An edge quality aware crossover operator for application to the capacitated vehicle routing problem.

Permutation type problems require vertices to be present once only in a given solution. To apply a Genetic Algorithm (GA) to permutation problems necessitates specialist crossover operators to avoid vertex repetition in offspring solutions whilst preserving parental paths or edges. However, these operators are typically blind in terms of the potential quality of a given edge relying on natural selection to ensure the quality of parental edges. Natural selection is a relative quality measure when perhaps consideration should be given to an absolute quality measure to select edges. Moreover, it is proposed that introduction of non-parental edges during crossover can be beneficial if selected using an absolute quality measure. Consequently, a novel crossover operator ER-Q is proposed that preserves parental edges whilst also exploiting edge quality. Applied to a set of Capacitated Vehicle Routing Problems (CVRP) of up to 150 vehicles ER-Q significantly improves upon blind crossover operators with results within just a few percent of the best known.