Metaheuristics for the permutation flowshop problem with a weighted quadratic tardiness objective

In this paper, we consider a permutation flowshop problem, with a weighted squared tardiness objective function, which addresses an important criterion for many customers. Our objective is to find metaheuristics that can, within acceptable computational times, provide sizeable improvements in solution quality over the best existing procedure (a dispatching rule followed by an improvement method). We consider four metaheuristics, namely iterated local search (ILS), iterated greedy (IG), variable greedy (VG) and steady-state genetic algorithms (SSGA). These are known for performing well on permutation flowshops and/or on tardiness criteria. For each metaheuristic, four versions are developed, differing on the choice of initial sequence and/or local search. Additionally, four different time limits are considered. Therefore, a total of 64 sets of results are obtained. The results show that all procedures greatly outperform the best existing method. The IG procedures provide the best results, followed by the SSGA procedures. The VG methods are usually inferior to SSGA, while the ILS metaheuristics tend to be the worst performers. The four metaheuristics prove to be robust in what regards initial solution and local search method, since both have little effect on the performance of the metaheuristics. Increasing the time limit does improve the performance of all procedures. Still, a sizeable improvement is obtained even for the lowest time limit. Therefore, even under restrictive time limits, the metaheuristics greatly outperform the best existing procedure.

Automated summary

This paper addresses the permutation flowshop problem with a weighted squared tardiness objective function. Four metaheuristics are proposed to improve the solution quality over existing methods, and the results show significant improvements. The iterated greedy method proves to be the most effective, followed by the steady-state genetic algorithms. The choice of initial sequence and local search has little effect on the performance of the metaheuristics. Increasing the time limit improves the performance of all procedures.