A branch-and-bound-based local search method for the flow shop problem

Abstract

It is well-known that exact branch and bound methods can only solve small or moderately sized 𝒩𝒫-hard combinatorial optimization problems. In this paper, we address the issue of embedding an approximate branch and bound algorithm into a local search framework. The resulting heuristic has been applied to the problem of finding a minimum makespan in the permutation flow shop problem. Computational experiments carried out on a large set of benchmark problems show that the proposed method consistently yields optimal or near-optimal solutions for instances with up to 200 jobs and 10 machines. In particular, for 19 instances, the heuristic produces solutions that outperform the best known ones.

Keywords:

• Local search
• branch and bound
• flow shop sequencing