非线性互补问题的粒子群算法

针对非线性互补问题求解的困难，利用粒子群算法并结合极大熵函数法给出了该类问题的一种新的有效算法。该算法首先利用极大熵函数将非线性互补问题转化为一个无约束最优化问题，将该函数作为粒子群算法的适应值函数；然后应用粒子群算法来优化该问题。数值结果表明，该算法收敛快、数值稳定性较好，是求解非线性互补问题的一种有效算法。

Particle swarm optimization for nonlinear complementarity problems

According to a class of nonlinear complementarity problems，a new algorithm is proposed；this algorithm combines Particle Swarm Optimization with maximum entropy function method.Firstly，the maximum entropy function is used to transform the nonlinear complementarity problems into unconstrained optimization problems，this function is used as Particle Swarm Optimization’s fitness function；Then Particle Swarm Optimization is applied to solving the unconstrained optimization problems.The numerical results show that the algorithm converges faster，numerical stability，and it is an effective algorithm for complementarity minimax problems.