The artificial bee colony (ABC) is a population-based optimization algorithm that mimics the foraging behavior of honeybees. Here, we focus on the parameter setting that ensures the ABC algorithm stability. Therefore, this paper introduces a matrix-iterative model, taking into account the coupling within bees. Moreover, the model considered the difference between update modes, i.e., synchronous or sequential. The necessary conditions for absolute stability were derived under the quasi-deterministic assumption. We further investigated the criteria for first and second-order stochastic stability. These criteria report on the ranges for setting the uniform distributions of the ABC algorithm. Finally, some supporting simulations were carried out on CEC 2017 benchmark functions in different search space dimensions (10, 30, and 50) and on twenty real-world problems (CEC 2011). Six considered ABC variants tested the derived and state-of-the-art criteria in different update modes. Moreover, ABC algorithms were compared with some state-of-the-art metaheuristics (Particle Swarm Optimization, Gravitational Search Algorithm, and Grey Wolf Optimizer). The overall results show that stochastic stability proffers ABC competitiveness. The two update modes may alter the ABC performance only slightly or drastically, depending on the problem, with no evidence on the supremacy of one of them.

人工蜂群（ABC）是一种基于种群的优化算法，它模仿蜜蜂的觅食行为。在这里，我们集中在确保ABC算法稳定性的参数设置上。因此，考虑到蜜蜂之间的耦合，本文引入了矩阵迭代模型。此外，模型考虑了更新模式之间的差异，即同步或顺序。绝对稳定性的必要条件是在准确定性假设下得出的。我们进一步研究了一阶和二阶随机稳定性的标准。这些标准报告了用于设置ABC算法均匀分布的范围。最后，针对CEC 2017基准函数在不同的搜索空间维度（10、30，和50）以及二十个现实世界中的问题（CEC 2011）。六个经过考虑的ABC变体在不同的更新模式下测试了派生标准和最新标准。此外，将ABC算法与一些最新的元启发式算法（粒子群优化，引力搜索算法和Gray Wolf优化器）进行了比较。总体结果表明，随机稳定性具有ABC竞争力。取决于问题，这两种更新模式可能仅会轻微或彻底改变ABC性能，而没有证据表明其中一种具有较高的优势。和“灰太狼优化器”）。总体结果表明，随机稳定性具有ABC竞争力。取决于问题，这两种更新模式可能仅会轻微或彻底改变ABC性能，而没有证据表明其中一种具有较高的优势。和“灰太狼优化器”）。总体结果表明，随机稳定性具有ABC竞争力。取决于问题，这两种更新模式可能仅会轻微或彻底改变ABC性能，而没有证据表明其中一种具有较高的优势。