A decentralized heuristic for multi-depot split-delivery vehicle routing problem

We introduce a Multi-Point Stochastic Insertion Cost Gradient Descent (MuPSICGD) heuristic algorithm to solve multi-depot split-delivery vehicle routing problem (MDSD-VRP) through an innovative approach. We also describe two solution improvement techniques that can further enhance a fairly good solution. Our contribution is threefold: First we present a heuristic-based mechanism to solve multi-depot, multi-vehicle per depot routing problems in split-delivery setting. Second, unlike related meta-heuristics approaches, we construct solutions from connecting fragments. This can be very helpful in projecting a fitting solution estimate during the searching mechanism along with the potential for adaptability to exogenous events during routing execution. Third, the approach is suitable for decentralized implementation as long as the operating nodes cooperate on solving a common problem instance. In this respect, we elaborate the decentralization procedure. The proposed technique is also resilient to the loss or addition of computing nodes. We also provide a case study, implementation guidelines and suitable benchmarks based on known problem instances.