An iterated greedy algorithm with optimization of partial solutions for the makespan permutation flowshop problem.

We present a new iterated greedy algorithm for the permutation flowshop problem under makespan objective.Our algorithm applies local search on partial solutions after the destruction phase.Our algorithm compares favorably with others from the literature on available benchmark sets.The experiments show that adding local search on partial solutions is crucial to obtain a new state-of-the-art algorithm. Permutation flowshop scheduling problems (PFSPs) and, in particular, the variant with the objective of minimizing makespan have received an enormous attention in scheduling research and combinatorial optimization. As a result, the algorithmic approaches to this PFSP variant have reached extremely high performance. Currently, one of the most effective algorithm for this problem is a structurally rather simple iterated greedy algorithm. In this paper, we explore the possibility of re-optimizing partial solutions obtained after the solution destruction step of the iterated greedy algorithm. We show that with this extension, the performance of the state-of-the-art algorithm for the PFSP under makespan criterion can be significantly improved and we give experimental evidence that the local search on partial solutions is the key component for the high performance of the algorithm.