一类特殊的非线性两层规划新解法

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (2): 403-406.

一类特殊的非线性两层规划新解法

王亚利¹, 刘志国², 王宇平³

1. 西安电子科技大学理学院, 陕西, 西安, 710071;
2. 西安电子科技大学雷达信号处理重点实验室, 陕西, 西安, 710071;
3. 西安电子科技大学计算机学院, 陕西, 西安, 710071

收稿日期:2007-11-02 修回日期:2008-04-02 出版日期:2009-02-20 发布日期:2010-01-03
作者简介:王亚利(1979- ),女,硕士研究生,主要研究方向为进化算法,双层规划.E-mail:yayahope@163.com
基金资助:
国家自然科学基金(60374063);陕西省自然科学基础研究计划(2006A12)资助课题

New solutions to a special class of nonlinear bi-level programming problem

WANG Ya-li¹, LIU Zhi-guo², WANG Yu-ping³

1. Dept. of Mathematics, Xidian Univ., Xi'an 710071, China;
2. Key Lab for Radar Signal Processing, Xidian Univ., Xi'an 710071, China;
3. School of Computer Science and Technology, Xidian Univ., Xi'an 710071, China

Received:2007-11-02 Revised:2008-04-02 Online:2009-02-20 Published:2010-01-03

摘要/Abstract

摘要： 针对下层为可微凸规划的非线性双层规划,提出了一种新算法.基于遗传算法,该算法利用下层规划的单调性将其化为若干个有界约束;这样,整个双层规划就化成了若干个并行且独立的单层规划问题,从而有效地简化了原问题的计算复杂度.对于化简后的单层规划问题,设计了遗传算法,并给出了算法的收敛性证明.最后进行了数值仿真,结果表明该算法具有高效性和鲁棒性.

Abstract: For a class of nonlinear bi-level programming whose follower-level problems are differentiable convex programming,a novel algorithm is proposed.Based on GA,by using its monotonicity,the lower-level programming is divided into a certain number of bounded constraints,which changes the whole bi-level programming into several parallel but independent one-level programming problems.In this way,the original calculation is simplified.For the simplified one-level programming,a genetic algorithm is designed and its global convergence is proved.Finally,the numerical simulation results show that the proposed algorithm is more effective and robust.

中图分类号:

O221

王亚利, 刘志国, 王宇平. 一类特殊的非线性两层规划新解法[J]. Journal of Systems Engineering and Electronics, 2009, 31(2): 403-406.

WANG Ya-li, LIU Zhi-guo, WANG Yu-ping. New solutions to a special class of nonlinear bi-level programming problem[J]. Journal of Systems Engineering and Electronics, 2009, 31(2): 403-406.

参考文献

[1] Blains W F,Chew M N.On two-level optimization[J].IEEE Transactions on Automatic Control,1982,AC-26:211-214.
[2] Ben-Aye O,Blair C.Computational difficulties of bilevel linear programming[J].Operations Research,1990,38:556-560.
[3] Candler W,Townsley R.A linear be-level programming problem[J].Computers and Operations Research,1982,9:59-76.
[4] Bard J F,Falk J E.An explicit solution to the bilevel programming problem[J].Computers and Operations Research,1982,9:77-100.
[5] Bialas W F,Karw an M H.Two level linear programming[J].Management Science,1984,30(8):1004-1020.
[6] Shimiyu K,Aiyoshi E.A solution method for the static constrained stackelberg problem via penalty method[J].IEEE Trans.Automat.Contr.,1984,AC-29(12):1111-1114.
[7] 盛昭瀚,曹忻.具有主从策略的多级规划的稳定性及其优化算法[J].南京工学院学报,1987,4(2):11-17.
[8] Bard J F.Convex two-level optimization[J].Mathematical Programming,1988,40:15-27.
[9] Bard J F.An algorithm for solving the General bi-level programming problem[J].Math of Operations Research,1983,8:260-272.
[10] Fortuny J,Me Carl B.A representation and economic interpretation of a two-level programming problem[J].Journal of Operational Research Society,1981,32(9):783-792.
[11] 向丽,顾培亮.一种基于遗传算法的双层非线性多目标决策方法[J].系统工程理论方法应用,1999,8(3):16-21.
[12] Michael Kifer,Georg Lausen,Wu James.Logical foundations of objectoriented and frame-based languages[J].Journal of the ACM,1995,42(4):741-843.
[13] Kiyotaka Shimizu,Lu Min.A global optimization method for the stackelberg problem with convex functions via problem transformation and concave programming[J].IEEE Trans.on Systems,Man,and Cybernetics,1995,25:1635-1640.
[14] Jonathan F Bard.Practical Bi-level optimization algorithms and application[M].The Netherlands:Kluwer Academic Publishers,1998:193-386.