Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to $$\lambda $$λ islands optimizing the so-called Maze fitness function (Kötzing and Molter in Proceedings of parallel problem solving from nature (PPSN XII), Springer, Berlin, pp 113–122, 2012). Previous work has shown that when a complete migration topology is used, migration must not occur too frequently, nor too soon before the optimum changes, to track the optimum of the Maze function. We show that using a sparse migration topology alleviates these restrictions. More specifically, we prove that there exist choices of model parameters for which using a unidirectional ring of logarithmic diameter as the migration topology allows the model to track the oscillating optimum through nMaze-like phases with high probability, while using any graph of diameter less than $$c\ln n$$clnn for some sufficiently small constant $$c>0$$c>0 results in the island model losing track of the optimum with overwhelming probability. Experimentally, we show that very frequent migration on a ring topology is not an effective diversity mechanism, while a lower migration rate allows the ring topology to track the optimum for a wider range of oscillation patterns. When migration occurs only rarely, we prove that dense migration topologies of small diameter may be advantageous. Combined, our results show that the sparse migration topology is able to track the optimum through a wider range of oscillation patterns, and cope with a wider range of migration frequencies.

中文翻译：

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动态优化中稀疏迁移拓扑对孤岛模型运行时间的影响

岛屿模型表示进化算法的分布式系统，它们独立运行，但偶尔会沿着所谓的迁移拓扑相互共享解决方案。我们通过引入一个简化的岛屿模型来研究迁移拓扑的影响，该模型的行为类似于 $$\lambda $$λ 岛屿，优化所谓的迷宫适应度函数（Kötzing 和 Molter 在《自然并行问题解决程序》（PPSN XII）中） ，施普林格，柏林，第 113-122 页，2012 年）。先前的工作表明，当使用完整的迁移拓扑时，迁移不能发生得太频繁，也不能在最优变化之前太早发生，以跟踪迷宫函数的最优值。我们证明使用稀疏迁移拓扑可以减轻这些限制。更具体地说，我们证明存在模型参数的选择，使用对数直径的单向环作为迁移拓扑允许模型以高概率通过类似 nMaze 的阶段跟踪振荡最佳值，同时使用任何直径小于$$c\ln n$$clnn 对于一些足够小的常数 $$c>0$$c>0 会导致岛模型以压倒性的概率失去对最优值的跟踪。实验表明，环形拓扑上非常频繁的迁移并不是一种有效的分集机制，而较低的迁移率允许环形拓扑跟踪更广泛振荡模式的最佳值。当迁移很少发生时，我们证明小直径的密集迁移拓扑可能是有利的。结合起来，我们的结果表明，稀疏偏移拓扑能够通过更广泛的振荡模式跟踪最优值，并应对更广泛的偏移频率。