Spatial, Temporal, and Hybrid Decompositions for Large-Scale Vehicle Routing with Time Windows

Abstract

This paper studies the use of decomposition techniques to quickly find high-quality solutions to large-scale vehicle routing problems with time windows. It considers an adaptive decomposition scheme which iteratively decouples a routing problem based on the current solution. Earlier work considered vehicle-based decompositions that partitions the vehicles across the subproblems. The subproblems can then be optimized independently and merged easily. This paper argues that vehicle-based decompositions, although very effective on various problem classes also have limitations. In particular, they do not accommodate temporal decompositions and may produce spatial decompositions that are not focused enough. This paper then proposes customer-based decompositions which generalize vehicle-based decouplings and allows for focused spatial and temporal decompositions. Experimental results on class R2 of the extended Solomon benchmarks demonstrates the benefits of the customer-based adaptive decomposition scheme and its spatial, temporal, and hybrid instantiations. In particular, they show that customer-based decompositions bring significant benefits over large neighborhood search in contrast to vehicle-based decompositions.