Grant Dick

Implicitly Controlling Bloat in Genetic Programming

During the evolution of solutions using genetic programming (GP) there is generally an increase in average tree size without a corresponding increase in fitness-a phenomenon commonly referred to as bloat. Although previously studied from theoretical and practical viewpoints there has been little progress in deriving controls for bloat which do not explicitly refer to tree size. Here, the use of spatial population structure in combination with local elitist replacement is shown to reduce bloat without a subsequent loss of performance. Theoretical concepts regarding inbreeding and the role of elitism are used to support the described approach. The proposed system behavior is confirmed via extensive computer simulations on benchmark problems. The main practical result is that by placing a population on a torus, with selection defined by a Moore neighborhood and local elitist replacement, bloat can be substantially reduced without compromising performance.

The behaviour of genetic drift in a spatially-structured evolutionary algorithm

Spatially-structured evolutionary algorithms (SSEAs) have allowed evolutionary search to be scaled up to increasingly larger and more difficult problems. While their use is becoming more widespread, the basic underlying theory behind them has some omissions. In particular, the effect of random genetic drift on spatial structures is largely unknown. This paper uses models derived from random walk theory to describe the behaviour of a specific class of SSEA. The match between the model and experimental findings is very good. It is the intention that this paper serves as the basis for a more abstract model of drift that encompasses all spatially-structured population models.

Evolutionary dynamics for the spatial Moran process

Evolutionary dynamics for the Moran process have been previously examined within the context of fixation behaviour for introduced mutants, where it was demonstrated that certain spatial structures act as amplifiers of selection. This article will revisit the assumptions for this spatial Moran process and show that proportional global fitness, introduced as part of the Moran process, is necessary for the amplification of selection to occur. Here it is shown that under the condition of local proportional fitness selection the amplification property no longer holds. In addition, regular structures are also shown to have a modified fixation probability from a panmictic population when local selection is applied. Theoretical results from population genetics, which suggest fixation probabilities are independent of geography, are discussed in relation to these local graph-based models and shown to have different assumptions and therefore not to be in conflict with the presented results. This paper examines the issue of fixation probability of an introduced advantageous allele in terms of spatial structure and various spatial parent selection models. The results describe the relationship between structured populations and individual selective advantage in a problem independent manner. This is of significant interest to the theory of fine-grained spatially-structured evolutionary algorithms since the interaction of selection and space for diversity maintenance, selection strength and convergence underlies resulting evolutionary trajectories.

On the mapping of genotype to phenotype in evolutionary algorithms

Analogies with molecular biology are frequently used to guide the development of artificial evolutionary search. A number of assumptions are made in using such reasoning, chief among these is that evolution in natural systems is an optimal, or at least best available, search mechanism, and that a decoupling of search space from behaviour encourages effective search. In this paper, we explore these assumptions as they relate to evolutionary algorithms, and discuss philosophical foundations from which an effective evolutionary search can be constructed. This framework is used to examine grammatical evolution (GE), a popular search method that draws heavily upon concepts from molecular biology. We identify several properties in GE that are in direct conflict with those that promote effective evolutionary search. The paper concludes with some recommendations for designing representations for effective evolutionary search.

Spatially-Structured Sharing Technique for Multimodal Problems

Spatially-structured populations are one approach to increasing genetic diversity in an evolutionary algorithm (EA). However, they are susceptible to convergence to a single peak in a multimodal fitness landscape. Niching methods, such as fitness sharing, allow an EA to maintain multiple solutions in a single population, however they have rarely been used in conjunction with spatially-structured populations. This paper introduces local sharing, a method that applies sharing to the overlapping demes of a spatially-structured population. The combination of these two methods succeeds in maintaining multiple solutions in problems that have previously proved difficult for sharing alone (and vice-versa).

Automatic identification of the niche radius using spatially-structured clearing methods

The goal of multimodal optimisation is to identify multiple desirable optima of a fitness landscape within a single run of an evolutionary algorithm. Typically, one must resort to niching methods to perform this task, and such methods often require the use of a niche radius to distinguish between optima. Typically, this niche radius is difficult to set, leading to suboptimal performance of niching methods on real-world problems. In this paper, local niching methods are used to acquire information about the shape of the fitness landscape during the course of a run. This information is subsequently used during the evolutionary process to adapt the niche radius online. Testing on four benchmark problems indicates that adaptive local niching methods are able to find optimal, or near-optimal, values for the niche radius, as part of the normal evolutionary process.

Genetic drift on networks : Ploidy and the time to fixation

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.

The spatially-dispersed genetic algorithm

Spatially structured population models improve the performance of genetic algorithms by assisting the selection scheme in maintaining diversity. A significant concern with these systems is that they need to be carefully configured in order to operate at their optimum. Failure to do so can often result in performance that is significantly under that of an equivalent non-spatial implementation. This paper introduces a GA that uses a population structure that requires no additional configuration. Early experimentation with this paradigm indicates that it is able to improve the searching abilities of the genetic algorithm on some problem domains.

A Re-Examination of the Use of Genetic Programming on the Oral Bioavailability Problem

Difficult benchmark problems are in increasing demand in Genetic Programming (GP). One problem seeing increased usage is the oral bioavailability problem, which is often presented as a challenging problem to both GP and other machine learning methods. However, few properties of the bioavailability data set have been demonstrated, so attributes that make it a challenging problem are largely unknown. This work uncovers important properties of the bioavailability data set, and suggests that the perceived difficulty in this problem can be partially attributed to a lack of pre-processing, including features within the data set that contain no information, and contradictory relationships between the dependent and independent features of the data set. The paper then re-examines the performance of GP on this data set, and contextualises this performance relative to other regression methods. Results suggest that a large component of the observed performance differences on the bioavailability data set can be attributed to variance in the selection of training and testing data. Differences in performance between GP and other methods disappear when multiple training/testing splits are used within experimental work, with performance typically no better than a null modelling approach of reporting the mean of the training data.

Spatially-Structured evolutionary algorithms and sharing: do they mix?

Spatially-structured populations are one approach to increasing genetic diversity in an evolutionary algorithm (EA). However, they are susceptible to convergence to a single peak in a multimodal fitness landscape. Niching methods, such as fitness sharing, allow an EA to maintain multiple solutions in a single population, however they have rarely been used in conjunction with spatially-structured populations. This paper introduces local sharing, a method that applies sharing to the overlapping demes of a spatially-structured population. The combination of these two methods succeeds in maintaining multiple solutions in problems that have previously proved difficult for sharing alone (and vice-versa).