Populations can be essential in tracking dynamic optima

TL;DR

This paper provides a theoretical framework demonstrating that large populations are crucial in evolutionary algorithms for reliably tracking moving optima in dynamic optimization problems.

Contribution

It offers a general theoretical explanation of the necessity of large populations in dynamic optimization, linking population size to tracking success.

Findings

Large populations are essential for reliable tracking of moving optima.

A relationship between population size and probability of losing track of the optimum is established.

Theoretical insights apply to a broad class of dynamic optimization problems.

Abstract

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.