线性等式约束多目标最优化问题的一个新降维算法  

A New Descending Dimension Algorithm for Multi-objective Optimization Problems with Linear Equality Constraints

作　　者：申合帅 SHEN Heshuai(Zhengzhou Vocational College of Finance and Taxation,Zhengzhou 450000,Henan,China)

机构地区：[1]郑州财税金融职业学院

出　　处：《山西师范大学学报（自然科学版）》2022年第4期5-9,共5页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：利用等式约束最优化问题的一个K-T条件,首先将等式约束最优化问题转化为无约束问题,利用Gauss-Newton法进行求解,得到求解最优化问题的一种新思路;然后针对线性等式约束多目标最优化问题,利用最短距离理想点法,将其转化为线性等式约束最优化问题,从而提出了一种新算法.最后给出算法收敛性的证明,例题表明算法是有效的.By using a K-T condition of equality constrained optimization problem,Firstly,the equality constrained optimization problem is transformed into an unconstrained problem,which is solved by Gauss Newton method,and a new idea for solving the optimization problem is obtained.Then,aiming at the linear equality constrained multi-objective optimization problem,the shortest distance ideal point method is used to transform it into a linear equality constrained optimization problem,so as to solve the problem a new algorithm is proposed.Finally,the convergence of the algorithm is proved,and an example shows that the algorithm is effective.

关 键 词：线性等式约束 降维算法 理想点法 多目标 

分 类 号：O224[理学—运筹学与控制论]