A speed-up procedure and new heuristics for the classical job shop scheduling problem: A computational evaluation

The speed-up procedure proposed for the permutation flowshop scheduling problem with makespan minimisation (commonly denoted as Taillard’s acceleration) remains, after 30 years, one of the most important and relevant studies in the scheduling literature. Since its proposal, this procedure has been included in countless approximate optimisation algorithms, and its use is mandatory for several scheduling problems. Unfortunately, despite the importance of such a procedure in solving scheduling problems, we are not aware of any related speed-up procedure proposed for the classical job-shop scheduling problem. First, this study aims to fill this gap by proposing a novel speed-up procedure for the job-shop scheduling problem with makespan minimisation, capable of reducing the complexity of insertion-based procedures $n$ times. Second, to test its performance, the procedure is embedded in a critical-path-based local search method. Furthermore, we thirdly propose five constructive and composite heuristics to obtain high-quality solutions in short time intervals. The composite heuristics apply the previous procedure to reduce their computational efforts. Finally, to complete the study, we conduct an extensive computational evaluation on 243 test instances from eight distinct benchmarks. In this evaluation, 30 heuristics are re-implemented and compared under the same computer conditions. The results indicate the superiority of the proposed approaches compared to the competitive algorithms for the problem under study.