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New variable depth local search for multiple depot vehicle scheduling problems

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Abstract

The multiple depot vehicle scheduling problem (MDVSP) is a well-known and important NP-hard problem in transport scheduling. In this study, we first provide an original interpretation of the search space of the MDVSP. Next, we present a local search algorithm which utilizes pruning and deepening techniques in the variable depth search framework. Computational results using well-known test cases show that our method achieves better results than the second-best local search based method does by 8.6–30.1 %, and exhibits the best short-term performance among the state-of-the-art methods.

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Notes

  1. Otsuki (2013) shows that there exists the case that the number of swaps required to obtain the nearest improved solution is as many as the number of trips.

  2. Here, ‘static’ pruning means that the condition is irrelevant to temporal evaluation values obtained by searching. On the other hand, ‘dynamic’ pruning means that the condition depends on the evaluation values.

  3. \(\mathrm CG\) and \(\mathrm LNS\) are implemented on the GENCOL, the commercial column generation solver and \(\mathrm LR\) on the CPLEX, the commercial mixed integer programming solver.

  4. The value 0.75 (\(\sim 1/1.33\)) is based on the fact that the computational time of Pepin et al. (2009) is 1.33 times that in Laurent and Hao (2009). The value 0.875 (\(=7/8\)) is based on the fact that X5365 3.00 GHz processor takes 7.9 (\(\sim \)8.0) s, while Xeon 2.60 GHz processor takes 7.0 s in an integer-calculation-based benchmark test in http://www32.ocn.ne.jp/~~yss/bench.html.

  5. Since optimality gaps are drawn from Laurent and Hao (2009) and Pepin et al. (2009), known best values may be out of date. However, even if we use updated known best values, the value of optimality gap should be more than the value shown.

  6. Note that these results are significant only in 10 out of 30 instances by one-sided 0.05 level t test. Since the number of test samples in Laurent and Hao (2009) is small (=5), it is difficult to increase the number of significant instances.

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Acknowledgments

This research is partially supported by the Aihara Project, the FIRST program from JSPS, initiated by CSTP.

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Authors and Affiliations

  1. Toshiba Corporation, 1, Komukai-Toshiba-cho, Saiwai-ku, Kawasaki, 212-8582, Japan

    Tomoshi Otsuki

  2. Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyou-ku, Tokyo, 113-8656, Japan

    Tomoshi Otsuki & Kazuyuki Aihara

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  1. Tomoshi Otsuki
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  2. Kazuyuki Aihara
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Correspondence to Tomoshi Otsuki.

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Otsuki, T., Aihara, K. New variable depth local search for multiple depot vehicle scheduling problems. J Heuristics 22, 567–585 (2016). https://doi.org/10.1007/s10732-014-9264-z

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