一类特殊的非线性两层规划新解法  

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

作　　者：王亚利[1] 刘志国[2] 王宇平[3] 

机构地区：[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

出　　处：《系统工程与电子技术》2009年第2期403-406,共4页Systems Engineering and Electronics

基　　金：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

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。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 hi-level programming into several paral- lel but independent one-level programming problems. In this way, the original calculation is simplified. For the simpli- fied 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.

关 键 词：两层规划 约束处理 遗传算法 收敛性 

分 类 号：O221[理学—运筹学与控制论]