Fast Vehicle Routing via Knowledge Transfer in a Reproducing Kernel Hilbert Space

Abstract

Vehicle routing problems (VRPs) are essential in logistics. In the literature, many exact and heuristic optimization algorithms have been proposed to solve the VRPs. These traditional approaches, however, generally start the optimization from scratch and ignore the experiences of solving related VRPs, which may lead to unnecessary computational costs in searching repeated problems and reduce the efficiency of vehicle routing. Recently, transfer optimization (TO) has been presented to speed up vehicle routing by reusing the knowledge learned from similarly solved VRPs. However, existing TO methods build connections across VRPs in a low-dimensional Euclidean space, which has limited modeling ability in the cases of having nonlinear correlations. Keeping this in mind, this article presents a study of TO equipped with the kernel method for fast vehicle routing. In contrast to existing TO methods, in this work, the learning of connections across VRPs for knowledge transfer is conducted in a reproducing kernel Hilbert space (RKHS), which thus has greater modeling capacity in nonlinear customer relationships between VPRs. To evaluate the performance of the proposed method, comprehensive empirical studies have been conducted using well-known VRP benchmarks, against existing state-of-the-art TO methods for vehicle routing. Finally, a well-known real-world VRP application given by a routing company (Jingdong), namely, the package delivery problem (PDP), is investigated to further assess the efficacy of our proposed method.