Local search methods for the flowshop scheduling problem with flowtime minimization

Flowshop scheduling is a very active research area. This problem still attracts a considerable amount of interest even after the sheer amount of available results. More precisely, the optimization objective of total flowtime minimization has been actively studied and many effective algorithms have been proposed in the last few years. New best solutions have been found for common benchmarks at a rapid pace. However, these improvements many times come at the cost of sophisticated algorithms. Complex methods hinder potential applications and are difficult to extend to small problem variations. Replicability of results is also a challenge. In this paper we examine simple and easy to implement methods that at the same time result in state-of-the-art performance. The first two proposed methods are based in the well known Iterated Local Search (ILS) and Iterated Greedy Algorithm (IGA) frameworks, which have been applied with great success to other flowshop problems. Additionally, we present extensions of these methods that work over populations, something that we refer to as population-based ILS (pILS) and population-based IGA (pIGA), respectively. We calibrate the presented algorithms by means of the Design of Experiments (DOE) approach. Extensive comparative evaluations are carried against the most recent state-of-the-art techniques for the considered problem in the literature. The results show that the presented algorithms are very effective after comprehensive computational and statistical analyses. Furthermore, we show that, despite their simplicity, the presented methods are able to improve 12 out of 120 best known solutions of Taillard’s flowshop benchmark with total flowtime criterion.