text: 427,109,1414969834115411968,869532833764831232,Thibaut Vidal,"New exponential-size neighborhoods for the pickup-and-delivery problem. Optimal solutions are attained for most problems with up to 30 nodes in a *single* local-search descent, giving 1,000x speedup over previous algorithms! Check our paper here: <LINK> #ORMS <LINK> work with Toni Pacheco, Rafael Martinelli (@rafaelmartinel8), Tulio Toffolo (@tuliotoffolo) and Anand Subramanian (@Subjectto_) 👉@pacheco_toni",https://arxiv.org/abs/2107.05189,"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 speed-up 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 of demand. ","Exponential-Size Neighborhoods for the Pickup-and-Delivery Traveling