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42
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 54 (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
A Schema Theory Analysis of the Evolution of Size in Genetic Programming With Linear Representations
, 2001
"... In this paper we use the schema theory presented in [20] to better understand the changes in size distribution when using GP with standard crossover and linear structures. Applications of the theory to problems both with and without fitness suggest that standard crossover induces specific biases ..."
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Cited by 30 (17 self)
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In this paper we use the schema theory presented in [20] to better understand the changes in size distribution when using GP with standard crossover and linear structures. Applications of the theory to problems both with and without fitness suggest that standard crossover induces specific biases in the distributions of sizes, with a strong tendency to over sample small structures, and indicate the existence of strong redistribution effects that may be a major force in the early stages of a GP run. We also present two important theoretical results: An exact theory of bloat, and a general theory of how average size changes on flat landscapes with glitches. The latter implies the surprising result that a single program glitch in an otherwise flat fitness landscape is sufficient to drive the average program size of an infinite population, which may have important implications for the control of code growth.
Genetic programming for attribute construction in data mining
 Genetic Programming, Proceedings of EuroGP’2003, volume 2610 of LNCS
, 2003
"... Abstract. For a given data set, its set of attributes defines its data space representation. The quality of a data space representation is one of the most important factors influencing the performance of a data mining algorithm. The attributes defining the data space can be inadequate, making it dif ..."
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Cited by 22 (0 self)
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Abstract. For a given data set, its set of attributes defines its data space representation. The quality of a data space representation is one of the most important factors influencing the performance of a data mining algorithm. The attributes defining the data space can be inadequate, making it difficult to discover highquality knowledge. In order to solve this problem, this paper proposes a Genetic Programming algorithm developed for attribute construction. This algorithm constructs new attributes out of the original attributes of the data set, performing an important preprocessing step for the subsequent application of a data mining algorithm. 1
Problem Difficulty and Code Growth in Genetic Programming
, 2004
"... This paper investigates the relationship between code growth and problem difficulty in genetic programming. The symbolic regression problem domain is used to investigate this relationship using two different types of increased instance difficulty. Results are supported by a simplified model of genet ..."
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Cited by 22 (4 self)
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This paper investigates the relationship between code growth and problem difficulty in genetic programming. The symbolic regression problem domain is used to investigate this relationship using two different types of increased instance difficulty. Results are supported by a simplified model of genetic programming and show that increased difficulty induces higher selection pressure and less genetic diversity, which both contribute toward an increased rate of code growth.
Visualizing tree structures in genetic programming
 Genetic and Evolutionary Computation – GECCO2003, volume 2724 of LNCS
"... Abstract. This paper presents methods to visualize the structure of trees that occur in genetic programming. These methods allow for the inspection of structure of entire trees of arbitrary size. The methods also scale to allow for the inspection of structure for an entire population. Examples are g ..."
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Abstract. This paper presents methods to visualize the structure of trees that occur in genetic programming. These methods allow for the inspection of structure of entire trees of arbitrary size. The methods also scale to allow for the inspection of structure for an entire population. Examples are given from a typical problem. The examples indicate further studies that might be enabled by visualizing structure at these scales. 1
What bloat? Cartesian Genetic Programming on Boolean problems
 2001 GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE LATE BREAKING PAPERS
, 2001
"... This paper presents an empirical study of the variation of program size over time, for a form of Genetic Programming called Cartesian Genetic Programming. Two main types of Cartesian genetic programming are examined: one uses a fully connected graph, with no redundant nodes, while the other al ..."
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Cited by 18 (6 self)
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This paper presents an empirical study of the variation of program size over time, for a form of Genetic Programming called Cartesian Genetic Programming. Two main types of Cartesian genetic programming are examined: one uses a fully connected graph, with no redundant nodes, while the other allows partial connectedness and has redundant nodes. Studies are reported here for fitness based search and for a flat fitness landscape.
Modification point depth and genome growth in genetic programming
 Evolutionary Computation
, 2003
"... The evolutionary computation community has shown increasing interest in arbitrarylength representations, particularly in the field of genetic programming. A serious stumbling block to the scalability of such representations has been bloat: uncontrolled genome growth during an evolutionary run. Bloat ..."
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Cited by 16 (1 self)
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The evolutionary computation community has shown increasing interest in arbitrarylength representations, particularly in the field of genetic programming. A serious stumbling block to the scalability of such representations has been bloat: uncontrolled genome growth during an evolutionary run. Bloat appears across the evolutionary computation spectrum, but genetic programming has given it by far the largest attention. Most genetic programming models explain this phenomenon as a result of the growth of introns, areas in an individual which serve no functional purpose. This paper presents evidence which directly contradicts intron theories. The paper then uses data drawn from this evidence to propose a new model of genome growth. In this model, bloat in genetic programming is a function of the mean depth of the modification (crossover or mutation) point. Points far from the root are correspondingly less likely to hurt the child’s survivability in the next generation. The modification point is in turn strongly correlated to average parent tree size and to removed subtree size, both of which are directly linked to the size of the resulting child.
The halting probability in von Neumann architectures
 Proceedings of the 9th European Conference on Genetic Programming, volume 3905 of Lecture
, 2006
"... Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps. Simulat ..."
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Cited by 13 (4 self)
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Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps. Simulations confirm Turing complete fitness landscapes of this type hold at most a vanishingly small fraction of usable solutions. 1
Enzyme genetic programming
 In Proceedings of the 2001 Congress on Evolutionary Computation
, 2001
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