Behaviour Study of an Evolutionary Design for Permutation Problems

This paper studies an evolutionary representation/crossover combination for permutation problems, which are met in many application fields. Many efficient methods exist to solve these various variants. Increasing performances of computers also permitted to tackle more complex instances. But real-life applications make new conjunctions of constraints appear every day. Then, searching new complementary ways to tackle efficiently these numerous constraints is still necessary. This paper focuses on such an approach. It deals with evolutionary algorithms, which have been already often used to solve permutation problems. It studies the behaviour of an evolutionary design, based on a Lehmer code representation coupled with a simple n-point crossover. The goal is not to propose a new problem-tailored method which provides good performances for solving a given variant of problem or for a given class of benchmarks. The paper uses various measures to study the transmission of properties from parents to children, and the behaviour in terms of exploitation and exploration. The paper gives a review on related works, illustrates the issues which remain quite ill-understood for this representation and also gives experimental results by comparison with the permutation encoding more classically used in the literature.