The performance of the Gravitational Search Algorithm (GSA) depends on the gravitational constant G, which controls the balance of exploration and exploitation abilities. Improving the setting of this parameter has attracted many researchers. In this paper, we analyzed the GSA stability using the von Neumann stability criterion. First, we modeled the iterative process by a second-order differential equation and derived the first and second-order stability conditions. Then, based on these criteria, we suggested a new law to adjust the initial value of the parameter G, depending on the distance between objects and then on the search space. Some supporting simulations were carried out using different update laws of the gravitational constant (e.g., exponential, log-sigmoid, linear, and chaotic) on CEC 2017 benchmark functions in different search space dimensions. The achieved results show that the new setting leads to significantly better outcomes in high-dimensional search spaces (greater than 20). A comparison with other metaheuristics (Particle Swarm Optimization, Artificial Bee Colony, and Grey Wolf Optimizer) reveals that the new setting proffers GSA competitiveness. Tests on 23 real-world problems (CEC 2011 benchmark problems and the iron ores sintering problem) further proved all the merits of the proposed parameter setting.

引力搜索算法（GSA）的性能取决于重力常数G，重力常数G控制着勘探和开发能力的平衡。改进此参数的设置吸引了许多研究人员。在本文中，我们使用冯·诺依曼稳定性准则分析了GSA稳定性。首先，我们通过一个二阶微分方程对迭代过程进行建模，并得出一阶和二阶稳定性条件。然后，基于这些标准，我们提出了一条新的定律来调整参数G的初始值，具体取决于对象之间的距离，然后取决于搜索空间。在不同的搜索空间维度上，使用CEC 2017基准函数的引力常数的不同更新定律（例如，指数，对数S型，线性和混沌）进行了一些支持模拟。取得的结果表明，新设置可以在高维搜索空间（大于20）中显着改善结果。与其他元启发式方法（粒子群优化，人工蜂群和灰狼优化器）的比较表明，新设置具有GSA竞争力。对23个实际问题（CEC 2011基准问题和铁矿石烧结问题）进行的测试进一步证明了建议的参数设置的所有优点。