On the Effects of Bit-Wise Neutrality on Fitness Distance Correlation, Phenotypic Mutation Rates and Problem Hardness

IEEE Trans. Evol. Computat.

2012

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Kimura's neutral theory of evolution has inspired researchers from the evolutionary computation community to incorporate neutrality into Evolutionary Algorithms (EAs) in the hope that it can aid evolution. The effects of neutrality on evolutionary search have been considered in a number of studies, the results of which, however, have been highly contradictory. In this paper, we analyse the reasons for this and we make an effort to shed some light on neutrality by addressing them. We consider two very simple forms of neutrality: constant neutrality -a neutral network of constant fitness, identically distributed in the whole search space -and bit-wise neutrality, where each phenotypic bit is obtained by transforming a group of genotypic bits via an encoding function. We study these forms of neutrality both theoretically and empirically (both for standard benchmark functions and a class of random MAX-SAT problems) to see how and why they influence the behaviour and performance of a mutation-based EA. In particular, we analyse how the fitness distance correlation of landscapes changes under the effect of different neutral encodings and how phenotypic mutation rates vary as a function of genotypic mutation rates. Both help explain why the behaviour of a mutation-based EA may change so radically as problem, form of neutrality and mutation rate are varied.

Section: ) Max-satsupporting

confidence: 71%

Section: Previous Work On Neutralitymentioning

confidence: 99%

See 1 more Smart Citation

The Effects of Constant and Bit-Wise Neutrality on Problem Hardness, Fitness Distance Correlation and Phenotypic Mutation Rates

Poli

IEEE Trans. Evol. Computat.

2012

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“…In other words synonymous redundancy (redundancy of genotypic neighbours) has the same effect as a small divergence of genotypic neighbours. Whether neutrality is beneficial in general is a complex question considered in detail in some previous work [11,12,16,19,37,44,45,61]; this issue deserves consideration as we will see. The situation is summarised (for discrete-valued phenotypic distances) in Table 1.…”

Section: Extending the Definition Of Locality To The Genotype-fitnessmentioning

confidence: 92%

“…Both [60] and [41] construct examples which demonstrate that the fdc can be "blinded" by particular qualities of the search space, and that it can be misleading. There is, however, a vast amount of work where Jones' approach has been successfully used in a wide variety of problems [12,16,44,45]. Of particular interest is the work by Vanneschi and colleagues [62,65] which concentrated on the use of fdc in the context of GP.…”

Section: Fitness Distance Correlationmentioning

confidence: 99%

Defining locality as a problem difficulty measure in genetic programming

Genet Program Evolvable Mach

McDermott

O’Neill

et al. 2011

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Publication information Genetic Programming and Evolvable Machines, 12 (4): 365-401Publisher Springer Abstract A mapping is local if it preserves neighbourhood. In Evolutionary Computation, locality is generally described as the property that neighbouring genotypes correspond to neighbouring phenotypes. A representation has high locality if most genotypic neighbours are mapped to phenotypic neighbours. Locality is seen as a key element in performing effective evolutionary search. It is believed that a representation that has high locality will perform better in evolutionary search and the contrary is true for a representation that has low locality. When locality was introduced, it was the genotype-phenotype mapping in bitstring-based Genetic Algorithms which was of interest; more recently, it has also been used to study the same mapping in Grammatical Evolution. To our knowledge, there are few explicit studies of locality in Genetic Programming (GP). The goal of this paper is to shed some light on locality in GP and use it as an indicator of problem difficulty. Strictly speaking, in GP the genotype and the phenotype are not distinct. We attempt to extend the standard quantitative definition of genotype-phenotype locality to the genotype-fitness mapping by considering three possible definitions. We consider the effects of these definitions in both continuous-and discrete-valued fitness functions. We compare three different GP representations (two of them induced by using different function sets and the other using a slightly different GP encoding) and six different mutation operators. Results indicate that one definition of locality is better in predicting performance.

The Effects of Constant Neutrality on Performance and Problem Hardness in GP

Lecture Notes in Computer Science

Dignum

Poli

2008

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The neutral theory of molecular evolution and the associated notion of neutrality have interested many researchers in Evolutionary Computation. The hope is that the presence of neutrality can aid evolution. However, despite the vast number of publications on neutrality, there is still a big controversy on its effects. The aim of this paper is to clarify under what circumstances neutrality could aid Genetic Programming using the traditional representation (i.e. tree-like structures) . For this purpose, we use fitness distance correlation as a measure of hardness. In addition we have conducted extensive empirical experimentation to corroborate the fitness distance correlation predictions. This has been done using two test problems with very different landscape features that represent two extreme cases where the different effects of neutrality can be emphasised. Finally, we study the distances between individuals and global optimum to understand how neutrality affects evolution (at least with the one proposed in this paper).