求解一类双层规划的自适应变异动态差分进化算法  

A self-adaptive mutation dynamic differential evolution algorithm for a class of bi-level programming problem

作　　者：吴亮红[1] 徐睿[1] 左词立 曾照福[1] 段伟涛[1] WU Lianghong XU Rui ZUO Cili ZEN Zhaofu DUAN Weitao(School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China)

机构地区：[1]湖南科技大学信息与电气工程学院,湖南湘潭411201

出　　处：《中南大学学报（自然科学版）》2016年第10期3436-3444,共9页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(61203309;51374107;61403134);湖南省教育厅优秀青年基金资助项目(12B043);湖南省研究生科研创新项目(CX2015B488)~~

摘　　要：针对一类上层函数和约束函数不具有凸性和可微性要求,而下层函数可微且凸的非线性双层规划问题,首先通过Karush-Kuhn-Tucher(KKT)条件将双层规划问题转换为单层约束非线性规划问题,并结合非固定多段映射罚函数法和精确罚函数法对约束条件进行无约束化处理,然后提出一种改进的动态差分进化算法优化对系列无约束优化问题进行求解。对8个测试实例进行数值计算并与现有算法进行比较。测试结果表明,所提方法是一种求解该类双层规划问题的有效方法。Considering a class of nonlinear bi-level programming problem with non-convex and non-differentiable upper-level function and constraints, convex and differentiable lower-level function and constraints was studied. The Karush-Kunh-Tucker（KKT） conditions were firstly used to transform the bi-level programming problem into a single-level optimization problem. Then, the non-fixed multi-segment mapping penalty function and fixed penalty function methods were combined to deal with the constraints. Thereafter, an improved dynamic differential evolution algorithm was proposed to solve the sequence non-constraint problems. Eight benchmarks problems were used to test the proposed method. The results show that, the proposed method is very effective for solving such class of bi-level programming problem compared with other algorithms.

关 键 词：双层规划 KKT条件 罚函数法 差分进化算法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]