求绝对值方程的改进自适应差分进化算法  

An Improved Adaptive Differential Evolution Algorithm for Solving Absolute Value Equations

作　　者：宁桂英[1] 周永权[2] 

机构地区：[1]广西科技大学鹿山学院,广西柳州545616 [2]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《计算机仿真》2015年第6期251-255,共5页Computer Simulation

基　　金：国家自然科学基金(61165015);广西科技大学鹿山学院科学基金(2013LSZK02)

摘　　要：由于绝对值方程在运筹学是一个不可微的NP—hard问题,传统方法求解绝对值方程速度慢且难以找到全局最优解的缺点,提出了一种求解绝对值方程的改进自适应差分进化算法。首先把绝对值方程问题转化为优化问题,然后对基本差分进化算法进行改进,将具有全局搜索能力和局部搜索能力的变异算子相结合操作,并设置自适应变异算子和交叉算子,改进后的算法在保证种群多样性的同时加快了收敛速度。对三个典型的绝对值方程进行了实验,数值仿真结果表明,改进后的算法能够快速而有效的找到绝对值方程尽可能多的解,是求解绝对值方程的一种有效的方法。Absolute value equation in operations research is a non - differentiable NP - hard problem. The tradi- tional method for solving the absolute value equation is slow and difficult to find global optimal solution. An improved adaptive differential evolution algorithm is proposed. Firstly, the absolute value equation problem is transformed into an optimization problem. Then the basic differential evolution algorithm is improved, the algorithm is combined global search ability with local search ability in the process of population mutation, and adaptive mutation operator and crossover are used. The improved algorithm ensures population diversity while accelerating the convergence speed. Three typical absolute value equations are tested. Numerical results show that the improved algorithm can quickly get the solutions of the equation as many as possible. It is an effective method to solve absolute value equations.

关 键 词：绝对值方程 差分进化算法 不可微 自适应 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]