求解非线性方程组的量子行为粒子群算法*

介绍了利用量子行为粒子群算法解决非线性方程组的问题。求方程组的解归结为一个最优化问题，当方程组有多个解时，它的适应值函数就是具有多个最优解的多峰函数。为此，引进一种物种形成原理算法，该算法根据群体微粒的相似度并行地分成子群体。每个子群体是围绕一个群体种子而建立的。对每个子群体进行QPSO最优搜索，从而保证方程组中每个可能的解都能被搜索到，具有良好的局部寻优特性。对几个重要的测试函数进行仿真实验，结果证明了所用算法可以保证找到方程组所有的解，并且具有很好的精确度。

Solving Systems of Nonlinear Equations Using Quantum behaved Particle Swarm Optimization

Quantum behaved particle swarm optimization was used to solve systems of nonlinear equations. When solving systems of nonlinear equations, the goal is to find an optimal solution for a fitness function. If there are multiple solutions, the fitness function is a multi peaks function with multiple optima. So the notion of species was introduced. By using this method, the swarm population was divided into paralleled species subpopulations based on their similarity. Each species was grouped around a dominating particle called the species seed. Over successive iterations, species are able to simultaneously optimize towards multiple optima, so each solutions is ensure to be searched equally. The experiments demonstrate that the new algorithm to be successful in locating multiple solutions and better accuracy.