同伦内点法求一类多目标优化问题的最小弱有效解

Homotopy Interior-point Method of Solving Minimal Weak Efficient Solution for a Multi-objective Programming Problem

本文针对客观实际中不同决策者在已有条件下自我需求实现问题,根据"自报公议"原则,将多目标优化问题转化成含有权系数变量的一个新单目标优化问题.利用组合同伦内点法来求解单目标问题,通过路径跟踪得到多目标优化问题的最小弱有效解,从而实现"公议",达到相对最佳目的,并证明了该方法是整体收敛的.

In order to fulfill the different needs of different decision-makers,the multi-objective optimization problem has been translated into a new single-object optimization problem with weight factors according to the ＂self-assessment and public discussion＂ principle.Combined homotopy interior-point method is used to solve the single-object optimization problem.The minimal weak efficient solution of the multi-objective optimization problem has been obtained by path tracking.The convergence of this method has also been investigated.