基于模式搜索的粒子群算法求解绝对值方程

Particle swarm algorithm based on pattern search for absolute value equations

利用改进的粒子群算法求解一类NP-hard且不可微的绝对值方程问题:Ax-|x|=b.该算法是将局部探索能力较强的模式搜索算法和全局开采能力较强的粒子群算法进行有效结合,混合后的算法充分发挥了各自的优点,平衡了局部和全局寻优能力,数值试验显示在求解具有不同类型解的绝对值方程时,误差小,迭代次数少.

Improved particle swarm algorithm was used to solve a class of NP-hard and non-differentiable problem of absolute value equations： Ax-｜x｜ = b. This algorithm effectively combined a strong local exploration ability of pattern search method with a strong global exploitation of the particle swarm algorithm. This hybrid method integrated the good advantages of the two methods and balanced the local and global optimization ability. Numerical experiments showed that this improved method had such advantages as a high precision and less number of iterations for solving absolute value equations with different types of solutions.