Note on the behaviour of an improvement heuristic on permutation and blocking flow-shop scheduling

This work deals with the permutation flow-shop scheduling problem with and without storage space between stages, where the performance criterion is the makespan. Many proposed procedures to solve these problems have an improvement phase based on the search in the pair-wise interchange neighbourhood. The authors have observed large plateaus in the solutions domain of these problems defined for this type of neighbourhood that make it difficult for the heuristics to search for a road to the optimum. An improvement heuristic is proposed, which uses two tools in order to evade these difficulties: a stochastic exploration of the neighbourhood (revolver) and a special consideration of ties. The improvement heuristic is applied, in conjunction with three adapted well-known heuristics in the literature, to the direct and inverse instances. The performance of the procedures was evaluated on nine generated sets of a thousand instances and on 90 instances from Taillard (1993). The obtained results recommend applying always the constructive heuristic procedures on the direct and inverse instance. The computational experience proves the effectiveness of the two tools implemented in the improvement phase.