多目标进化计算收敛到Pareto最优解集的证明

多目标优化方法经历了一个从确定性搜索算法到随机搜索算法的过程 ,本质上仍是单目标优化的目标组合方法到真正意义上的向量优化方法的过程 ,至今仍在不断地发展中 ,但仍有大量未解决的问题。对多目标进化计算的研究是近年来求解多目标优化问题的重点 ,但目前仍未能证明多目标进化计算的收敛性 ,同时 ,单目标进化计算的收敛性结论不一定能推广到多目标的情况。对该问题进行了探讨 ,提出并证明了三个定理 ,并且算例说明了该理论的正确性。

Convergence of Multi-Objective Evolutionary Computation to Its Pareto Optimal Set

Much work has been done on multi-objective optimization methods to make them turn from deterministic searching algorithm to stochastic searching one, and from single objective optimizing method in nature to veritably vector optimization method. At present there are still many unsolved problems on it. Research on foundation theory on multi-objective evolutionary computation is still very important, among them the proof of convergence of multi-objective evolutionary computation to its Pareto optimal set is the most attracting one, and the resutls of convergence of single-objective problem can not be extended to multi-objective ones. In this paper, three theorems are presented, and the numerical experiment gives more definite support.;