Self-adaptive perturbation and multi-neighborhood search for iterated local search on the permutation flow shop problem

• A self-adaptive perturbation for iterated local search is developed and found to be effective.
• Multi-neighborhood search performance is improved through the application of self-adaptive perturbation.
• The performance of the proposed methods are found to be superior to other compared algorithms.
• New best solutions are found for 20 benchmark instances.

The flow shop scheduling problem minimizing total flow time is a famous combinatorial optimization problem. Among the many algorithms proposed to solve this problem, iterated local search (ILS) is a simple, effective and efficient one. Research shows that the perturbation method and neighborhood structure play key roles in the performance of ILS. However, existing ILS lacks the self-adaptive ability to adjust the degree of perturbation relative to the search status. Also, only one basic insertion neighborhood is often used, greatly limiting the size of the search space and the ability to escape from a local optimum. In this work, a self-adaptive strategy is proposed, evaluating the neighborhoods around the local optimum and adjusting the perturbation strength according to this evaluation. If neighboring solutions are found to be considerably worse than the best known solution, indicating that it may be hard to escape from the local optimum, then the perturbation strength is amplified. Additionally, a swap neighborhood is incorporated with an insertion neighborhood to form a new version of multi-neighborhood search. Experimental results on benchmark instances show that the self-adaptive search performs significantly better than three state of the art algorithms, particularly when tested with extended CPU time. The multi-neighborhood search performs even better, also outperforming two state of the art variable neighborhood search algorithms, indicating that the hybrid use of insertion and swap neighborhoods is effective for the discussed problem.