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95
Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
 Proceedings of the Sixth International Conference on Genetic Algorithms
, 1995
"... A measure of search difficulty, fitness distance correlation (FDC), is introduced and examined in relation to genetic algorithm (GA) performance. In many cases, this correlation can be used to predict the performance of a GA on problems with known global maxima. It correctly classifies easy deceptiv ..."
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Cited by 204 (5 self)
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A measure of search difficulty, fitness distance correlation (FDC), is introduced and examined in relation to genetic algorithm (GA) performance. In many cases, this correlation can be used to predict the performance of a GA on problems with known global maxima. It correctly classifies easy deceptive problems as easy and difficult nondeceptive problems as difficult, indicates when Gray coding will prove better than binary coding, and is consistent with the surprises encountered when GAs were used on the Tanese and royal road functions. The FDC measure is a consequence of an investigation into the connection between GAs and heuristic search. 1 INTRODUCTION A correspondence between evolutionary algorithms and heuristic state space search is developed in (Jones, 1995b). This is based on a model of fitness landscapes as directed, labeled graphs that are closely related to the state spaces employed in heuristic search. We examine one aspect of this correspondence, the relationship between...
An Overview of Evolutionary Computation
, 1993
"... Evolutionary computation uses computational models of evolutionary processes as key elements in the design and implementation of computerbased problem solving systems. In this paper we provide an overview of evolutionary computation, and describe several evolutionary algorithms that are current ..."
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Cited by 106 (5 self)
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Evolutionary computation uses computational models of evolutionary processes as key elements in the design and implementation of computerbased problem solving systems. In this paper we provide an overview of evolutionary computation, and describe several evolutionary algorithms that are currently of interest. Important similarities and differences are noted, which lead to a discussion of important issues that need to be resolved, and items for future research.
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...
Balancing accuracy and parsimony in genetic programming
 EVOLUTIONARY COMPUTATION
, 1995
"... Genetic programming is distinguished from other evolutionary algorithms in that it uses tree representations of variable size instead of linear strings of fixed length. The flexible representation scheme is very important because it allows the underlying structure of the data to be discovered automa ..."
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Cited by 85 (18 self)
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Genetic programming is distinguished from other evolutionary algorithms in that it uses tree representations of variable size instead of linear strings of fixed length. The flexible representation scheme is very important because it allows the underlying structure of the data to be discovered automatically. One primary difficulty, however, is that the solutions may grow too bigwithout any improvement oftheir generalization ability. In this article we investigate the fundamental relationship between the performance and complexity of the evolved structures. The essence of the parsimony problem is demonstrated empirically by analyzing error landscapes of programs evolved for neural network synthesis. We consider genetic programming as a statistical inference problem and apply the Bayesian modelcomparison framework to introduce a class of fitness functions with error and complexity terms. An adaptive learning method is then presented that automatically balances the modelcomplexity factor to evolve parsimonious programs without losing the diversity of the population needed for achieving the desired training accuracy. The effectiveness of this approach is empirically shown on the induction of sigmapi neural networks for solving a realworld medical diagnosis problem as well as benchmark tasks.
Crossover or Mutation?
 Foundations of Genetic Algorithms 2
, 1992
"... Genetic algorithms rely on two genetic operators  crossover and mutation. Although there exists a large body of conventional wisdom concerning the roles of crossover and mutation, these roles have not been captured in a theoretical fashion. For example, it has never been theoretically shown that mu ..."
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Cited by 70 (3 self)
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Genetic algorithms rely on two genetic operators  crossover and mutation. Although there exists a large body of conventional wisdom concerning the roles of crossover and mutation, these roles have not been captured in a theoretical fashion. For example, it has never been theoretically shown that mutation is in some sense "less powerful" than crossover or vice versa. This paper provides some answers to these questions by theoretically demonstrating that there are some important characteristics of each operator that are not captured by the other.
A Measure of Landscapes
 Evolutionary Computation
, 1995
"... The structure of a fitness landscape is still an illdefined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the explanatory ..."
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Cited by 55 (3 self)
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The structure of a fitness landscape is still an illdefined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the explanatory and predictive value of this model, can serve as a measure for the structure of the landscape. The analysis is based on a statistical time series analysis known as the BoxJenkins approach, that, among others, estimates the autocorrelations of a time series of fitness values generated by a random walk on the landscape. From these estimates, a correlation length for the landscape can be derived. Keywords: Fitness landscapes, Correlation structure, Correlation length 1 Introduction "We need a real theory relating the structure of rugged multipeaked fitness landscapes to the flow of a population upon those landscapes. We do not yet have such a theory." This quote, from Stuart A. Kauffman [...
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
"... ..."
Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning
 Evolutionary Computation
, 2000
"... The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis ..."
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Cited by 48 (13 self)
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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.
Fitness distance correlation analysis: An instructive counterexample
 In Proceedings of the Seventh International Conference on Genetic Algorithms
, 1997
"... Fitness distance correlation (FDC) has been offered as a summary statistic with apparent success in predicting the performance of genetic algorithms for global optimization. Here, a counterexample to Hammingdistance based FDC is examined for what it reveals about how GAs work. The counterexample is ..."
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Cited by 43 (0 self)
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Fitness distance correlation (FDC) has been offered as a summary statistic with apparent success in predicting the performance of genetic algorithms for global optimization. Here, a counterexample to Hammingdistance based FDC is examined for what it reveals about how GAs work. The counterexample is a fitness function that is ‘GAeasy ’ for global optimization, but which shows no relationship between fitness and Hamming distance from the global optimum. Fitness is a function that declines with the number of switches between 0 and 1 along the bitstring. The test function is ‘GAeasy’, in that a GA using only singlepoint crossover can find the global optimum with a sample on the order of 10 ¡ 3 to 10 ¡ 9 of the points in the search space, an efficiency which increases with the size of the search space. This result confirms the suspicion that predictors for genetic algorithm performance are vulnerable if they are based on arbitrary properties of the search space, and not the actual dynamics of the genetic algorithm. The test function’s solvability by a GA is accurately predicted, however, by another property—its evolvability, the probability that the genetic operator produces offspring that are fitter than their parents. It is also accurately predicted by FDC that uses a distance measure defined by the crossover operator itself, instead of Hamming distance. Mutationbased distance measures are also investigated, and are found to predict the GA’s performance when mutation is the only genetic operator acting. A comparison is made between Hammingdistance based FDC analysis, crossoverdistance based FDC analysis, evolvability analysis, and other methods of predicting GA performance. 1