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154
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 172 (14 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
General Schema Theory for Genetic Programming with SubtreeSwapping Crossover
 In Genetic Programming, Proceedings of EuroGP 2001, LNCS
, 2001
"... In this paper a new, general and exact schema theory for genetic programming is presented. The theory includes a microscopic schema theorem applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. A more macroscopic schema ..."
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Cited by 45 (28 self)
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In this paper a new, general and exact schema theory for genetic programming is presented. The theory includes a microscopic schema theorem applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. A more macroscopic schema theorem is also provided which is valid for crossover operators in which the probability of selecting any two crossover points in the parents depends only on their size and shape. The theory is based on the notions of Cartesian node reference systems and variablearity hyperschemata both introduced here for the first time. In the paper we provide examples which show how the theory can be specialised to specific crossover operators and how it can be used to derive an exact definition of effective fitness and a sizeevolution equation for GP. 1
Towards an analytic framework for analysing the computation time of evolutionary algorithms
 Artificial Intelligence
, 2003
"... In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optim ..."
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Cited by 36 (13 self)
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In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise. This paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms. The framework is built on the absorbing Markov chain model of evolutionary algorithms. The first step towards a systematic comparative study among different EAs and their first hitting times has been made in the paper.
A Mathematical Framework for the Study of Coevolution
 Foundations of Genetic Algorithms 7
, 2003
"... Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still ..."
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Cited by 36 (11 self)
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Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still more art than science. In this paper, we present a theoretical framework for studying coevolution based on the mathematics of ordered sets.
Exact Schema Theory for Genetic Programming and Variablelength Genetic Algorithms with OnePoint Crossover
, 2001
"... A few schema theorems for Genetic Programming (GP) have been proposed in the literature in the last few years. Since they consider schema survival and disruption only, they can only provide a lower bound for the expected value of the number of instances of a given schema at the next generation rathe ..."
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Cited by 30 (16 self)
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A few schema theorems for Genetic Programming (GP) have been proposed in the literature in the last few years. Since they consider schema survival and disruption only, they can only provide a lower bound for the expected value of the number of instances of a given schema at the next generation rather than an exact value. This paper presents theoretical results for GP with onepoint crossover which overcome this problem. Firstly, we give an exact formulation for the expected number of instances of a schema at the next generation in terms of microscopic quantities. Thanks to this formulation we are then able to provide an improved version of an earlier GP schema theorem in which some (but not all) schema creation events are accounted for. Then, we extend this result to obtain an exact formulation in terms of macroscopic quantities which makes all the mechanisms of schema creation explicit. This theorem allows the exact formulation of the notion of effective fitness in GP and opens the way to future work on GP convergence, population sizing, operator biases, and bloat, to mention only some of the possibilities.
Generalisation of the limiting distribution of program sizes in treebased genetic programming and analysis of its effects on bloat
 in GECCO ’07: Proceedings of the 9th Annual Conference on Genetic and Evolutionary
, 2007
"... Abstract. We provide strong theoretical and experimental evidence that standard subtree crossover with uniform selection of crossover points pushes a population of aary GP trees towards a distribution of tree sizes of the form: Pr{n} =(1−apa) an +1 ..."
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Cited by 23 (11 self)
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Abstract. We provide strong theoretical and experimental evidence that standard subtree crossover with uniform selection of crossover points pushes a population of aary GP trees towards a distribution of tree sizes of the form: Pr{n} =(1−apa) an +1
How to analyse evolutionary algorithms
, 2002
"... Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of att ..."
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Cited by 22 (1 self)
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Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.
Group Properties of Crossover and Mutation
"... It is supposed that the finite search space Omega has certain symmetries which can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries then these operators can be described in terms of a mixing matrix and a group of permutation matrices ..."
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Cited by 19 (9 self)
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It is supposed that the finite search space Omega has certain symmetries which can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Omega are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Omega to induce a group structure on Omega itself.
Aggregating disparate estimates of chance
, 2004
"... We consider a panel of experts asked to assign probabilities to events, both logically simple and complex. The events evaluated by different experts are based on overlapping sets of variables but may otherwise be distinct. The union of all the judgments will likely be probabilistic incoherent. We ad ..."
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Cited by 19 (4 self)
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We consider a panel of experts asked to assign probabilities to events, both logically simple and complex. The events evaluated by different experts are based on overlapping sets of variables but may otherwise be distinct. The union of all the judgments will likely be probabilistic incoherent. We address the problem of revising the probability estimates of the panel so as to produce a coherent set that best represents the group’s expertise.
Some Exact Results from a Coarse Grained Formulation of Genetic Dynamics
 Proceedings of GECCO 2001
, 2001
"... We consider the dynamics of variablelength Genetic Algorithms (GAs) with strings of length � using a recently developed exact, coarsegrained formulation where the relevant coarsegrained degrees of freedom are “building block ” schemata. We derive an exact formal solution of the equations showing ..."
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Cited by 18 (11 self)
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We consider the dynamics of variablelength Genetic Algorithms (GAs) with strings of length � using a recently developed exact, coarsegrained formulation where the relevant coarsegrained degrees of freedom are “building block ” schemata. We derive an exact formal solution of the equations showing how a hierarchical structure in time and degree of coarsegraining emerges, the effect of recombination being to successively form more finegrained objects from their more coarsegrained building blocks, where in this case the building blocks can come from strings of different lengths. We examine the limit distributions of the dynamics in the case of a flat fitness landscape, onepoint homologous crossover and no mutation. By taking advantage of the existence of a set of conserved quantities in the dynamics we provide exact solutions for the cases � � and use these to investigate the phenomenon of interlengthclass allele diffusion. We also study the general case showing what exact results may be easily derived using our particular coarsegrained formulation. 1