The Diversity Metric Of The Solution Set Obtained By Multi-objective Evolutionary Algorithms: Design And Application

Multi-objective evolutionary algorithms (MOEAs), as one of the swarm intelligenceheuristic optimization strategy, because of its validity and accuracy search ability onmany complex multi-objective optimization problems, has become one of the hotesttopics in the research field of multiobjective optimization. Because of thecharacteristics of the MOEAs optimization model without any requirements, often toreplace the traditional optimization method is used to solve complex optimizationproblems in engineering practice. With the deep research of MOEAs, many MOEAshave been proposed, how to compare the optimization effect in different type ofproblem of these algorithms, becomes one of the difficult problems in the field.Performance assessment of multi-objective evolutionary algorithms’ solution set, as aquantitative description of the solution set, have been widely used in many aspects,such as select algorithm, to improve the algorithm, and design algorithm. Research onperformance evaluation metric of multi-objective evolutionary algorithm solution set,focus on understanding the two main aspects set distribution metric (uniformity,spread). And the basic elements of each evaluation metric model should be followedin the design process, and according to the elements of design2kinds of solution setuniformity evaluation metric and1kinds of solution sets spread evaluation metric,through the principle of comparative and experimental analysis, the proposed metriccan evaluate the solution set of MOEAs accurately and effectively.As the application of performance metrics, this paper from two aspects, respectively,let the performance metric be used to guide the search process, the distributionmaintaining mechanism and selection strategy. Firstly gives the framework of thePareto-based and the Indicator-based algorithms. Then, from a set of experiments weconcludes that the total-order-based selection mechanism preference a better abilityon many-objective optimization problems than partial-order-based ones.In general, the main work of this paper includes the following3aspects:1) Set distribution evaluation metric classifies and discusses the solution ofexisting, summarize the general rules and basic ideas of each evaluation metric shouldbe followed in the design process; 2) Put forward3kinds of solutions set distribution evaluation metric, including2kinds of solution set for the evaluation of uniformity,1widely used to evaluate thesolution set of;3) Choose the non-dominated layered environment strategies and performancemetrics based on the environmental selection strategies were compared in thehigh-dimensional optimization problem based on the ability of the MOEAs design,evaluation metric based on the basic research.This article from the evaluation metric of performance of multi-objective evolutionaryalgorithm, to study the distribution of solution set of performance metrics areanalyzed and discussed the related problems, solutions are standardized, and theevaluation model is applied to the algorithm design framework, and expanded therange of application of MOEAs performance evaluation metric, provides the generalideas and the reference for the design of high performance algorithm.