Particle swarm optimization (PSO) is one of the most commonly used stochastic optimization algorithms for many researchers and scientists of the last two decades, and the pattern search (PS) method is one of the most important local optimization algorithms. In this paper, we test three methods of hybridizing PSO and PS to improve the global minima and robustness. All methods let PSO run first followed by PS. The first method lets PSO use a large number of particles for a limited number of iterations. The second method lets PSO run normally until tolerance is reached. The third method lets PSO run normally until the average particle distance from the global best location is within a threshold. Numerical results using non-differentiable test functions reveal that all three methods improve the global minima and robustness versus PSO. The third hybrid method was also applied to a basin network optimization problem and outperformed PSO with filter method and genetic algorithm with implicit filtering.

粒子群优化（PSO）是最近二十年来许多研究人员和科学家最常用的随机优化算法之一，而模式搜索（PS）方法是最重要的局部优化算法之一。在本文中，我们测试了三种将PSO和PS混合以提高全局最小值和鲁棒性的方法。所有方法都让PSO首先运行，然后再运行PS。第一种方法允许PSO在有限数量的迭代中使用大量粒子。第二种方法使PSO可以正常运行，直到达到公差为止。第三种方法允许PSO正常运行，直到距全局最佳位置的平均粒子距离在阈值内。使用不可微分测试函数的数值结果表明，与PSO相比，所有三种方法均提高了全局最小值和鲁棒性。