摘要
在研究多目标规划的有效解集的连通性时,许多文献通过将集合的有效点集表示为某个连通集上闭的点集映射的象集以得到结果.本文通过反例说明了连通集上闭的点集映射的象集未必是连通集,从而揭示了多目标规划有效解集连通性研究中存在的问题.据此,借助于点集映射的上半连续性,本文给出了集合的Pareto有效点集和Pareto弱有效点集的另一形式的连通性结果.
The connectedness of efficient solution set of multiobjective programming problem is of great interest and has been studied extensively. The research has been carried out basing on the conclusion that the image of connected set under the closed point-to-set map is a connected set. This paper disproves the conclusion by a counterexample, and with the help of the concept of upper-semicontinuity, proves the connectedness of efficient point set and weak efficient point set of the set.
出处
《运筹学学报》
CSCD
北大核心
2005年第1期32-36,共5页
Operations Research Transactions
基金
Project supported by the National Natural Science Foundation(No.70071026).
关键词
有效点集
连通性
有效解集
半连续性
多目标规划
映射
连通集
Operations research, multiobjective programming, upper-semicontinuity, efficient point set, connectedness
