On the Limiting Distribution of Program Sizes in Tree-Based Genetic Programming

Poli, Roberto; Langdon, William B.; Dignum, Stephen

doi:10.1007/978-3-540-71605-1_18

Cited by 50 publications

(42 citation statements)

References 15 publications

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“…(Colour scales below each histograms.) Crossover is producing large numbers of unfit leafs (vertical lines at 540 and 600) [Poli et al, 2007]. Local convergence and the production of species is visible (esp.…”

Section: Fine Grained Diffusion Model Of Overlapping Demesmentioning

confidence: 99%

A SIMD Interpreter for Genetic Programming on GPU Graphics Cards

Langdon

Banzhaf

2008

Lecture Notes in Computer Science

105

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Abstract. Mackey-Glass chaotic time series prediction and nuclear protein classification show the feasibility of evaluating genetic programming populations directly on parallel consumer gaming graphics processing units. Using a Linux KDE computer equipped with an nVidia GeForce 8800 GTX graphics processing unit card the C++ SPMD interpretter evolves programs at Giga GP operations per second (895 million GPops). We use the RapidMind general processing on GPU (GPGPU) framework to evaluate an entire population of a quarter of a million individual programs on a non-trivial problem in 4 seconds. An efficient reverse polish notation (RPN) tree based GP is given.

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Section: Fine Grained Diffusion Model Of Overlapping Demesmentioning

confidence: 99%

A SIMD Interpreter for Genetic Programming on GPU Graphics Cards

Langdon

Banzhaf

2008

Lecture Notes in Computer Science

105

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“…For a comprehensive review on previous theories and methods, the reader is referred to the work by Silva and Costa [31]. Currently, the most plausible theory for bloat is the crossover bias theory (CBT), proposed by Dignum and Poli [5,28]. Focusing on standard Koza style GP with a tree representation [11], the CBT states that bloat is produced by the effect that subtree crossover has on the distribution of tree sizes in the population.…”

Section: Recent Advances In Bloatmentioning

confidence: 99%

“…Over the years, many bloat theories have been developed and many bloat control methods have been proposed [31,32]. One of the most promising attempts at explaining the bloat phenomenon is the crossover bias theory [5,28], that has lead to a powerful bloat control method called operator equalisation [32]. However, recent experimental results have blurred what is understood regarding the causes of bloat [29], as well as what are the best strategies that can be used to eliminate it from GP runs [7,29].…”

Section: Introductionmentioning

confidence: 99%

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Trujillo

Naredo

Martínez

2013

EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation IV

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Abstract. Bloat is one of the most interesting theoretical problems in genetic programming (GP), and one of the most important pragmatic limitations in the development of real-world GP solutions. Over the years, many theories regarding the causes of bloat have been proposed and a variety of bloat control methods have been developed. It seems that one of the underlying causes of bloat is the search for fitness; as the fitness-causes-bloat theory states, selective bias towards fitness seems to unavoidably lead the search towards programs with a large size. Intuitively, however, abandoning fitness does not appear to be an option. This paper, studies a GP system that does not require an explicit fitness function, instead it relies on behavior-based search, where programs are described by the behavior they exhibit and selective pressure is biased towards unique behaviors using the novelty search algorithm. Initial results are encouraging, the average program size of the evolving population does not increase with novelty search; i.e., bloat is avoided by focusing on novelty instead of quality.

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“…In this paper we look at the application of standard crossover with uniform selection of crossover points, an operator for which recent research [9,2] has enabled the accurate prediction of the limiting distribution in the absence of selection, i.e., when GP is applied to a flat fitness landscape. In that work, however, tree sizes are measured in terms of number of internal nodes, which is not what GP users normally want and use.…”

Section: Introductionmentioning

confidence: 99%

“…Recent research [9,2] has enabled the accurate prediction of the limiting distribution of tree sizes for Genetic Programming with standard sub-tree swapping crossover when GP is applied to a flat fitness landscape. In that work, however, tree sizes are measured in terms of number of internal nodes.…”

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confidence: 99%

Crossover, Sampling, Bloat and the Harmful Effects of Size Limits

Dignum

Poli

2008

Lecture Notes in Computer Science

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Abstract. Recent research [9,2] has enabled the accurate prediction of the limiting distribution of tree sizes for Genetic Programming with standard sub-tree swapping crossover when GP is applied to a flat fitness landscape. In that work, however, tree sizes are measured in terms of number of internal nodes. While the relationship between internal nodes and length is one-to-one for the case of a-ary trees, it is much more complex in the case of mixed arities. So, practically the length bias of subtree crossover remains unknown. This paper starts to fill this theoretical gap, by providing accurate estimates of the limiting distribution of lengths approached by tree-based GP with standard crossover in the absence of selection pressure. The resulting models confirm that short programs can be expected to be heavily resampled. Empirical validation shows that this is indeed the case. We also study empirically how the situation is modified by the application of program length limits. Surprisingly, the introduction of such limits further exacerbates the effect. However, this has more profound consequences than one might imagine at first. We analyse these consequences and predict that, in the presence of fitness, size limits may initially speed up bloat, almost completely defeating their original purpose (combating bloat). Indeed, experiments confirm that this is the case for the first 10 or 15 generations. This leads us to suggest a better way of using size limits. Finally, this paper proposes a novel technique to counteract bloat, sampling parsimony, the application of a penalty to resampling.

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On the Limiting Distribution of Program Sizes in Tree-Based Genetic Programming

Cited by 50 publications

References 15 publications

A SIMD Interpreter for Genetic Programming on GPU Graphics Cards

A SIMD Interpreter for Genetic Programming on GPU Graphics Cards

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Crossover, Sampling, Bloat and the Harmful Effects of Size Limits

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