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25
The Schema Theorem and Price's Theorem
 FOUNDATIONS OF GENETIC ALGORITHMS
, 1995
"... Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implications f ..."
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Cited by 93 (3 self)
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Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implications for how well a GA is performing. Interpretations of the Schema Theorem have implicitly assumed that a correlation exists between parent and offspring fitnesses, and this assumption is made explicit in results based on Price's Covariance and Selection Theorem. Schemata do not play a part in the performance theorems derived for representations and operators in general. However, schemata reemerge when recombination operators are used. Using Geiringer's recombination distribution representation of recombination operators, a "missing" schema theorem is derived which makes explicit the intuition for when a GA should perform well. Finally, the method of "adaptive landscape" analysis is exa...
Schemata evolution and building blocks
 Evolutionary Computation
, 1999
"... In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially ..."
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Cited by 63 (12 self)
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In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The equation makes manifest the content of the building block hypothesis showing how fit schemata are constructed from fit subschemata. However, we show that generically there is no preference for short, loworder schemata. In the case where schema reconstruction is favored over schema destruction large schemata tend to be favored. As a corollary of the evolution equation we prove Geiringerâ€™s theorem.
The Algebra of Genetic Algorithms
, 1994
"... A rigorous formulation of the generalisation of schema analysis known as forma analysis is presented. This is shown to provide a direct mechanism for harnessing knowledge about a search space, codified through the imposition of equivalence relations over that space, to generate a genetic represen ..."
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Cited by 63 (10 self)
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A rigorous formulation of the generalisation of schema analysis known as forma analysis is presented. This is shown to provide a direct mechanism for harnessing knowledge about a search space, codified through the imposition of equivalence relations over that space, to generate a genetic representation and operators. It is shown that a single characterisation of a space leads to a unique genetic representation, and the kinds of representations that are possible are classified and discussed. A relatively new operator, call random assorting recombination (RARw ), is defined rigorously and is shown to be, in an important sense, a universal recombination operator.
Fitness Variance of Formae and Performance Prediction
, 1994
"... Representation is widely recognised as a key determinant of performance in evolutionary computation. The development of families of representationindependentoperators allows the formulation of formal representationindependent evolutionary algorithms. These formal algorithms can be instantiated ..."
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Cited by 61 (7 self)
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Representation is widely recognised as a key determinant of performance in evolutionary computation. The development of families of representationindependentoperators allows the formulation of formal representationindependent evolutionary algorithms. These formal algorithms can be instantiated for particular search problems by selecting a suitable representation. The performance of different representations, in the context of any given formal representationindependent algorithm, can then be measured. Simple analyses suggest that fitness variance of formae (generalised schemata) for the chosen representation might act as a performance predictor for evolutionary algorithms. This hypothesis is tested and supported through studies of four different representations for the travelling salesrep problem (TSP) in the context of both formal representationindependentgenetic algorithms and corresponding memetic algorithms. 1 Motivation The subject of this paper is representation i...
NonLinear Genetic Representations
, 1992
"... The limitations of linear chromosomes and conventional recombination operators are reviewed. It is argued that there are at least three classes of problems for which such representations and operators are likely to be ineffective. Methods for constructing operators which manipulate more complex stru ..."
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Cited by 29 (2 self)
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The limitations of linear chromosomes and conventional recombination operators are reviewed. It is argued that there are at least three classes of problems for which such representations and operators are likely to be ineffective. Methods for constructing operators which manipulate more complex structures with evolutionary search methods are presented, and it is argued that whenever possible, genetic operators and analogues of schemata should be defined directly in space of phenotypes, rather than in the genotype (representation) space.
Application of Evolutionary Algorithms to Protein Folding Prediction
, 1998
"... . The aim of this paper is to show how evolutionary algorithms can be applied to protein folding prediction. We start reviewing previous similar approaches, that we criticize emphasizing the key issue of representation. A new evolutionary algorithm is described, based on the notion of distance matri ..."
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Cited by 11 (0 self)
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. The aim of this paper is to show how evolutionary algorithms can be applied to protein folding prediction. We start reviewing previous similar approaches, that we criticize emphasizing the key issue of representation. A new evolutionary algorithm is described, based on the notion of distance matrix representation, together with a software package that implements it. Finally, experimental results are discussed. 1 Protein folding prediction Proteins are molecules of extraordinary relevance for live beings. They are chains of aminoacids (called also residues) that assume very rich and involved shapes in vivo. The prediction of protein tertiary structure (3D shape) from primary structure (sequence of aminoacids) is a daunting as well as a fundamental task in molecular biology. A large amount of experimental data is available as far as it concerns sequence, and large projects are creating huge amounts of sequence data. But to infer the biological function (the ultimate goal for molecula...
A Study in Set Recombination
, 1993
"... A family of problems for which the solution is a fixed size set is studied, using fitness functions with varying degrees of epistasis. An empirical comparison between a traditional crossover operator with a binary representation and a penalty function, and the representationindependent Random Assort ..."
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Cited by 8 (1 self)
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A family of problems for which the solution is a fixed size set is studied, using fitness functions with varying degrees of epistasis. An empirical comparison between a traditional crossover operator with a binary representation and a penalty function, and the representationindependent Random Assorting Recombination Operator (RAR) is performed. RAR is found to perform marginally better in all cases. Since RAR is a parameterised operator, a study of the effect of varying its parameter, which can control any tradeoff between respect and assortment, is also presented. 1 Introduction Throughoutthe short history of genetic algorithms there has been a creative tension between two quite distinct schools of thought on the subjects of representations and operators. The fundamental disagreement concerns the relative merits of simple, low cardinality representations used with standard recombination operatorstypically "npoint" and more recently uniform crossover 1 and more complex, prob...
The Reproductive Plan Language RPL2: Motivation, Architecture and Applications
 GENETIC ALGORITHMS IN OPTIMISATION, SIMULATION AND MODELLING. IOS
, 1994
"... The reproductive plan language RPL2 is a computer language designed to facilitate the writing, execution and modification of evolutionary algorithms. It provides a number of data parallel constructs appropriate to evolutionary computing, facilitating the building of efficient parallel interpret ..."
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Cited by 7 (3 self)
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The reproductive plan language RPL2 is a computer language designed to facilitate the writing, execution and modification of evolutionary algorithms. It provides a number of data parallel constructs appropriate to evolutionary computing, facilitating the building of efficient parallel interpreters and compilers. This facility is exploited by the current interpreted implementation. RPL2 supports all current structured population models and their hybrids at language level. Users can extend the system by linking against the supplied framework Ccallable functions, which may then be invoked directly from an RPL2 program. There are no restrictions on the form of genomes, making the language particularly well suited to realworld optimisation problems and the production of hybrid algorithms. This paper describes the theoretical and practical considerations that shaped the design of RPL2, the language, interpreter and runtime system built, and a suite of industrial applications...
Fitness Distance Correlation, as statistical measure of Genetic Algorithm difficulty, revisited
 In Proceedings of the European Conference on Artificial Intelligence
, 1998
"... This paper revisits past works on fitness distance correlation (FDC) in relation to genetic algorithms (GA) performance, and puts forth evidence that this statistical measure is relevant to predict the performance of a GA. We propose an interpretation of Hammingdistance based FDC, which takes into ..."
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Cited by 7 (3 self)
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This paper revisits past works on fitness distance correlation (FDC) in relation to genetic algorithms (GA) performance, and puts forth evidence that this statistical measure is relevant to predict the performance of a GA. We propose an interpretation of Hammingdistance based FDC, which takes into account the GA dynamics and the effects of crossover operator. We base this proposition on the notion of predicates developed by Vose. The aim of this article is double since, using results obtained with the FDC, it confirms Vose's theory, and starting from this theory, it corroborates FDC as a relevant predictor measure of problem difficulty for GAs. 1
Crossover Nonlinearity Ratios and the Genetic Algorithm: Escaping the Blinkers of Schema Processing and Intrinsic Parallelism
, 1993
"... The initial work in the field of Genetic Algorithms (GAs) sought to explain and understand their behaviour by considering such factors as Schema Processing and Intrinsic Parallelism. These theories underlie much of the research into GAs over the past 2 decades. In this paper we examine these contrib ..."
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Cited by 5 (1 self)
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The initial work in the field of Genetic Algorithms (GAs) sought to explain and understand their behaviour by considering such factors as Schema Processing and Intrinsic Parallelism. These theories underlie much of the research into GAs over the past 2 decades. In this paper we examine these contributions in detail and demonstrate that while they offer an interesting viewpoint of the GA, they cannot be used to argue for the GA's effectiveness. Focusing on crossover as the GA's trademark operator, we consider effective crossover partition coefficients and use these to develop a new theory of crossover nonlinearity ratios. Experimental runs are used to demonstrate the power of this theory in characterising problems suitable for solution by GAs. We believe that the GA's concept of generating new solutions from the best elements of existing solutions is a powerful one. However, for this to be accepted by the wider body of optimisation practitioners, the GA community needs to adopt a more ...