基于灰关联度的多目标规划新求解算法

Journal of Systems Engineering and Electronics ›› 2010, Vol. 32 ›› Issue (3): 544-547.

基于灰关联度的多目标规划新求解算法

柯宏发1,2，刘思峰1，陈永光3，方志耕1

(1. 南京航空航天大学经济与管理学院，江苏南京 210016;2. 中国人民解放军63880部队，河南洛阳 471003;3. 军械工程学院，河北石家庄 050003)

出版日期:2010-03-18 发布日期:2010-01-03

New solution algorithm for multiple objective programming model based on grey relational degree

KE Hong-fa 1,2，LIU Si-feng 1，CHEN Yong-guang 3，FANG Zhi-geng 1

（1. Coll. of Economics and Management, Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China; 2. Unit 63880 of the PLA, Luoyang 471003, China;3. Ordance Engineering College, Shijiazhuang 050003, China)

Online:2010-03-18 Published:2010-01-03

摘要/Abstract

摘要：

针对多目标规划的求解问题，提出了一种新的基于灰色关联度的求解算法, 该算法将多目标规划模型的多个目标函数理想值组成一个理想目标向量。在相同的约束条件下，基于目标函数向量与理想目标向量之间的灰色关联度而构造一个实值偏好函数。通过最大化这个实值偏好函数，可把多目标规划问题转变为单目标规划问题，并给出了基于遗传算法的求解步骤。通过实际算例表明，该算法正确有效，且相对于线性加权和法、平方加权和法和理想点法而言，具有较好的综合距离均衡性能。

Abstract:

Aiming at the solving of the multiple objective programming model, a new algorithm based on grey relational degree is put forward. Firstly, the ideal target value vector is constructed by all the ideal target values of the multiple objective programming model, and under the same constraint conditions, a grey relational function is formed based on grey relationol degree between the actual target value vector and the ideal target value vector. Then, the multiple objective programming model is changed into a single objective programming model through maximizing the grey relational function. Its solution steps based on genetic algorithm are introduced. The example shows that the proposed algorithm is correct and effective, and has the better synthetical performance of distance equilibrium compared with the linear weighted summation, square weighted summation and ideal point method.

柯宏发1,2，刘思峰1，陈永光3，方志耕1. 基于灰关联度的多目标规划新求解算法[J]. Journal of Systems Engineering and Electronics, 2010, 32(3): 544-547.

KE Hong-fa 1,2，LIU Si-feng 1，CHEN Yong-guang 3，FANG Zhi-geng 1. New solution algorithm for multiple objective programming model based on grey relational degree[J]. Journal of Systems Engineering and Electronics, 2010, 32(3): 544-547.