Automatic generation of iterated greedy algorithms for the non-permutation flow shop scheduling problem with total completion time minimization

In this paper we address the non-permutation flow shop scheduling problem, a more general variant of the flow shop problem in which the machines can have different sequences of jobs. We aim to minimize the total completion time. We propose a template to generate iterated greedy algorithms, and use an automatic algorithm configuration to obtain efficient methods. This is the first automated approach in the literature for the non-permutation flow shop scheduling problem. The algorithms start by building a high-quality permutation solution, which is then improved during a second phase that generates non-permutation solutions by changing the job order on some machines. The obtained algorithms are evaluated against two well-known benchmarks from the literature. The results show that they can find better schedules than the state-of-the-art methods for both the permutation and non-permutation flow shop scheduling problems in comparable experimental conditions, as evidenced by comprehensive computational and statistical testing. We conclude that using non-permutation schedules is a viable alternative to reduce the total completion time that production managers should consider.