The goal of Lennard-Jones (LJ) clusters optimization is to find the minimum value of the potential function of a cluster and thereby determine the stable configuration of the cluster. It is essentially a completely inseparable multimodal global optimization problem, and using the traditional particle swarm algorithm to solve it often results in local convergence, which means that the solution accuracy of the algorithm is not high. Thus, in this study, we develop a LJ algorithm using a particle swarm optimization (PSO) method and a physical approach to improve the solution accuracy. In this quasi-physical strategy (QPS), the particle swarm algorithm is used to simulate the real atomic structure and incorporates the interatomic force to construct a convergence model so that the algorithm performs well in both global and local space. The potential energy functions of a variety of LJ cluster systems are selected as test functions, and the improved PSO algorithm (QPS-PSO) is analyzed and compared with a competitive swarm optimizer, cooperative coevolution PSO, and differential-group cooperative coevolution, variable-length PSO for feature selection, heterogeneous comprehensive learning PSO, ensemble PSO and cooperative coevolution with differential optimization. The results show that the PSO algorithm for LJ clusters using the proposed QPS has noticeably superior solution accuracy, especially in high-dimensional spaces.

Lennard-Jones（LJ）群集优化的目标是找到群集的潜在函数的最小值，从而确定群集的稳定配置。它本质上是一个完全不可分割的多峰全局优化问题，使用传统的粒子群算法求解通常会导致局部收敛，这意味着该算法的求解精度不高。因此，在这项研究中，我们开发了一种使用粒子群优化（PSO）方法和物理方法来提高求解精度的LJ算法。在这种准物理策略（QPS）中，粒子群算法用于模拟真实的原子结构，并结合原子间的力来构建收敛模型，从而使该算法在全局空间和局部空间中均具有良好的性能。选择各种LJ集群系统的势能函数作为测试函数，并对改进的PSO算法（QPS-PSO）进行分析，并与竞争群优化器，协作协进化PSO和差分群协作协进化，变长度PSO用于特征选择，异构全面学习PSO，集成PSO以及具有差分优化的协同协进化。结果表明，使用提出的QPS的LJ集群的PSO算法具有明显优越的求解精度，尤其是在高维空间中。用于特征选择的可变长度PSO，异构全面学习PSO，集成PSO和具有差分优化的协同协同进化。结果表明，使用提出的QPS的LJ群集的PSO算法具有明显优越的求解精度，尤其是在高维空间中。用于特征选择的可变长度PSO，异构全面学习PSO，集成PSO和具有差分优化的协同协同进化。结果表明，使用提出的QPS的LJ集群的PSO算法具有明显优越的求解精度，尤其是在高维空间中。