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A new scater search approach for the singe machine total weighted tardiness scheduling problem with sequence-dependent setup times

In this paper, we propose a scatter search based meta-heuristic algorithm to solve the single machine total weighted tardiness problem with sequence-dependent setup times. Both construction heuristics and random strategy based heuristics are adopted to generate the diversified population. A variable neighborhood search based local search method is adopted to improve the trial solutions and the combined solutions. To measure the diversification value between two solutions, we count the number of edges by which the two solutions differ from each other. We also propose a new strategy that the length of the reference set could be adjusted adaptively to balance the computing time and solving ability. Three different combination methods are presented to generate the new trial solutions with the solutions in the subsets. Computational results of the benchmark problems indicate that the proposed method is stable and can find 19 better solutions among the total 120 test problems than the best known solutions. The yielded average relative percentage deviations from the best known solutions and a recent scatter search algorithm were 1.98% and −3.14%.