Research On The Distribution Performance Of Solution Set For MOEAs

Evolutionary Algorithms (EAs) are new optimazation algorithms developed on the basis of biological evolution mechanism. They are successfully applied in many fields due to their merits of simplicity, easiness to operate, low requirement, parallelity and globality. Multi-Objective Evolutionary Algorithms (MOEAs) are adept in solving non-liner Multi-objective optimization problems with high complexity. They can find many candidate solutions through a single run and providing the decider a Pareto solution set to choose an appropriate one. However, MOEAs can't make sure to obtain the Pareto optimal solutions but try to gain an approximate Pareto set. A good solution set is vital to the decider; hence it becomes a very important aim for the designers to obtain a solution set with high quality. The distribution performance is a vital aspect of the quality of the solution set, ideally, the solution set obtained by a MOEA shoud be as close to the PFtrue as possible, covering the PFtrue most extensively and with good uniformity.This paper introduced my research results on distribution performance of solution set for MOEAs. My work includes three major aspects:First, we researched into the overlapping individuals in MOEAs, probed into the cause for them. We discovered that whether the outputting solution set contains overlapping ones deponds on the fitness assigning method and the solution reserving strategy that the MOEA used. According to numerical experiment: for one problem, the binary-coded MOEA obtained much less overlapping solutions than the real-coded one did; for different problems, the variable dimension is a significant factor for the amount of overlapping solutions while the objective dimension has little influence for it. Additionally, the elimination of overlapping solution made the NSGA-II steadier and the distribution of the obtained solution set was better than that by the original NSGA-II.Second, we pointed out that theε-MOEA has its inherent vice that when the PFtrue's slope to one dimension changes a lot along the coordinate, it loses many extreme or representative individuals, which has obvious influence on the distribution performance of the solution sets. In order to solve this problem, a newδ-dominance concept was defined and the suppositional optimum point concept was proposed and used, we designed a new grid-based elitist-reserving strategy (δ-GS).Theδ-GS allows some individual's (satisfying certain conditions) to be preserved in theε-dominated grids. It keeps down the merit ofε-dominance but avoids the individual-losing phenomenon. The suppositional optimum point gathered the information of former elitist in the grid and its use makes sure that the archive won't degenerate.Third, we applied the newδ-dominance concept andδ-GS to EMO Archive Algorithm (δ-MOEA). We usedδ-GS as archive updating measure to maintain the diversity of the archive population. The experiment results showed thatδ-MOEA can overcome the weakness ofε-MOEA and NSGA-II, outperform them at gaining solution sets with good distribution performance.