Exponential-size neighborhoods for the pickup-and-delivery traveling salesman problem.
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Date
2022
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Abstract
Neighborhood search is a cornerstone of state-of-the-art traveling salesman and vehicle routing metaheuristics. While neighborhood exploration procedures are well developed for problems with individual services,
their counterparts for one-to-one pickup-and-delivery problems have been more scarcely studied. A direct
extension of classic neighborhoods is often inefficient or complex due to the necessity of jointly considering service pairs. To circumvent these issues, we introduce major improvements to existing neighborhood
searches for the pickup-and-delivery traveling salesman problem and new large neighborhoods. We show
that the classical Relocate-Pair neighborhood can be fully explored in O(n
2
) instead of O(n
3
) time. We
adapt the 4-Opt and Balas-Simonetti neighborhoods to consider precedence constraints. Moreover, we
introduce an exponential-size neighborhood called 2k-Opt, which includes all solutions generated by multiple nested 2-Opts and can be searched in O(n
2
) time using dynamic programming. We conduct extensive
computational experiments, highlighting the significant contribution of these new neighborhoods and speedup strategies within two classical metaheuristics. Notably, our approach permits to repeatedly solve small
pickup-and-delivery problem instances to optimality or near-optimality within milliseconds, and therefore it
represents a valuable tool for time-critical applications such as meal delivery or mobility on demand.
Description
Keywords
Local search, Large neighborhood search, Dynamic programming, Computational complexity
Citation
PACHECO, T. T. da S. et al. Exponential-size neighborhoods for the pickup-and-delivery traveling salesman problem. Transportation Science, v. 57, n. 2, 2022. Disponível em: <https://pubsonline.informs.org/doi/abs/10.1287/trsc.2022.1176?journalCode=trsc>. Acesso em: 06 jul. 2023.