Hybrid flow shop scheduling with not-all-machines options via local search with controlled deterioration

•Hybrid flow shop scheduling with not-all-machines options is considered.•A novel CDLS is proposed, which is composed of two main steps•The first step is multiple neighborhood search with the prefixed number of iterations•The second is deterioration one, which control deteriorated degree on the solution quality•A simple way is used to decide the number of the used machines

In this study we consider hybrid flow shop scheduling problem with a decision referring to the number of machines to be used. A simple way is used to decide the number of the used machines. A novel local search with controlled deterioration (CDLS) is proposed, which is composed of multiple neighborhood searches with the prefixed number of iterations and deterioration step. The deterioration step tries to obtain a new current solution with the controlled deteriorated degree on the solution quality. CDLS is tested on a number of instances and the computational results show that CDLS can provide the promising results for the considered problem.