Theoretically and empirically it is clear that a genetic algorithm with crossover will outperform a genetic algorithm without crossover in some fitness landscapes, and vice versa in other landscapes. Despite an extensive literature on the subject, and recent proofs of a principled distinction in the abilities of crossover and non-crossover algorithms for a particular theoretical landscape, buil...

Previous studies have shown that hitchhiking in standard GAs can cause premature convergence. In this study we show that hitchhiking also occurs in adaptive operators, specifically, selective crossover an adaptive recombination operator. We compare selective crossover with uniform crossover (a highly disruptive operator) and show that although selective crossover favours hitchhikers more than u...

We have studied the superconducting state of Sr2RuO4 under a magnetic field parallel to the superconducting plane. We show that due to a weak spin-orbit coupling, non-unitary ky(ẑ − iαŷ) state is formed right at Hc2, then changes to unitary kyẑ state, as a magnetic field is lowered. In terms of this crossover, we address the origin of the observed double peaks of specific heat and the disappear...

Motivated by a practical interpretation of the Geiringer’s theorem, we define the class of “Pure Crossovers” independently of the solution representation used and explain why they are important for both theorists and practitioners. We then give a geometric characterization of this class of operators and prove some general properties common to all pure crossovers.

An often-mentioned issue with Grammatical Evolution is that a small change in the genotype, through mutation or crossover, may completely change the meaning of all of the following genes. This paper analyses the crossover and mutation operations in GE, in particular examining the constructive or destructive nature of these operations when occurring at points throughout a genotype. The results w...

This paper develops a new crossover operator, Sequential Constructive crossover (SCX), for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The sequential constructive crossover operator constructs an offspring from a pair of parents using better edges on the basis of their values that may be present in the parents' structure maintaining the seq...

The choice of genetic operators is one way in which genetic algorithms can be tailored to speciic optimization problems. For bit represented problems, the choice of crossover operator , or the choice not to use a crossover operator, can dramatically aaect search performance. The eecacy of crossover for genetic search is governed by the relationship between the crossover biases and the search pr...

Exponential crossover in Differential Evolution (DE), which is similar to 1-point crossover in genetic algorithms, continues to be used today as a default crossover operator for DE. We demonstrate that exponential crossover exploits an unnatural feature of some widely used synthetic benchmarks such as the Rosenbrock function – dependencies between adjacent variables. We show that for standard D...