LCS-Based Selective Route Exchange Crossover for the Pickup and Delivery Problem with Time Windows
The pickup and delivery problem with time windows (PDPTW) is an NP-hard discrete optimization problem of serving transportation requests using a fleet of homogeneous trucks. Its main objective is to minimize the number of vehicles, and the secondary objective is to minimize the distance traveled during the service. In this paper, we propose the longest common subsequence based selective route exchange crossover (LCS-SREX), and apply this operator in the memetic algorithm (MA) for the PDPTW. Also, we suggest the new solution representation which helps handle the crossover efficiently. Extensive experimental study performed on the benchmark set showed that using LCS-SREX leads to very high-quality feasible solutions. The analysis is backed with the statistical tests to verify the importance of the elaborated results. Finally, we report one new world’s best routing schedule found using a parallel version of the MA exploiting LCS-SREX.
KeywordsMemetic algorithm LCS Crossover PDPTW
This research was supported by the National Science Centre under research Grant No. DEC-2013/09/N/ST6/03461, and performed using the Intel CPU and Xeon Phi platforms provided by the MICLAB project No. POIG.02.03.00.24-093/13.
- 3.Kececi, B., Altiparmak, F., Kara, I.: A hybrid constructive mat-heuristic algorithm for the heterogeneous vehicle routing problem with simultaneous pick-up and delivery. In: Chicano, F., Hu, B., García-Sánchez, P. (eds.) EvoCOP 2016. LNCS, vol. 9595, pp. 1–17. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-30698-8_1 CrossRefGoogle Scholar
- 11.Zhou, C., Tan, Y., Liao, L., Liu, Y.: Solving multi-vehicle pickup and delivery with time widows by new construction heuristic. In: Procedings of CISDA, pp. 1035–1042 (2006)Google Scholar
- 14.Nalepa, J., Blocho, M.: Enhanced guided ejection search for the pickup and delivery problem with time windows. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, T.-P. (eds.) ACIIDS 2016. LNCS (LNAI), vol. 9621, pp. 388–398. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49381-6_37 CrossRefGoogle Scholar
- 16.Nagata, Y., Kobayashi, S.: A memetic algorithm for the pickup and delivery problem with time windows using selective route exchange crossover. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 536–545. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-15844-5_54 Google Scholar
- 18.Kalina, P., Vokrinek, J.: Parallel solver for vehicle routing and pickup and delivery problems with time windows based on agent negotiation. In: Proceedings of IEEE SMC, pp. 1558–1563 (2012)Google Scholar
- 20.Blocho, M., Nalepa, J.: A parallel algorithm for minimizing the fleet size in the pickup and delivery problem with time windows. In: Proceedings of 22nd European MPI Users’ Group Meeting, EuroMPI 2015, pp. 15:1–15:2. ACM, New York (2015)Google Scholar
- 21.Nalepa, J., Blocho, M.: A parallel algorithm with the search space partition for the pickup and delivery with time windows. In: Proceedings of 3PGCIC, pp. 92–99 (2015)Google Scholar
- 23.Szudzik, M.: An Elegant Pairing Function. Wolfram Research, Champaign (2006). pp. 1–12Google Scholar