Lagrange Distributions of the Second Kind and Weighted Distributions

Janardan, K. G.; Rao, B. Raja

doi:10.1137/0143021

Cited by 25 publications

(10 citation statements)

References 8 publications

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“…However, as the population undergoes repeated crossover operations, it approaches a particular limiting distribution of tree sizes. It has been hypothesized and experimentally demonstrated that this distribution, without considering the effect of selection, 1 is a Lagrange distribution of the second kind [42,43,89], where small individuals are much more frequent than the larger ones (see Fig. 1 as illustration).…”

Section: Program Size Distributions and Bloatmentioning

confidence: 98%

Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Silva

Dignum

Vanneschi

2011

Genet Program Evolvable Mach

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Bloat can be defined as an excess of code growth without a corresponding improvement in fitness. This problem has been one of the most intensively studied subjects since the beginnings of Genetic Programming. This paper begins by briefly reviewing the theories explaining bloat, and presenting a comprehensive survey and taxonomy of many of the bloat control methods published in the literature through the years. Particular attention is then given to the new Crossover Bias theory and the bloat control method it inspired, Operator Equalisation (OpEq). Two implementations of OpEq are described in detail. The results presented clearly show that Genetic Programming using OpEq is essentially bloat free. We discuss the advantages and shortcomings of each different implementation, and the unexpected effect of OpEq on overfitting. We observe the evolutionary dynamics of OpEq and address its potential to be extended and integrated into different elements of the evolutionary process.

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Section: Program Size Distributions and Bloatmentioning

confidence: 98%

Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Silva

Dignum

Vanneschi

2011

Genet Program Evolvable Mach

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“…Table 1 gives a list of some basic distributions and their size biased forms. It is seen that the size biased form belongs to the same family as the original distribution in all cases except the logarithmic series [see Rao (1965), Patil and Ord (1975), Janardhan and Rao (1983) for characterizations and examples of size biased distributions].…”

Section: Weighted Distributionsmentioning

confidence: 97%

Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?

Rao¹

1985

A Celebration of Statistics

127

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The concept of weighted distributions can be traced to the study of the effects of methods of ascertainment upon the estimation of frequencies by Fisher in 1934, and it was formulated in general terms by the author in a paper presented at the First International Symposium on Classical and Contagious Distributions held in Montreal in 1963. Since then, a number of papers have appeared on the subject. This paper reviews 'some previous work, points out, through appropriate examples, some situations where weighted distributions arise, and discusses the associated methods of statistical analysis.Weighted distributions occur in a natural way in specifying probabilities of events as observed and recorded by making adjustments to probabilities of actual occurrence of events taking into account methods of ascertainment. Failure to make such adjustments can lead to wrong conclusions.

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“…The mean tree size remains unchanged. However, as the population undergoes repeated crossover operations, it approaches a particular distribution of tree sizes (a Lagrange distribution of the second kind [25,26,55]), where small individuals are much more frequent than the larger ones. For example, crossover generates a high amount of single-node individuals.…”

Section: Crossover Biasmentioning

confidence: 99%

Dynamic limits for bloat control in genetic programming and a review of past and current bloat theories

Silva

Costa

2009

Genet Program Evolvable Mach

128

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Bloat is an excess of code growth without a corresponding improvement in fitness. This is a serious problem in Genetic Programming, often leading to the stagnation of the evolutionary process. Here we provide an extensive review of all the past and current theories regarding why bloat occurs. After more than 15 years of intense research, recent work is shedding new light on what may be the real reasons for the bloat phenomenon. We then introduce Dynamic Limits, our new approach to bloat control. It implements a dynamic limit that can be raised or lowered, depending on the best solution found so far, and can be applied either to the depth or size of the programs being evolved. Four problems were used as a benchmark to study the efficiency of Dynamic Limits. The quality of the results is highly dependent on the type of limit used: depth or size. The depth variants performed very well across the set of problems studied, achieving similar fitness to the baseline technique while using significantly smaller trees. Unlike many other methods available so far, Dynamic Limits does not require specific genetic operators, modifications in fitness evaluation or different selection schemes, nor does it add any parameters to the search process. Furthermore, its implementation is simple and its efficiency does not rely on the usage of a static upper limit. The results are discussed in the context of the newest bloat theory.

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Lagrange Distributions of the Second Kind and Weighted Distributions

Cited by 25 publications

References 8 publications

Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?

Dynamic limits for bloat control in genetic programming and a review of past and current bloat theories

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