluation indicators is shown in detail.This paper summarizes the meanings of the existing related indicator formulas,theoretically analyze compare the advantages and disadvantages of several evaluation indicators and proves it through experimental tests.(2)Because the Pareto dominance relationship is difficult to evaluate solutions in the high-dimensional space,the selection pressure of the algorithm is too small.In order to solve this problem,the non-contributing solution strategy is introduced into the IGD~+indicator,and an improved and efficient anti-generation distance indicatorIGD~+S is proposed.This indicator not only satisfies Pareto's dominance to improve the rate of solutions convergence,but also retains non-dominated non-dominated solutions to avoid loss of diversity.In the evolution process,IGD~+S indicator is used to comprehensively measure the merits of solutionss,and a multi-objective evolution algorithm based on IGD~+S indicators is proposed.Experimental results show that the algorithm shows good performance in dealing with the DTLZ problem and WFG problem,which is better than the existing good comparison algorithm.(3)Because different indicators may judge the same solutions in different rankings,using a single evaluation criterion is one-sided and inaccurate.Therefore,multiple indicators should be considered simultaneously in the process of environmental selection.The IGD~+S indicator balances solutions convergence and diversity,the R2indicator has weak dominance and focuses on convergence.Therefore,these two indicators are used for fusion,a many-objective optimization Evolutionary Algorithm based on dual indicators is proposed,and an adaptive reference vector method is provided to calculate the indicator value.In the process of environment selection,the solutions are ranked based on the dual indicator which uses IGD~+S indicator and R2indicator.The experimental results demonstrate that the proposed algorithm is versatile for DTLZ problems,outperforming several state-of-the-art algorithms.(4)In order to verify the performance of the algorithm in this paper,the algorithm in Chapter 4 of this paper is applied to the wireless backhaul topology planning problem.Wireless backhaul topology planning is an NP-hard problem.When the constraints are met,consider minimizing construction cost and path loss,construct an optimized objective function model,and use this algorithm to optimize the wireless backhaul solution.Experimental results show that compared with the comparison algorithm,the proposed algorithm can provide a higher-quality topology planning and deployment scheme,which verifies the effectiveness of the proposed algorithm in handling multi-objective optimization problems.