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Predictive Models for the Breeder Genetic Algorithm  I. Continuous Parameter Optimization
 EVOLUTIONARY COMPUTATION
, 1993
"... In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented which is derived from quantitative genetics. The model is used to predict t ..."
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Cited by 342 (25 self)
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In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented which is derived from quantitative genetics. The model is used to predict the behavior of the BGA for simple test functions. Different mutation schemes are compared by computing the expected progress to the solution. The numerical performance of the BGA is demonstrated on a test suite of multimodal functions. The number of function evaluations needed to locate the optimum scales only as n ln(n) where n is the number of parameters. Results up to n = 1000 are reported.
A ParameterLess Genetic Algorithm
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1999
"... From the user's point of view, setting the parameters of a genetic algorithm (GA) is far from a trivial task. Moreover, the user is typically not interested in population sizes, crossover probabilities, selection rates, and other GA technicalities. He is just interested in solving a problem, a ..."
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Cited by 231 (33 self)
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From the user's point of view, setting the parameters of a genetic algorithm (GA) is far from a trivial task. Moreover, the user is typically not interested in population sizes, crossover probabilities, selection rates, and other GA technicalities. He is just interested in solving a problem, and what he would really like to do, is to handin the problem to a blackbox algorithm, and simply press a start button. This paper explores the development of a GA that fulfills this requirement. It has no parameters whatsoever. The development of the algorithm takes into account several aspects of the theory of GAs, including previous research work on population sizing, the schema theorem, building block mixing, and genetic drift.
Evolutionary computation: Comments on the history and current state
 IEEE Transactions on Evolutionary Computation
, 1997
"... Abstract — Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950’s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general struc ..."
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Cited by 207 (0 self)
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Abstract — Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950’s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure, and the working principles of different approaches, including genetic algorithms (GA) [with links to genetic programming (GP) and classifier systems (CS)], evolution strategies (ES), and evolutionary programming (EP) by analysis and comparison of their most important constituents (i.e., representations, variation operators, reproduction, and selection mechanism). Finally, we give a brief overview on the manifold of application domains, although this necessarily must remain incomplete. Index Terms — Classifier systems, evolution strategies, evolutionary computation, evolutionary programming, genetic algorithms,
Niching Methods for Genetic Algorithms
, 1995
"... Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This ..."
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Cited by 191 (1 self)
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Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This study presents a comprehensive treatment of niching methods and the related topic of population diversity. Its purpose is to analyze existing niching methods and to design improved niching methods. To achieve this purpose, it first develops a general framework for the modelling of niching methods, and then applies this framework to construct models of individual niching methods, specifically crowding and sharing methods. Using a constructed model of crowding, this study determines why crowding methods over the last two decades have not made effective niching methods. A series of tests and design modifications results in the development of a highly effective form of crowding, called determin...
On the Analysis of the (1+1) Evolutionary Algorithm
 THEORETICAL COMPUTER SCIENCE
, 2002
"... Many experimental results are reported on all types of Evolutionary Algorithms but only few results have been proved. A step towards a theory on Evolutionary Algorithms, in particular, the socalled (1 + 1) Evolutionary Algorithm, is performed. Linear functions are proved to be optimized in expected ..."
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Cited by 184 (41 self)
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Many experimental results are reported on all types of Evolutionary Algorithms but only few results have been proved. A step towards a theory on Evolutionary Algorithms, in particular, the socalled (1 + 1) Evolutionary Algorithm, is performed. Linear functions are proved to be optimized in expected time O(n ln n) but only mutation rates of size #(1/n) can ensure this behavior. For some polynomial of degree 2 the optimization needs exponential time. The same is proved for a unimodal function. Both results were not expected by several other authors. Finally, a hierarchy result is proved. Moreover, methods are presented to analyze the behavior of the (1 + 1) Evolutionary Algorithm.
Convergence Analysis of Canonical Genetic Algorithms
 IEEE Transactions on Neural Networks
, 1994
"... This paper analyzes the convergence properties of the canonical genetic algorithm (CGA) with mutation, crossover and proportional reproduction applied to static optimization problems. It is proved by means of homogeneous finite Markov chain analysis that a CGA will never converge to the global optim ..."
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Cited by 173 (0 self)
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This paper analyzes the convergence properties of the canonical genetic algorithm (CGA) with mutation, crossover and proportional reproduction applied to static optimization problems. It is proved by means of homogeneous finite Markov chain analysis that a CGA will never converge to the global optimum regardless of the initialization, crossover operator and objective function. But variants of CGAs that always maintain the best solution in the population, either before or after selection, are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent CGA. These results are discussed with respect to the schema theorem. Keywords: canonical genetic algorithm, global convergence, Markov chains, schema theorem 1 Introduction Canonical genetic algorithms (CGA) as introduced in [1] are often used to tackle static optimization problems of the type maxff(b) j b 2 IB l g (1) assuming that 0 ! f(b) ! 1 for all b 2 IB l = f0; 1g l and ...
Serial and parallel genetic algorithms as function optimizers
 In Proceedings of the Fifth International Conference on Genetic Algorithms
, 1993
"... Parallel genetic algorithms are often very different from the \traditional " genetic algorithm proposed by Holland, especially with regards to population structure and selection mechanisms. In this paper we compare several parallel genetic algorithms across a wide range of optimization functions in ..."
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Cited by 122 (3 self)
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Parallel genetic algorithms are often very different from the \traditional " genetic algorithm proposed by Holland, especially with regards to population structure and selection mechanisms. In this paper we compare several parallel genetic algorithms across a wide range of optimization functions in an attempt to determine whether these changes have positive or negative impact on their problemsolving capabilities. The ndings indicate that the parallel structures perform as well as or better than standard versions, even without taking parallel hardware into account. 1
SelfAdaptation in Genetic Algorithms
 Proceedings of the First European Conference on Artificial Life
, 1992
"... Within Genetic Algorithms (GAs) the mutation rate is mostly handled as a global, external parameter, which is constant over time or exogeneously changed over time. In this paper a new approach is presented, which transfers a basic idea from Evolution Strategies (ESs) to GAs. Mutation rates are chang ..."
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Cited by 115 (2 self)
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Within Genetic Algorithms (GAs) the mutation rate is mostly handled as a global, external parameter, which is constant over time or exogeneously changed over time. In this paper a new approach is presented, which transfers a basic idea from Evolution Strategies (ESs) to GAs. Mutation rates are changed into endogeneous items which are adapting during the search process. First experimental results are presented, which indicate that environment dependent selfadaptation of appropriate settings for the mutation rate is possible even for GAs. Furthermore, the reduction of the number of external parameters of a GA is seen as a first step towards achieving a problemdependent selfadaptation of the algorithm. Introduction Natural evolution has proven to be a powerful mechanism for emergence and improvement of the living beings on our planet by performing a randomized search in the space of possible DNAsequences. Due to this knowledge about the qualities of natural evolution, some resea...
Optimal Mutation Rates in Genetic Search
"... The optimization of a single bit string by means of iterated mutation and selection of the best (a (1+1)Genetic Algorithm) is discussed with respect to three simple tness functions: The counting ones problem, a standard binary encoded integer, and a Gray coded integer optimization problem. A mutati ..."
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Cited by 114 (0 self)
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The optimization of a single bit string by means of iterated mutation and selection of the best (a (1+1)Genetic Algorithm) is discussed with respect to three simple tness functions: The counting ones problem, a standard binary encoded integer, and a Gray coded integer optimization problem. A mutation rate schedule that is optimal with respect to the success probabilityofmutation is presented for each of the objective functions, and it turns out that the standard binary code can hamper the search process even in case of unimodal objective functions. While normally a mutation rate of 1=l (where l denotes the bit string length) is recommendable, our results indicate that a variation of the mutation rate is useful in cases where the tness function is a multimodal pseudoboolean function, where multimodality may be caused by the objective function as well as the encoding mechanism.
The Science of Breeding and its Application to the Breeder Genetic Algorithm BGA
 EVOLUTIONARY COMPUTATION
, 1994
"... The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection eq ..."
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Cited by 100 (23 self)
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The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection equation and the concept of heritability can be applied to predict the behavior of the BGA. Selection, recombination and mutation are analyzed within this framework. It is shown that recombination and mutation are complementary search operators. The theoretical results are obtained under the assumption of additive gene effects. For general fitness landscapes regression techniques for estimating the heritability are used to analyze and control the BGA. The method of decomposing the genetic variance into an additive and a nonadditive part connects the case of additive fitness functions with the general case.