求解群体多目标决策问题的一种方法

引进了群体多目标决策问题的一种新的最优解概念──s-最优平衡解,它的实际意义是对于每个决策者而言在每个目标下都给出一个让步值.证明了求解s-最优平衡解等价于求解一个对应的单目标优化问题,并在一定条件下s-最优平衡解总是存在的.讨论了具有不同让步值的s-最优平衡解.数值例子表明这个方法对解决群体多目标决策问题具有一定的有效性.

A Method for Solving Group Multiobjective Decision Problems

This paper introduces a new concept called s-optimal coalition solutions for group multiobjective decision problems(GMDP),where s is a nonnegative constant.Its practical meaning is to achieve the optimality within a same value in each objective for each decision maker.This value is called the giving-up value. We show that to solve s-optimal coalition solutions is equivalent to solve a single objective programming.Based on this,we easily prove the existence of s-optimal coalition solutions under some conditions.We also discuss s-optimal coalition solutions when the giving-up value is a vector,i.e.,the value in each objective is different.Numerical examples illustrate that the method presented here is efficient for GMDP.This paper presents a new way to solve the group multiobjective decision problems.