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Riccardo Poli - One of the best experts on this subject based on the ideXlab platform.
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Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover
Genetic Programming and Evolvable Machines, 2004Co-Authors: Riccardo Poli, Nicholas Freitag Mcphee, Jonathan E. RoweAbstract:Genetic Programming (GP) homologous Crossovers are a group of operators, including GP one-Point Crossover and GP uniform Crossover, where the offspring are created preserving the position of the genetic material taken from the parents. In this paper we present an exact schema theory for GP and variable-length Genetic Algorithms (GAs) which is applicable to this class of operators. The theory is based on the concepts of GP Crossover masks and GP recombination distributions that are generalisations of the corresponding notions used in GA theory and in population genetics, as well as the notions of hyperschema and node reference systems, which are specifically required when dealing with variable size representations. In this paper we also present a Markov chain model for GP and variable-length GAs with homologous Crossover. We obtain this result by using the core of Vose's model for GAs in conjunction with the GP schema theory just described. The model is then specialised for the case of GP operating on 0/1 trees: a tree-like generalisation of the concept of binary string. For these, symmetries exist that can be exploited to obtain further simplifications. In the absence of mutation, the Markov chain model presented here generalises Vose's GA model to GP and variable-length GAs. Likewise, our schema theory generalises and refines a variety of previous results in GP and GA theory.
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general schema theory for genetic programming with subtree swapping Crossover part ii
Evolutionary Computation, 2003Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract: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 indudes 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.
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exact schema theory for gp and variable length gas with homologous Crossover
Genetic and Evolutionary Computation Conference, 2001Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract:In this paper we present a new exact schema theory for genetic programming and variable-length genetic algorithms which is applicable to the general class of homologous Crossovers. These are a group of operators, including GP one-Point Crossover and GP uniform Crossover, where the offspring are created preserving the position of the genetic material taken from the parents. The theory is based on the concepts of GP Crossover masks and GP recombination distributions (both introduced here for the first time), as well as the notions of hyperschema and node reference systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory.
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Exact Schema Theory for Genetic Programming and Variable-Length Genetic Algorithms with One-Point Crossover
Genetic Programming and Evolvable Machines, 2001Co-Authors: Riccardo PoliAbstract: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 one-Point Crossover which overcome this problem. First, we give an exact formulation for the expected number of instances of a schema at the next generation in terms of microscopic quantities. Due 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.
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exact schema theorems for gp with one Point and standard Crossover operating on linear structures and their application to the study of the evolution of size
European Conference on Genetic Programming, 2001Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract:In this paper, firstly we specialise the exact GP schema theorem for one-Point Crossover to the case of linear structures of variable length, for example binary strings or programs with arity-1 primitives only. Secondly, we extend this to an exact schema theorem for GP with standard Crossover applicable to the case of linear structures. Then we study, both mathematically and numerically, the schema equations and their fixed Points for infinite populations for both a constant and a length-related fitness function. This allows us to characterise the bias induced by standard Crossover. This is very peculiar. In the case of a constant fitness function, at the fixed-Point, structures of any length are present with non-zero probability. However, shorter structures are sampled exponentially much more frequently than longer ones.
Nicholas Freitag Mcphee - One of the best experts on this subject based on the ideXlab platform.
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Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover
Genetic Programming and Evolvable Machines, 2004Co-Authors: Riccardo Poli, Nicholas Freitag Mcphee, Jonathan E. RoweAbstract:Genetic Programming (GP) homologous Crossovers are a group of operators, including GP one-Point Crossover and GP uniform Crossover, where the offspring are created preserving the position of the genetic material taken from the parents. In this paper we present an exact schema theory for GP and variable-length Genetic Algorithms (GAs) which is applicable to this class of operators. The theory is based on the concepts of GP Crossover masks and GP recombination distributions that are generalisations of the corresponding notions used in GA theory and in population genetics, as well as the notions of hyperschema and node reference systems, which are specifically required when dealing with variable size representations. In this paper we also present a Markov chain model for GP and variable-length GAs with homologous Crossover. We obtain this result by using the core of Vose's model for GAs in conjunction with the GP schema theory just described. The model is then specialised for the case of GP operating on 0/1 trees: a tree-like generalisation of the concept of binary string. For these, symmetries exist that can be exploited to obtain further simplifications. In the absence of mutation, the Markov chain model presented here generalises Vose's GA model to GP and variable-length GAs. Likewise, our schema theory generalises and refines a variety of previous results in GP and GA theory.
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general schema theory for genetic programming with subtree swapping Crossover part ii
Evolutionary Computation, 2003Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract: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 indudes 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.
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exact schema theory for gp and variable length gas with homologous Crossover
Genetic and Evolutionary Computation Conference, 2001Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract:In this paper we present a new exact schema theory for genetic programming and variable-length genetic algorithms which is applicable to the general class of homologous Crossovers. These are a group of operators, including GP one-Point Crossover and GP uniform Crossover, where the offspring are created preserving the position of the genetic material taken from the parents. The theory is based on the concepts of GP Crossover masks and GP recombination distributions (both introduced here for the first time), as well as the notions of hyperschema and node reference systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory.
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exact schema theorems for gp with one Point and standard Crossover operating on linear structures and their application to the study of the evolution of size
European Conference on Genetic Programming, 2001Co-Authors: Riccardo Poli, Nicholas Freitag McpheeAbstract:In this paper, firstly we specialise the exact GP schema theorem for one-Point Crossover to the case of linear structures of variable length, for example binary strings or programs with arity-1 primitives only. Secondly, we extend this to an exact schema theorem for GP with standard Crossover applicable to the case of linear structures. Then we study, both mathematically and numerically, the schema equations and their fixed Points for infinite populations for both a constant and a length-related fitness function. This allows us to characterise the bias induced by standard Crossover. This is very peculiar. In the case of a constant fitness function, at the fixed-Point, structures of any length are present with non-zero probability. However, shorter structures are sampled exponentially much more frequently than longer ones.
W B Langdon - One of the best experts on this subject based on the ideXlab platform.
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schema theory for genetic programming with one Point Crossover and Point mutation
Evolutionary Computation, 1998Co-Authors: Riccardo Poli, W B LangdonAbstract: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.
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genetic programming with one Point Crossover
1998Co-Authors: Riccardo Poli, W B LangdonAbstract: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 one-Point 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 one-Point Crossover highlighting their useful theoretical and practical features. We also present experimental evidence which shows that one-Point Crossover compares favourably with standard Crossover.
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on the ability to search the space of programs of standard one Point and uniform Crossover in genetic programming
1998Co-Authors: Riccardo Poli, W B LangdonAbstract:In this paper we study and compare the search properties of different Crossover operators in genetic programming (GP) using probabilistic models and experiments to assess the amount of genetic material exchanged between the parents to generate the offspring. These operators are: standard Crossover, one-Point Crossover and a new operator, uniform Crossover. Our analysis suggests that standard Crossover is a local and biased search operator not ideal to explore the search space of programs effectively. One-Point Crossover is better in some cases as it is able to perform a global search at the beginning of a run, but it suffers from the same problems as standard Crossover later on. Uniform Crossover largely overcomes these limitations as it is global and less biased.
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genetic programming with one Point Crossover and Point mutation
: Birmingham B15 2TT UK., 1997Co-Authors: Riccardo Poli, W B LangdonAbstract: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 one-Point 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 one-Point Crossover highlighting their useful theoretical and practical features. We also present experimental evidence which shows that one-Point Crossover compares favourably with standard Crossover.
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a new schema theory for genetic programming with one Point Crossover and Point mutation
: The University of Birmingham B15 2TT UK., 1997Co-Authors: Riccardo Poli, W B LangdonAbstract:In this paper we first review the main results obtained in the theory of schemata in Genetic Programming (GP) emphasising their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP which is quite close 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 which describes the propagation of schemata from one generation to the next. In the paper 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.
P S Mohamed - One of the best experts on this subject based on the ideXlab platform.
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a real coded genetic algorithm involving a hybrid Crossover method for power plant control system design
Congress on Evolutionary Computation, 2002Co-Authors: Kwang Y Lee, P S MohamedAbstract:This paper introduces a new hybrid Crossover method for a real-coded genetic algorithm and its application to control system design of a power plant. Determining gains for controllers by using a genetic algorithm method usually involves multiple training stages. This method is not necessarily optimal. This paper applies a hybrid Crossover method in a real-coded genetic algorithm to simultaneously find gains of three PI control loops and six other coupled gains in a boiler-turbine control system. The real-coded genetic algorithm with the hybrid Crossover method has a better convergence rate when applied to this problem, as compared to other methods. A better convergence rate reduces execution time and is particularly relevant to problems having significant simulation times. A comparison between hybrid Crossover and convex Crossover in a real-coded genetic algorithm together with multi Point Crossover using a binary coded genetic algorithm has also been made.
R Naresh - One of the best experts on this subject based on the ideXlab platform.
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efficient real coded genetic algorithm to solve the non convex hydrothermal scheduling problem
International Journal of Electrical Power & Energy Systems, 2007Co-Authors: Sushil Kumar, R NareshAbstract:A simple and efficient optimisation procedure based on real coded genetic algorithm is proposed for the solution of short-term hydrothermal scheduling problem with continuous and non-smooth/non-convex cost function. The constraints like load-generation balance, unit generation limits, reservoir flow balance, reservoir physical limitations and reservoir coupling are also considered. The effectiveness of the proposed algorithm is demonstrated on a multichain-cascaded hydrothermal system that uses non-linear hydro generation function, includes water travel times between the linked reservoirs, and considers the valve Point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint-handling technique, which eliminates the need for penalty parameters. A simple strategy based on allowing infeasible solutions to remain in the population is used to maintain diversity. The same problem is also solved using binary coded genetic algorithm. The features of both algorithms are same except the Crossover and mutation operators. In real coded genetic algorithm, simulated binary Crossover and polynomial mutation are used against the single Point Crossover and bit-flipping mutation in binary coded genetic algorithm. The comparison of the two genetic algorithms reveals that real coded genetic algorithm is more efficient in terms of thermal cost minimisation for a short-term hydrothermal scheduling problem with continuous search space.