Certified Genetic Algorithms: Crossover Operators for Permutations

摘要

In the context of Genetic Algorithms, the use of permutations for representing the chromosomes, instead of the most common binary encoding, has turned out to be more natural and convenient in order to resolve some optimization problems. With the purpose of adapting the classical crossover to this special representation, several proposals can be found in the literature [2,3,8]. In this paper we use Coq to formally implement some of these crossover operators and also to verify that they satisfy the required specifications. As we have considered permutations of (possibly) repeated elements, we can cover a wider collection of applications.