表型空间上几何交叉的数学统一
A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space
摘要：
几何交叉是一种与表示无关的交叉定义，它基于被解释为度量空间的搜索空间的距离。它概括了传统的交叉二进制字符串和其他重要的重组运营商最常用的表示。使用针对手头问题定制的距离，交叉的抽象定义可以用于设计新的问题特定的交叉，在搜索中嵌入问题知识。本文的动机是，基因型-表型映射可以用数学中的商空间概念进行理论解释。在本文中，我们研究了度量变换，商度量空间，从而产生了商几何交叉的概念。这是一个非常通用的概念。我们给出了许多例子的商几何交叉的应用。
英文摘要：
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover.
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