The discrete formulation of Particle Swarm Optimization (PSO) is nowadays widely used. The paper presents a continuous formulation of the PSO problem along with its analytic solution. The aim is to verify whenever an amelioration of the standard discrete PSO is achievable by employing its continuous counterpart. The convergence of the proposed continuous PSO scheme is analyzed accounting for variation of the algorithm’s parameters. Moreover, looking for the minimization of an a-priori chosen modified Rastringrin function, a comparison with the standard PSO is also given in terms of computational time and likelihood of success of finding the global optimum points using a Monte Carlo like analysis to consider the stochastic nature of the PSO. Last, comparisons with other optimization methods such as genetic algorithm and tabu search as well as with some extension PSO methods have been investigated. Different objective functions have been taken into account and a success rate greater that \(93\%\) has always been obtained.

如今，粒子群优化（PSO）的离散公式被广泛使用。本文提出了PSO问题及其解析解的连续表述。目的是通过使用其连续对应项来验证何时可以实现标准离散PSO的改进。考虑到算法参数的变化，分析了所提出的连续PSO方案的收敛性。此外，为使先验选择的修正拉弦蛋白函数最小化，在计算时间和使用类似于蒙特卡洛的分析来考虑随机性的情况下成功找到全局最优点的可能性方面，还与标准PSO进行了比较。 PSO的性质。持续，研究了与其他优化方法（例如遗传算法和禁忌搜索）以及某些扩展PSO方法的比较。考虑了不同的目标功能，成功率大于始终获得\（93 \％\）。