Abstract
Traditionally, an evolutionary algorithm (EA) operates on a single population with no restrictions on possible mating pairs. Interesting changes to the behaviour of EAs emerge when the structure of the population is altered so that mating between individuals is restricted. Variants of EAs that use such populations are grouped into the field of spatially-structured EAs (SSEAs).
Previous research into the behaviour of SSEAs has primarily focused on the impact space has on the selection pressure in the system. Selection pressure is usually characterised by takeover times and the ratio between the neighbourhood size and the overall dimension of space. While this research has given indications into where and when the use of an SSEA might be suitable, it does not provide a complete coverage of system behaviour in SSEAs. This thesis presents new research into areas of SSEA behaviour that have been left either unexplored or briefly touched upon in current EA literature.
The behaviour of genetic drift in finite panmictic populations is well understood. This thesis attempts to characterise the behaviour of genetic drift in spatially-structured populations. First, an empirical investigation into genetic drift in two commonly encountered topologies, rings and torii, is performed. An observation is made that genetic drift in these two configurations of space is independent of the genetic structure of individuals and additive of the equivalent-sized panmictic population. In addition, localised areas of homogeneity present themselves within the structure purely as a result of drifting. A model based on the theory of random walks to absorbing boundaries is presented which accurately characterises the time to fixation through random genetic drift in ring topologies.
A large volume of research has gone into developing niching methods for solving multimodal problems. Previously, these techniques have used panmictic populations. This thesis introduces the concept of localised niching, where the typically global niching methods are applied to the overlapping demes of a spatially structured population. Two implementations, local sharing and local clearing are presented and are shown to be frequently faster and more robust to parameter settings, and applicable to more problems than their panmictic counterparts.
Current SSEAs typically use a single fitness function across the entire population. In the context of multimodal problems, this means each location in space attempts to discover all the optima. A preferable situation would be to use the inherent spatial properties of an SSEA to localise optimisation of peaks. This thesis adapts concepts from multiobjective optimisation with environmental gradients and applies them to multimodal problems. In addition to adapting to the fitness landscape, individuals evolve towards their preferred environmental conditions. This has the effect of separating individuals into regions that concentrate on different optima with the global fitness function. The thesis also gives insights into the expected number of individuals occupying each optima in the problem.
The SSEAs and related models developed in this thesis are of interest to both researchers and end-users of evolutionary computation. From the end-user’s perspective, the developed SSEAs require less a priori knowledge of a given problem domain in order to operate effectively, so they can be more readily applied to difficult, poorly-defined problems. Also, the theoretical findings of this thesis provides a more complete understanding of evolution within spatially-structured populations, which is of interest not only to evolutionary computation practitioners, but also to researchers in the fields of population genetics and ecology.