Populations can be essential in tracking dynamic optima

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.