The Diversity Of The Solution Set For Multi-objective Evolutionary Algorithm

Many objective optimization problems involve almost all the real issues in life,to optimize this kind of problems, we need to make all the required sub-goals, whichare competing with each other and can’t compared with each other, achieve the largestor least value at the same time. The many objective optimization algorithms, whichwith uncertainty and height are parameterized, catch the researchers’ and scholars’attentions for its effective and do not have many constraints in the solvingmulti-objective optimization problems. And it witnessed a great growth in a shortperiod of time.Since the rapidly development in the field of many objective optimizationtechnologies, the performance evaluation become much more significant, anddeveloped into a new as well as independent research field gradually in the researchof the many objective evolutionary. The performance of the algorithm is oftenreflected by the features of the solution set. In particular, the performance of thesolution set mainly has three aspects: convergence (the proximity between theobtained solution set and the true Pareto optimal front), uniformity (the uniformdegree for solutions in the target space), spread (the extent of solution set on the targetspace), uniformity and spread construct diversity of solutions. Our article is mainlyaimed to the mesurenment of the solution set’s uniformity on target space, and weproposed a new metric to measure the uniformity of the solution set. We have donetwo jobs--analysis of principle and compare experiment to prove the feasibility andcredibility of our method.After the detailed analysis of the distribution, we put our method into the specificalgorithms framework (NSGA-II) to make better performing for the algorithm.According to the laboratory result, we find that our approach, which used to maintainthe distribution of the solutions, is effective in the use of embedding algorithm. In anutshell, this paper mainly does the following three tasks:1) Analyzing and summarizing the existing evaluation method. Besides analysisof convergence metrics of solution set briefly, we also analyze the index ofuniversality and uniformity in detailed, thus summed up the main characteristic andapplicability of various kinds of measurement methods. 2) The paper proposed a concept of space, and we put forward a metric named avariable influence space-based uniformity metric for solution sets of multi-objectiveevolutionary algorithms according to the conception of space, which is useful in thesolution’s uniformity coefficient judging.3) We add the corresponding retention policy of spread into the proposed metricto further improve the metric’s performance. Based on the specific algorithmsframework, we put the adjusted metric embedded into it to improve the distributionperformance of the algorithm.The paper, which begin to analysis the measurement to the performance of themany objective evolutionary algorithms’ solutions, reviewed a summarized theresearch status of performance evaluation of solution set. In the aspect of theuniformity measurement to the solution set, we present a new idea about it, and weadd the operation of boundary sets to the new idea, which makes the new increase itspractical value. What’s more, we put this improved scheme into many objectiveevolutionary algorithms to keep the distribution for solutions. This provides a certainreference for how evaluation index and guiding algorithm embedding algorithmsearch.