Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness
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We present an Iterated Local Search (ILS) algorithm for solving the single-machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness. The proposed ILS algorithm exhibits several distinguishing features, including a new neighborhood structure called Block Move and a fast incremental evaluation technique, for evaluating neighborhood solutions. Applying the proposed algorithm to solve 120 public benchmark instances widely used in the literature, we achieve highly competitive results compared with a recently proposed exact algorithm and five sets of best solutions of state-of-the-art metaheuristic algorithms in the literature. Specifically, ILS obtains the optimal solutions for 113 instances within a reasonable time, and it outperforms the previous best-known results obtained by metaheuristic algorithms for 34 instances and matches the best results for 82 instances. In addition, ILS is able to obtain the optimal solutions for the remaining seven instances under a relaxed time limit, and its computational efficiency is comparable with the state-of-the-art exact algorithm by Tanaka and Araki (Comput Oper Res 40:344–352, 2013). Finally, on analyzing some important features that affect the performance of ILS, we ascertain the significance of the proposed Block Move neighborhood and the fast incremental evaluation technique.
KeywordsSingle-machine scheduling Total weighted tardiness Sequence dependent setup Iterated Local Search Block Move
The authors thank four anonymous referees for their many helpful comments on earlier versions of our article. The research was supported in part by the Hong Kong Scholars Program, The Hong Kong Polytechnic University under Grant number G-YZ07, The National Natural Science Foundation of China under Grant number 61100144, and The Program for New Century Excellent Talents in University (NCET).
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