Particle swarm optimization (PSO) is a member of nature-inspired metaheuristic algorithms. Its formulation is simple and does not need the computation of derivatives. It and its many variants have been applied to many different types of optimization problems across several disciplines. There have been many attempts to study the convergence properties of PSO, but a rigorous and complete proof of its almost sure convergence to the global optimum is still lacking. We propose two modified versions of PSO and prove their convergence to the global optimum. We conduct simulation studies to gain further insights into their properties and evaluate their performance relative to PSO.

粒子群优化（PSO）是自然启发式元启发式算法的成员。它的公式很简单，不需要计算导数。它和它的许多变体已被应用于跨多个学科的许多不同类型的优化问题。已经进行了许多尝试来研究PSO的收敛特性，但是仍然缺乏对其几乎确定的收敛到全局最优值的严格而完整的证明。我们提出了PSO的两个修改版本，并证明了它们向全局最优的收敛。我们进行仿真研究，以进一步了解其性能并评估其相对于PSO的性能。