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R.: The Effects of Constant Neutrality on Performance and Problem Hardness in GP
, 2008
"... Abstract. 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 bi ..."
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Abstract. 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). 1
The Effects of Constant and Bit-Wise Neutrality on Problem Hardness, Fitness Distance Correlation and Phenotypic Mutation Rates
"... 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, ..."
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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.
Efficient graph-based genetic programming representation with multiple outputs
- International Journal of Automation and Computing
"... Abstract: In this work, we explore and study the implication of having more than one output on a Genetic Programming (GP) graph-representation. This approach, called, Multiple Interactive Outputs in a Single Tree (MIOST) is based on two ideas: (a) Firstly, we defined an approach, called Interactivit ..."
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Abstract: In this work, we explore and study the implication of having more than one output on a Genetic Programming (GP) graph-representation. This approach, called, Multiple Interactive Outputs in a Single Tree (MIOST) is based on two ideas: (a) Firstly, we defined an approach, called Interactivity Within an Individual (IWI), which is based on a graph-GP representation. Secondly, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As first step, we analyse the effects of IWI by using only mutations and analyse its implications (i.e., presence of neutrality). Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conduct extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this work, indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions.
When to Use Bit-Wise Neutrality ∗
, 2008
"... Representation techniques are important issues when designing successful evolutionary algorithms. Within this field the use of neutrality plays an important role. We examine the use of bit-wise neutrality introduced by Poli and López (2007) from a theoretical point of view and show that this mechani ..."
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Representation techniques are important issues when designing successful evolutionary algorithms. Within this field the use of neutrality plays an important role. We examine the use of bit-wise neutrality introduced by Poli and López (2007) from a theoretical point of view and show that this mechanism only enhances mutation-based evolutionary algorithms if not the same number of genotypic bits for each phenotypic bit is used. Using different numbers of genotypic bits for the bits in the phenome we point out by rigorous runtime analyses that it may reduce the optimization time significantly. 1
Practical Search Index as a Hardness Measure for Genetic Algorithms
"... Use of the Building Block Hypothesis to illuminate GA search behavior, as pursued by J. H. Holland and D. E. Goldberg, invites additional investigation.This paper investigates the space actually searched by a GA, in light of the Building Block Hypothesis, GA sampling and population size, in an effor ..."
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Use of the Building Block Hypothesis to illuminate GA search behavior, as pursued by J. H. Holland and D. E. Goldberg, invites additional investigation.This paper investigates the space actually searched by a GA, in light of the Building Block Hypothesis, GA sampling and population size, in an effort to develop more quantitative measures of GA hardness for problems where building block sizes can be estimated. A Practical Search Index (PSI) is defined, related to the size of the space actively searched by the GA, in terms of sizes and numbers of building blocks. The results of the analysis suggest that hardness depends strongly on the sizes of the largest building blocks, premature convergence prevails when population size is not big enough to allow sampling and assembly of building blocks, and appropriate sizing depends on balancing the BB sampling and mixing costs. A set of simple GA experiments on classical test functions at various population sizes, illustrates the relationship between the PSI, population size, and efficiency of search.
[Problem Solving, Control Methods and Search]: Heuristic methods
"... Over the last years, researchers have added neutrality in the evolutionary search in the hope that it can aid evolution. In this paper, we study the presence of neutrality that is already and to do so, we analised the fitness landscape of the Sudoku problem. How and why neutrality affects evolutiona ..."
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Over the last years, researchers have added neutrality in the evolutionary search in the hope that it can aid evolution. In this paper, we study the presence of neutrality that is already and to do so, we analised the fitness landscape of the Sudoku problem. How and why neutrality affects evolutionary search is a reasonably well-studied but still not clearly understood topic. Here, we use neutral walks, neutrality trajectories and fitness distance correlation to attempt to throw new light on this topic.
An Empirical Investigation of How Degree Neutrality Affects GP Search
"... Abstract. Over the last years, neutrality has inspired many researchers in the area of Evolutionary Computation (EC) systems in the hope that it can aid evolution. However, there are contradictory results on the effects of neutrality in evolutionary search. The aim of this paper is to understand how ..."
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Abstract. Over the last years, neutrality has inspired many researchers in the area of Evolutionary Computation (EC) systems in the hope that it can aid evolution. However, there are contradictory results on the effects of neutrality in evolutionary search. The aim of this paper is to understand how neutrality-named in this paper degree neutrality- affects GP search. For analysis purposes, we use a well-defined measure of hardness (i.e., fitness distance correlation) as an indicator of difficulty in the absence and in the presence of neutrality, we propose a novel approach to normalise distances between a pair of trees and finally, we use a problem with deceptive features where GP is well-known to have poor performance and see the effects of neutrality in GP search. 1
Heuristic
"... Despite the vast work on neutrality, there are not general conclusions on its effects. In this paper we make an effort to understand how neutrality influences evolution. For this purpose we will use a type of neutrality that allows locality (which is believed to be a desirable feature of neutrality) ..."
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Despite the vast work on neutrality, there are not general conclusions on its effects. In this paper we make an effort to understand how neutrality influences evolution. For this purpose we will use a type of neutrality that allows locality (which is believed to be a desirable feature of neutrality).
