求解互补问题的极大熵差分进化算法

Solving complementarity problem based on maximum-entropy differential evolution algorithm

针对传统算法无法获得互补问题多个最优解的困难,提出了求解互补问题的差分进化算法。首先利用NCP函数,将互补问题转换为一个非光滑方程组问题,然后用凝聚函数对其进行光滑化,进而把互补问题的求解转换为无约束优化问题,利用差分进化算法对其进行求解。该算法对目标函数的解析性质没有要求且容易实现,数值结果表明了该方法在求解互补问题中的有效性。

Aiming at the difficulty of fact that classical algorithms unable to obtain many solutions to complementarity problem,presented a new method,referred to as differential evolution algorithm.First,reformulated complementarity problem as a system of nonsmooth equations via an NCP-function,given a smoothing approximation to the nonsmooth equations by the aggregate function,furthermore,complementarity problem could be transformed into unconstrained optimization,then using the differential evolution algorithm to solve this problem.The objective function of the algorithm does not require analytical nature and easy to achieve,numerical results show that the method is effective in solving complementarity problem.