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首页> 外文期刊>Genetic programming and evolvable machines >Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover
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Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover

机译：遗传规划的精确图式理论和马尔可夫链模型及具有同源交叉的变长遗传算法

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摘要

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.
机译：遗传编程（GP）同源交叉是一组算子，包括GP单点交叉和GP统一交叉，在此处创建后代以保留从父母那里获得的遗传材料的位置。在本文中，我们为GP和可变长度遗传算法（GA）提供了一种精确的模式理论，适用于此类算子。该理论基于GP交叉掩码和GP重组分布的概念，这些概念是GA理论和群体遗传学中使用的相应概念以及超模式和结点参考系统的概念的概括，这些概念在处理时特别需要可变大小的表示形式。在本文中，我们还提出了具有同源交叉的GP和变长GA的马尔可夫链模型。我们通过将Vose模型用于GA的核心与刚刚描述的GP模式理论结合使用来获得此结果。然后，该模型专用于GP在0/1树上运行的情况：二进制字符串概念的树式概括。对于这些，存在可以用来获得进一步简化的对称性。在没有突变的情况下，此处介绍的马尔可夫链模型将Vose的GA模型推广到GP和可变长度GA。同样，我们的图式理论可以概括和完善GP和GA理论中的各种先前结果。

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