Results 1  10
of
19
Schema Theory for Genetic Programming with Onepoint Crossover and Point Mutation
 Evolutionary Computation
, 1998
"... We 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 closer to the original concept of schema in genetic algorithms (GAs). Along with ..."
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Cited by 60 (30 self)
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We 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 closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, onepoint 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. 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. 1 Introduction Genetic Programming (GP) has been applied successfully to a large number of difficult problems like automatic design, pattern recognition, robotic control, synthesis on neural architectures, symbolic regression, music and picture generation [2, 9, 10, 11, 12, 13]. However a relatively small numbe...
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
Solving HighOrder Boolean Parity Problems with Smooth Uniform Crossover, SubMachine Code GP and Demes
, 2000
"... We propose and study new search operators and a novel node representation that can make GP fitness landscapes smoother. Together with a tree evaluation method known as submachine code GP and the use of demes, these make up a recipe for solving very large parity problems using GP. We tested this rec ..."
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Cited by 25 (2 self)
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We propose and study new search operators and a novel node representation that can make GP fitness landscapes smoother. Together with a tree evaluation method known as submachine code GP and the use of demes, these make up a recipe for solving very large parity problems using GP. We tested this recipe on parity problems with up to 22 input variables, solving them with a very high success probability.
An Experimental Analysis of Schema Creation, Propagation and Disruption in Genetic Programming
, 1997
"... In this paper we first review the main results in the theory of schemata in Genetic Programming (GP) and summarise a new GP schema theory which is based on a new definition of schema. ..."
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Cited by 20 (13 self)
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In this paper we first review the main results in the theory of schemata in Genetic Programming (GP) and summarise a new GP schema theory which is based on a new definition of schema.
Smooth Uniform Crossover with Smooth Point Mutation in Genetic Programming: A Preliminary Study
 Genetic Programming, Proceedings of EuroGP’99, volume 1598 of LNCS
, 1999
"... In this paper we examine the behaviour of the uniform crossover and point mutation GP operators [12] on the evennparity problem for n = 3; 4; 6 and present a novel representation of function nodes, designed to allow the search operators to make smaller movements around the solution space. Using ..."
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Cited by 17 (9 self)
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In this paper we examine the behaviour of the uniform crossover and point mutation GP operators [12] on the evennparity problem for n = 3; 4; 6 and present a novel representation of function nodes, designed to allow the search operators to make smaller movements around the solution space. Using this representation, performance on the even6parity problem is improved by three orders of magnitude relative to the estimate given for standard GP in [5]. 1 Introduction Although a mutation operator is defined, the canonical form of Genetic Programming (GP) [4] relies almost exclusively on the crossover operator for exploring the solution space. GP crossover selects a random subtree from one parent program and splices it to a random location in another, affording GP the ability to search a space of arbitrarysized programs. Its insensitivity to position in cutting and splicing (aside of satisfying constraints on tree depth), combined with the fact that multiple instances of function n...
Size Control via Size Fair Genetic Operators in the PushGP Genetic Programming System
 In
, 2002
"... The growth of program size during evolution (code “bloat”) is a welldocumented and wellstudied problem in genetic programming. This paper examines the use of “size fair ” genetic operators to combat code bloat in the PushGP genetic programming system. Size fair operators are compared to naive oper ..."
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Cited by 10 (4 self)
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The growth of program size during evolution (code “bloat”) is a welldocumented and wellstudied problem in genetic programming. This paper examines the use of “size fair ” genetic operators to combat code bloat in the PushGP genetic programming system. Size fair operators are compared to naive operators and to operators that use “node selection” as described by Koza. The effects of the operator choices are assessed in runs on symbolic regression, parity and multiplexor problems (2,700 runs in total). The results show that the size fair operators control bloat well while producing unusually parsimonious solutions. The computational effort required to find a solution using size fair operators is about equal to, or slightly better than, the effort required using the comparison operators. 1
Maximum homologous crossover for linear genetic programming
 In Genetic Programming: 6th European Conference, Lecture Notes in Computer Science
, 2003
"... Abstract. We introduce a new recombination operator, the Maximum Homologous Crossover for Linear Genetic Programming. In contrast to standard crossover, it attempts to preserve similar structures from parents, by aligning them according to their homology, thanks to an algorithm used in BioInformati ..."
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Cited by 9 (2 self)
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Abstract. We introduce a new recombination operator, the Maximum Homologous Crossover for Linear Genetic Programming. In contrast to standard crossover, it attempts to preserve similar structures from parents, by aligning them according to their homology, thanks to an algorithm used in BioInformatics. To highlight disruptive effects of crossover operators, we introduce the Royal Road landscapes and the Homology Driven Fitness problem, for Linear Genetic Programming. Two variants of the new crossover operator are described and tested on this landscapes. Results show a reduction in the bloat phenomenon and in the frequency of deleterious crossovers. 1
Smooth Uniform Crossover, SubMachine Code GP and Demes: A Recipe For Solving HighOrder Boolean Parity Problems
 Proceedings of the Genetic and Evolutionary Computation Conference, Volume
, 1999
"... We describe a recipe to solve very large parity problems using GP. The recipe includes: smooth uniform crossover (a crossover operator inspired by our theoretical research), submachinecode GP (a technique to speed up fitness evaluation in Boolean classification problems), and interacting dem ..."
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Cited by 7 (5 self)
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We describe a recipe to solve very large parity problems using GP. The recipe includes: smooth uniform crossover (a crossover operator inspired by our theoretical research), submachinecode GP (a technique to speed up fitness evaluation in Boolean classification problems), and interacting demes (subpopulations) running on separate workstations. We tested this recipe on parity problems with up to 22 input variables, solving them with a very high success probability.
SubMachineCode GP: New Results and Extensions
 Genetic Programming, Proceedings of EuroGP'99, LNCS, Goteborg, Sweeden
, 1999
"... Submachinecode GP (SMCGP) is a technique to speed up genetic programming (GP) and to extend its scope based on the idea of exploiting the internal parallelism of sequential CPUs. In previous work [20] we have shown examples of applications of this technique to the evolution of parallel program ..."
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Cited by 4 (2 self)
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Submachinecode GP (SMCGP) is a technique to speed up genetic programming (GP) and to extend its scope based on the idea of exploiting the internal parallelism of sequential CPUs. In previous work [20] we have shown examples of applications of this technique to the evolution of parallel programs and to the parallel evaluation of 32 or 64 fitness cases per program execution in Boolean classification problems.
On the Ability to Search the Space of Programs of Standard, Onepoint and Uniform Crossover in Genetic Programming
, 1998
"... 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, ..."
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Cited by 4 (1 self)
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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, onepoint 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. Onepoint 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. 1 Introduction Genetic programming (GP) is nondeterministic search technique to explore the space of possible programs. It is very well known from the AI literature that the performance of any search algorithm depends cruci...