基于混合中心引力算法求解一类非线性双层规划问题  

Hybrid Central Force Optimization Approach for Solving a Class of Nonlinear Bilevel Programming Problems

作　　者：任爱红[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《小型微型计算机系统》2015年第6期1384-1388,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61272119)资助

摘　　要：针对下层问题是一个关于下层变量的线性规划,而上层目标是任意函数的一类非线性双层规划问题,提出一种基于Nelder-M ead单纯形法的混合中心引力算法来求解此类问题.利用线性规划的性质处理下层问题,设计了一种混合中心引力算法.所提出的算法运用均匀设计方法产生初始种群.为了增强算法的局部搜索能力和加快收敛速度,将当前种群分成两个子种群,Nelder-Mead单纯形法更新精英粒子构成的子群,而中心引力算法更新普通粒子构成的子群,再将新产生的两个新子群重组.实验研究表明,本文提出的算法不仅能有效求解此类非线性双层规划问题,而且还可以获得高质量的全局最优解.此外,实验结果也表明本文提出的算法是稳定的,且实验结果优于相比较的算法结果.This paper considers a class of nonlinear bilevel programming problems in which the follower＇s problem is linear with re- spect to the lower level variable. Using optimality conditions of the linear programming problem,the follower＇s problem can be dealt with. Then a hybrid algorithm by combining the central force optimization algorithm with Nelder-Mead simplex method is proposed to solve the leader＇s problem. In proposed algorithm ,uniform design is first applied to produce the initial population. In order to improve the local search ability of the algorithm and speed up the rate of convergence, the current population is divided into two parts where the top individuals are updated by the Nelder-Mead simplex method and the last individuals are adjusted by the central force algorithm, and all the offspring are reorganized. The experimental results demonstrate that the proposed algorithm is efficient and stable, and can also find a high-quality approximate global solution for test problems. Moreover,these results indicate that the proposed algorithm performs better than the compared algorithms.

关 键 词：双层规划 中心引力算法 Nelder-Mead单纯形法 现代启发式算法 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]