双目标规划问题的像集与求解

摘要

The objective of decision‐making in economic management is often related to cost and benefit .A good case in point is that bi‐objective programming based on cost‐benefit analysis is widely used in economic management .However ,so far , there is still a lack of mature algorithms to determine the full solution of the Bi ‐objective programming problem .A general method ,which was used to get the Pareto solution or weak Pareto solution for double objective optimization problems ,was put forward in this research .To be specific ,we constructed a single objective programming with equality constrain to determine the frontier of the image set of double objective optimization problems .Furthermore ,we could determine the frontier's functional monotonicity using Lagrange multiplier and finally get the Pareto solution or weak Pareto solution .Base on above steps ,A gen‐eral framework was presented to solve double objective programming problem .%经济管理的决策目标往往与成本、收益相关，双目标规划在经济管理中具有广泛应用。然而，尚缺乏成熟的算法确定双目标规划问题的全部解。给出双目标规划问题像集的一般性确定法，以求其解，为研究目的所在。具体而言，构造一个带等式约束的单目标规划问题，以确定双目标规划问题像集之部分边界，并借助拉格朗日乘子符号判断其单调性，据此确定原问题的帕累托解与弱帕累托解。这相当于提供了一个求解双目标规划问题的一般性框架。