Permutation Flowshop Scheduling by Genetic Local Search

In this paper, the landscape for the permutation flowshop scheduling problem (PFSP) with stochastic local search and a critical block-based neighbourhood structure has been investigated. Numerical experiments using small benchmark problems show that there are good correlations between the makespans of local optima, the average distances to other local optima and the distances to the known global optima. These correlations suggest the existence of a ‘big valley’ structure, where local optima occur in clusters over the landscape. An approximation method for PFSP that would make use of this big valley structure is proposed by using a critical block-based neighbourhood structure, and a genetic local search method called MSXF-GA, previously developed for the job shop scheduling problem. Computational experiments using more challenging benchmark problems demonstrate the effectiveness of the proposed method.