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Riccardo Poli
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Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2014) 22 (1): 159–188.
Published: 01 March 2014
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Several previous studies have focused on modelling and analysing the collective dynamic behaviour of population-based algorithms. However, an empirical approach for identifying and characterising such a behaviour is surprisingly lacking. In this paper, we present a new model to capture this collective behaviour, and to extract and quantify features associated with it. The proposed model studies the topological distribution of an algorithm's activity from both a genotypic and a phenotypic perspective, and represents population dynamics using multiple levels of abstraction. The model can have different instantiations. Here it has been implemented using a modified version of self-organising maps. These are used to represent and track the population motion in the fitness landscape as the algorithm operates on solving a problem. Based on this model, we developed a set of features that characterise the population's collective dynamic behaviour. By analysing them and revealing their dependency on fitness distributions, we were then able to define an indicator of the exploitation behaviour of an algorithm. This is an entropy-based measure that assesses the dependency on fitness distributions of different features of population dynamics. To test the proposed measures, evolutionary algorithms with different crossover operators, selection pressure levels and population handling techniques have been examined, which lead populations to exhibit a wide range of exploitation-exploration behaviours.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2013) 21 (4): 533–560.
Published: 01 November 2013
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Modeling the behavior of algorithms is the realm of evolutionary algorithm theory. From a practitioner's point of view, theory must provide some guidelines regarding which algorithm/parameters to use in order to solve a particular problem. Unfortunately, most theoretical models of evolutionary algorithms are difficult to apply to realistic situations. However, in recent work (Graff and Poli, 2008 , 2010 ), where we developed a method to practically estimate the performance of evolutionary program-induction algorithms (EPAs), we started addressing this issue. The method was quite general; however, it suffered from some limitations: it required the identification of a set of reference problems, it required hand picking a distance measure in each particular domain, and the resulting models were opaque, typically being linear combinations of 100 features or more. In this paper, we propose a significant improvement of this technique that overcomes the three limitations of our previous method. We achieve this through the use of a novel set of features for assessing problem difficulty for EPAs which are very general, essentially based on the notion of finite difference. To show the capabilities or our technique and to compare it with our previous performance models, we create models for the same two important classes of problems—symbolic regression on rational functions and Boolean function induction—used in our previous work. We model a variety of EPAs. The comparison showed that for the majority of the algorithms and problem classes, the new method produced much simpler and more accurate models than before. To further illustrate the practicality of the technique and its generality (beyond EPAs), we have also used it to predict the performance of both autoregressive models and EPAs on the problem of wind speed forecasting, obtaining simpler and more accurate models that outperform in all cases our previous performance models.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2007) 15 (1): 95–131.
Published: 01 March 2007
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This is the second part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. In Part I, we derived both microscopic and coarse-grained evolution equations for strings and schemata for a selecto-recombinative GA using generalised recombination, and we explained the hierarchical nature of the schema evolution equations. In this part, we provide a variety of fixed points for evolution in the case where recombination is used alone, thereby generalising Geiringer's theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2006) 14 (4): 411–432.
Published: 01 December 2006
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This is the first part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings, where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals that the notion of schema emerges naturally from the model's equations. In Part I, after describing and characterising the notion of generalised recombination, we derive both microscopic and coarse-grained evolution equations for strings and schemata and illustrate their features with simple examples. Also, we explain the hierarchical nature of the schema evolution equations and show how the theory presented here generalises past work in evolutionary computation. In Part II, the study provides a variety of fixed points for evolution in the case where recombination is used alone, which generalise Geiringer's theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2006) 14 (1): v.
Published: 01 March 2006
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2003) 11 (2): 169–206.
Published: 01 June 2003
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This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)). Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. The theory is based on a Cartesian node reference system, introduced in Part I, and on the notion of a variable-arity hyperschema, introduced here, which generalises previous definitions of a schema. The theory includes two main theorems describing the propagation of GP schemata: a microscopic and a macroscopic schema theorem. The microscopic version is applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. Therefore, this theorem is applicable to Koza's GP crossover with and without uniform selection of the crossover points, as well as one-point crossover, size-fair crossover, strongly-typed GP crossover, context-preserving crossover and many others. The macroscopic version is applicable to crossover operators in which the probability of selecting any two crossover points in the parents depends only on the parents' size and shape. In the paper we provide examples, we show how the theory can be specialised to specific crossover operators and we illustrate how it can be used to derive other general results. These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2003) 11 (1): 53–66.
Published: 01 March 2003
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This is the first part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover. The theory is based on a Cartesian node reference system which makes it possible to describe programs as functions over the space N 2 and allows one to model the process of selection of the crossover points of subtree-swapping crossovers as a probability distribution over N 4 . In Part I, we present these notions and models and show how they can be used to calculate useful quantities. In Part II we will show how this machinery, when integrated with other definitions, such as that of variable-arity hyperschema, can be used to construct a general and exact schema theory for the most commonly used types of GP
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (1998) 6 (3): 231–252.
Published: 01 September 1998
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We review the main results obtained in the theory of schemata in genetic programming (GP), emphasizing their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP, which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation, this concept of schema has been used to derive an improved schema theorem for GP that describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.