We study the variant of Particle Swarm Optimization that applies random velocities in a dimension instead of the regular velocity update equations as soon as the so-called potential of the swarm falls below a certain small bound in this dimension, arbitrarily set by the user. In this case, the swarm performs a forced move. In this paper, we are interested in how, by counting the forced moves, the swarm can decide for itself to stop its movement because it is improbable to find better candidate solutions than the already-found best solution. We formally prove that when the swarm is close to a (local) optimum, it behaves like a blind-searching cloud and that the frequency of forced moves exceeds a certain, objective function-independent value. Based on this observation, we define stopping criteria and evaluate them experimentally showing that good candidate solutions can be found much faster than setting upper bounds on the iterations and better solutions compared to applying other solutions from the literature.

我们研究粒子群算法，在一个维度，而不是常规的速度更新方程尽快应用于随机速度为所谓的变异潜力的群体降低到低于某一个小这个空间，由用户任意设置约束。在这种情况下，虫群会强制移动。在本文中，我们感兴趣的是，通过计数强制移动，群可以决定自己停止移动，因为不可能找到比已经找到的最佳解决方案更好的候选解决方案。我们正式证明，当群接近（局部）最优值时，它的行为就像盲目的搜索云，并且强迫移动的频率超过了某个与目标函数无关的确定值。基于此观察，我们定义了停止标准，并通过实验进行了评估，表明与在文献中应用其他解决方案相比，找到好的候选解决方案比在迭代上设置上限和更好的解决方案要快得多。