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262
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 49 (30 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
The Island Model Genetic Algorithm: On Separability, Population Size and Convergence
 Journal of Computing and Information Technology
, 1998
"... Parallel Genetic Algorithms have often been reported to yield better performance than Genetic Algorithms which use a single large panmictic population. In the case of the Island Model genetic algorithm, it has been informally argued that having multiple subpopulations helps to preserve genetic di ..."
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Cited by 40 (0 self)
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Parallel Genetic Algorithms have often been reported to yield better performance than Genetic Algorithms which use a single large panmictic population. In the case of the Island Model genetic algorithm, it has been informally argued that having multiple subpopulations helps to preserve genetic diversity, since each island can potentially follow a different search trajectory through the search space. It is also possible that since linearly separable problems are often used to test Genetic Algorithms, that Island Models may simply be particularly well suited to exploiting the separable nature of the test problems. We explore this possibility by using the infinite population models of simple genetic algorithms to study how Island Models can track multiple search trajectories. We also introduce a simple model for better understanding when Island Model genetic algorithms may have an advantage when processing some test problems. We provide empirical results for both linearly separa...
An Overview of Evolutionary Algorithms: Practical Issues and Common Pitfalls
 Information and Software Technology
, 2001
"... An overview of evolutionary algorithms is presented covering genetic algorithms, evolution strategies, genetic programming and evolutionary programming. The schema theorem is reviewed and critiqued. Gray codes, bit representations and realvalued representations are discussed for parameter optimi ..."
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An overview of evolutionary algorithms is presented covering genetic algorithms, evolution strategies, genetic programming and evolutionary programming. The schema theorem is reviewed and critiqued. Gray codes, bit representations and realvalued representations are discussed for parameter optimization problems. Parallel Island models are also reviewed, and the evaluation of evolutionary algorithms is discussed.
A Schema Theorem for ContextFree Grammars
 In 1995 IEEE Conference on Evolutionary Computation
, 1995
"... The basic Schema Theorem for genetic algorithms is modified for a grammaticallybased learning system. A contextfree grammar is used to define a language in which each sentence is mapped to a fitness value. The derivation trees associated with these sentences are used to define the structure of sch ..."
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Cited by 39 (0 self)
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The basic Schema Theorem for genetic algorithms is modified for a grammaticallybased learning system. A contextfree grammar is used to define a language in which each sentence is mapped to a fitness value. The derivation trees associated with these sentences are used to define the structure of schemata. The effect of crossover and mutation on schemata is described. A schema theorem is developed which describes how sentences of a language are propagated during evolution. 1. Introduction The Schema Theorem for genetic algorithms (GA) [3] defines how useful structures in a population of strings are propagated during the evolution of a solution. It gives a lower bound on the propagation of schemata from one generation to the next. A GA uses a fitness function to evaluate the population, and the genetic operations of crossover and mutation to search for new strings. The fixedlength nature of GA's has been extended with genetic programming (GP) [4], which uses a treebased representati...
Comparison of linear, nonlinear, and feature selection methods for EEG signal classification
 IEEE Trans. Neural Syst. Rehabil. Eng
"... Abstract—The reliable operation of brain–computer interfaces (BCIs) based on spontaneous electroencephalogram (EEG) signals requires accurate classification of multichannel EEG. The design of EEG representations and classifiers for BCI are open research questions whose difficulty stems from the need ..."
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Cited by 35 (1 self)
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Abstract—The reliable operation of brain–computer interfaces (BCIs) based on spontaneous electroencephalogram (EEG) signals requires accurate classification of multichannel EEG. The design of EEG representations and classifiers for BCI are open research questions whose difficulty stems from the need to extract complex spatial and temporal patterns from noisy multidimensional time series obtained from EEG measurements. The highdimensional and noisy nature of EEG may limit the advantage of nonlinear classification methods over linear ones. This paper reports the results of a linear (linear discriminant analysis) and two nonlinear classifiers (neural networks and support vector machines) applied to the classification of spontaneous EEG during five mental tasks, showing that nonlinear classifiers produce only slightly better classification results. An approach to feature selection based on genetic algorithms is also presented with preliminary results of application to EEG during finger movement. Index Terms—Brain–computer interface (BCI) , electroencephalogram (EEG), feature selection, genetic algorithms (GA), neural networks, pattern classification, support vector machines (SVM). I.
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 34 (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.
Topological Interpretation of Crossover
 IN PROCEEDINGS OF THE GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE
, 2004
"... In this paper we give a representationindependent topological definition of crossover that links it tightly to the notion of fitness landscape. Building around this definition, a geometric/topological framework for evolutionary algorithms is introduced that clarifies the connection between repre ..."
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Cited by 32 (23 self)
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In this paper we give a representationindependent topological definition of crossover that links it tightly to the notion of fitness landscape. Building around this definition, a geometric/topological framework for evolutionary algorithms is introduced that clarifies the connection between representation, genetic operators, neighbourhood structure and distance in the landscape. Traditional genetic operators for binary strings are shown to fit the framework. The advantages of this interpretation are discussed
Hyperschema Theory for GP with OnePoint Crossover, Building Blocks, and Some New Results in GA Theory
 Genetic Programming, Proceedings of EuroGP 2000
, 2000
"... Two main weaknesses of GA and GP schema theorems axe that they provide only information on the expected value of the number of instances of a given schema at the next generation E[m(H,t + 1)], and they can only give a lower bound for such a quantity. This paper presents new theoretical results o ..."
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Cited by 25 (18 self)
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Two main weaknesses of GA and GP schema theorems axe that they provide only information on the expected value of the number of instances of a given schema at the next generation E[m(H,t + 1)], and they can only give a lower bound for such a quantity. This paper presents new theoretical results on GP and GA schemata which laxgely overcome these weaknesses. Firsfly, unlike previous results which concentrated on schema survival and disruption, our results extend to GP recent work on GA theory by Stephens and Waelbroeck, and make the effects and the mechanisms of schema creation explicit. This allows us to give an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. Thanks to this formulation we are then able to provide in improved version for an eaxlier GP schema theorem in which some schema creation events axe accounted for, thus obtaining a tighter bound for E[m(H, t + 1)]. This bound is a function of the selection probabilities of the schema itself and of a set of lowerorder schemata which onepoint crossover uses to build instances of the schema. This result supports the existence of building blocks in GP which, however, axe not necessaxily all short, loworder or highly fit. Building on eaxlier work, we show how Stephens and Waelbroeck 's GA results and the new GP results described in the paper can be used to evaluate schema vaxiance, signaltonoise ratio and, in general, the probability distribution of re(H, t + 1). In addition, we show how the expectation operator can be removed from the schema theorem so as to predict with a known probability whether re(H, t + 1) (rather than Elm(H, t + 1)]) is going to be above a given threshold.
A Graphical User Interface For Genetic Algorithms
, 1995
"... this paper. For a more detailed description we recommend [Gol89], [Whi93] and [SHF94]. ..."
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Cited by 23 (0 self)
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this paper. For a more detailed description we recommend [Gol89], [Whi93] and [SHF94].
Genetic Programming with OnePoint Crossover and Point Mutation
 Soft Computing in Engineering Design and Manufacturing
, 1997
"... In recent theoretical and experimental work on schemata in genetic programming we have proposed a new simpler form of crossover in which the same crossover point is selected in both parent programs. We call this operator onepoint crossover because of its similarity with the corresponding operator ..."
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Cited by 22 (14 self)
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In recent theoretical and experimental work on schemata in genetic programming we have proposed a new simpler form of crossover in which the same crossover point is selected in both parent programs. We call this operator onepoint crossover because of its similarity with the corresponding operator in genetic algorithms. One point crossover presents very interesting properties from the theory point of view. In this paper we describe this form of crossover as well as a new variant called strict onepoint crossover highlighting their useful theoretical and practical features. We also present experimental evidence which shows that onepoint crossover compares favourably with standard crossover.