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...

Starting from a mathematical reinterpretation of the classical crossover operator, a new type of crossover is introduced. The proposed new crossover operator gives better performances than the classical 1 point, 2 point or uniform crossover operators. In the paper a theorical investigation of the behaviour of the new crossover is presented. In comparison to the classical crossover operator, it ...

This paper suggests a exible framework for n-dimensional crossover, consisting of cutting, classi cation, and copying of genes. We prove that under this framework, any cutting strategy generates two equivalence classes of genes, making the framework appropriate as a crossover scheme. Three notable features of this framework are: (i) it enables more e ective use of genes' geographical linkage, (...

In this paper we present some theoretical results on two forms of multi-point crossover: n-point crossover and uniform crossover. This analysis extends the work from De long's thesis, which dealt with dis~ption of n-point crossover on 2nd order hyperplanes. We present various extensions to this theory, including 1) an analysis of the disruption of n-point crossover on kth order hyperplanes: 2) ...

We present evidence indicating that adding a crossover island greatly improves the performance of a Dynamic Island Model for Adaptive Operator Selection. Two combinatorial optimisation problems are considered: the Onemax benchmark, to prove the concept; and a real-world formulation of the course timetabling problem to test practical relevance. Crossover is added to the recently proposed dynamic...

The investigation of genetic and evolutionary algorithms on Ising model problems gives much insight into how these algorithms work as adaptation schemes. The onedimensional Ising model with periodic boundary conditions has been considered as a typical example with a clear building block structure suited well for two-point crossover. It has been claimed that GAs based on recombination and approp...

Exploration of the search space occurs at the cost of destructing existing good solutions. This cost will grow as the search progresses. The parametric uniform crossover is a general form of the uniform crossover operator. Using this operator, it would be possible to control the swapping probability of each locus. An adaptive method proposed that control the value of the exchange probability of...

After decades of success, research on evolutionary algorithms aims at developing a sound theory that describes and predict the behavior of these algorithms. One research topic of interest is the analysis of the role of crossover and recombination in genetic algorithms, especially since various papers come to diierent conclusions. The goals of this paper are to revisit some well-known concepts a...

In certain organisms, numbers of crossover events for any single chromosome are limited ("crossover interference") so that double crossover events are obtained at much lower frequencies than would be expected from the simple product of independent single-crossover events. We present a number of observations during which we examined interference over a large region of Caenorhabditis elegans chro...

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as basis for geometric crossover, one can design new crossovers for any representation. In previous work we have applied geometric crossover to simple permutations. In t...