A Hybrid Discrete Differential Evolution Approach for the Single Machine Total Stepwise Tardiness Problem with Release Dates

In this paper, a novel hybrid discrete differential evolution based approach is proposed to address a single machine scheduling problem where each job has a release date and the tardiness cost of the job increases stepwise with respect to various due dates. In the literature, this problem is termed as the single machine total stepwise tardiness problem with release dates (SMTSTP-R). The objective of the problem is to find a schedule of jobs which minimizes the total tardiness cost. The stepwise increase in tardiness cost is more prevalent in several real life scenario, especially in transportation. We have used two constructive heuristics and concept of opposition based solutions to generate initial population. Our proposed approach uses a series of local searches to further enhance the quality of solutions obtained by the proposed discrete differential evolution approach. In order to justify the superiority of proposed approach, various comparisons are done with the existing approaches available in the literature. The results of these comparisons validate the superiority of our approach in comparison to the existing state-of-the-art approaches.