Populations can be essential in tracking dynamic optima
This provides foundational insights for researchers in evolutionary computation and dynamic optimization, addressing a key theoretical gap.
The paper tackles the lack of rigorous theoretical demonstrations for why populations are essential in evolutionary dynamic optimization, showing that a sufficiently large population is necessary to reliably track moving optima in a general setting.
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.