Fitness landscape of the factoradic representation on the permutation flowshop scheduling problem

Abstract

Because permutation problems are particularly challenging to model and optimise, the possibility to represent solutions by means of factoradics has recently been investigated, allowing algorithms from other domains to be used. Initial results have shown that methods using factoradics can efficiently explore the search space, but also present difficulties to exploit the best areas. In the present paper, the fitness landscape of the factoradic representation and one of its simplest operator is studied on the Permutation Flowshop Scheduling Problem (PFSP). The analysis highlights the presence of many local optima and a high ruggedness, which confirms that the factoradic representations is not suited for local search. In addition, comparison with the classic permutation representation establishes that local moves on the factoradic representation are less able to lead to the global optima on the PFSP. The study ends by presenting directions for using and improving the factoradic representation.