Real-world optimisation problems are often dynamic. Previously good solutions must be updated or replaced due to changes in objectives and constraints. It is often claimed that evolutionary algorithms are particularly suitable for dynamic optimisation because a large population can contain different solutions that may be useful in the future. However, rigorous theoretical demonstrations for how populations in dynamic optimisation can be essential are sparse and restricted to special cases. This paper provides theoretical explanations of how populations can be essential in evolutionary dynamic optimisation in a general and natural setting. We describe a natural class of dynamic optimisation problems where a sufficiently large population is necessary to keep track of moving optima reliably. We establish a relationship between the population-size and the probability that the algorithm loses track of the optimum.

中文翻译：

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人口在跟踪动态最优中是必不可少的

现实世界的优化问题通常是动态的。由于目标和约束的变化，必须更新或替换以前好的解决方案。人们经常声称进化算法特别适合动态优化，因为大量的种群可能包含不同的解决方案，这些解决方案可能在未来有用。然而，关于动态优化中的种群如何必不可少的严格理论论证是稀疏的，并且仅限于特殊情况。本文提供了关于种群如何在一般和自然环境中的进化动态优化中至关重要的理论解释。我们描述了一类自然的动态优化问题，其中需要足够大的种群才能可靠地跟踪移动最优解。