Scatter search for mixed blocking flowshop scheduling

•A scatter search algorithm for mixed blocking permutation flowshop scheduling.•A new and effective NEH-based heuristic is used in initial solution generation.•A greedy job selection within insert and swap operators are used in local search.•Outperforms state-of-the-art algorithms on well-known benchmark problem sets. Empty or limited storage capacities between machines introduce various types of blocking constraint in the industries with flowshop environment. While large applications demand flowshop scheduling with a mix of different types of blocking, research in this area mainly focuses on using only one kind of blocking in a given problem instance. In this paper, using makespan as a criterion, we study permutation flowshops with zero capacity buffers operating under mixed blocking conditions. We present a very effective scatter search (SS) algorithm for this. At the initialisation phase of SS, we use a modified version of the well-known Nawaz, Enscore and Ham (NEH) heuristic. For the improvement method in SS, we use an Iterated Local Search (ILS) algorithm that adopts a greedy job selection and a powerful NEH-based perturbation procedure. Moreover, in the reference set update phase of SS, with small probabilities, we accept worse solutions so as to increase the search diversity. On standard benchmark problems of varying sizes, our algorithm very significantly outperforms well-known existing algorithms in terms of both the solution quality and the computing time. Moreover, our algorithm has found new upper bounds for 314 out of 360 benchmark problem instances.