变异自适应混沌粒子群算法求解线性超定方程

Mutated Adaptive Constraint Particle Swarm Optimization for Solving Linear Over Determined Equation System

针对粒子群算法容易陷入局部最优值和全局局部搜索平衡能力较差的问题,提出来变异自适应混沌粒子群算法。根据进化代数调节惯性权重和加速因子,新算法较好平衡了粒子群算法中的全局和局部搜索模型,利用变异因子可以使得粒子跳出局部最优值,保证种群后期仍然具有进化潜力。新算法在5个测试函数上和标准粒子群算法,自适应粒子群算法,混沌粒子群算法进行了比较,通过三种比较标准,结果说明了新算法具有较快的收敛速度,和较强的进化潜力。通过对线性超定方程组的求解,说明了新算法在数学方面具有较高的使用价值。

Since the Particle Swarm Optimization （PSO） is vulnerable to be trapped in the local optimum and not skillful at balancing the global and local search, an adaptive mutated PSO was proposed in this paper. Depending on the evolutionary generations, the balance of global and local search was improved in the new algorithm; the factor of mutation can help the new algorithm jumping out local optima, which can enhance the evolutionary potential in late period. The new algorithm was compared with other 3 variant PSOs such as the canonical PSO, adaptive PSO （AP- SO） and chaos PSO （CPSO）. By using three evaluating standards, the resuhs demonstrate that the new algorithm owns a faster convergence velocity and improves evolutionary potential. By solving an over determined equation sys- tem, it is noticeable that the new algorithm can he applied to solve a real-world mathematical problem with high utili- zation.