线性等式约束多目标规划的一个降维算法

摘要

本文提出具有线性等式约束多目标规划问题的一个降维算法.当目标函数全是二次或线性但至少有一个二次型时,用线性加权法转化原问题为单目标二次规划,再用降维方法转化为求解一个线性方程组.若目标函数非上述情形,首先用线性加权法将原问题转化为具有线性等式约束的非线性规划,然后,对这一非线性规划的目标函数二次逼近,构成线性等式约束二次规划序列,用降维法求解,直到满足精度要求为止.%In this paper, we introduce a new algorithm for the multi-objective programming with linear equality constraints. Firstly, when the objective functions are all quadratic or linear but at least there is a quadratic form, we use the linear weighting method to add them all into a single one. Then we use the descending dimension algorithm to transform the quadratic program problems into solving a system of linear equations. Secondly,when objective functions are general, by using linear weighting method and the secondorder form of Taylor expansion to approach the function, we obtain a quadratic program with linear equality constraints. Thus, we transfer primal problem into solving quadratic program problem.