区间多目标优化中决策空间约束、支配及同序解筛选策略

针对优化函数未知的昂贵区间多目标优化, 根据决策空间数据挖掘, 提出了一种基于最近邻法和主成分分析法(Principal component analysis, PCA)的NSGA-II算法. 该算法首先通过约束条件将待测解集分为可行解和非可行解, 利用最近邻法对待测解和样本解进行相似性计算, 判断待测解是否满足约束. 然后对于两个解的Pareto支配性同样利用最近邻法来区分解之间的被支配和非被支配关系. 由于目标空间拥挤距离无法求出, 为此在决策空间利用主成分分析法将K-均值聚类后的解集降维, 找出待测解的前、后近距离解, 通过决策空间拥挤距离对同序值解进行筛选. 实现NSGA-II算法的改进.

Strategy of Constraint,Dominance and Screening Solutions with Same Sequence in Decision Space for Interval Multi-objective Optimization

For the problem of expensive interval multi-objective optimization with unknown optimization functions, a kind of NSGA-II is proposed based on data mining technology in decision space which includes nearest neighbor and PCA. Firstly, candidate solutions in the solution set are divided into feasible solutions and non-feasible solutions according to constraints. And nearest neighbor is used to distinguish the solutions which meet constraints through computing similarity between candidate solutions and sample solutions. Secondly, nearest neighbor is also applied to distinguish dominance relationship and non-dominance relationship for Pareto dominance relationship of the two solutions. Finally, due to the absence of the crowding distance in objective space, the solution set is clustered by K-means clustering, in order to compare the solutions with same sequence, then the dimensions of the solutions of each category are reduced by PCA, thus the closest solutions before and after candidate solutions can be found. So that the solutions with same sequence are screened by crowding distance in decision space. Therefore, the NSGA-II is improved.