求解互补问题的极大熵和声搜索算法*

针对传统算法无法获得互补问题的多个最优解的困难, 提出了求解互补问题的和声搜索算法。利用NCP函数, 将互补问题转换为一个非光滑方程组问题,用极大熵函数对其进行光滑换处理,进而把互补问题的求解转化为无约束优化,利用和声搜索算法对其进行求解。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。

Solving complementarity problem based on maximum-entropy harmony search algorithm

Aiming at the difficulty of fact that classical algorithms unable to obtain many solutions to complementarity problem, a new method, referred to as harmony search algorithm was presented. First, complementarity problem is reformulated as a system of nonsmooth equations via an NCP-function, a smoothing approximation to the nonsmooth equations is given by the aggregate function, furthermore, complementarity problem can be transformed into unconstrained optimization, then using the harmony search 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.