Variable neighborhood search for consistent vehicle routing problem

This article presents a variable neighborhood search (VNS) algorithm for the consistent vehicle routing problem (ConVRP). ConVRP is a variant of the vehicle routing problem (VRP). In ConVRP, vehicle routes must be designed for multiple days, and each customer must be visited by the same driver at approximately an identical time on each day. VNS is an efficient algorithmic framework and is widely used. The proposed algorithm consists of two stages. In the first stage, VNS is applied to obtain approximately optimized solutions. The solutions obtained might be infeasible. If a solution is of acceptable quality, the second stage is applied to make it feasible and optimize it further. Several techniques are employed to reduce computation time of the local search stage. A special shaking method is introduced and proofed to be more effective than ordinary methods by experiments. A new method for computing time difference excess is proposed to solve the problem that change of time difference excess caused by operations on an individual day is not obvious. The proposed algorithm is tested on the benchmark ConVRP data set and compared with extant ConVRP approaches from the literature. The results demonstrate that VNS outperforms all the extant ConVRP approaches in terms of quality of solutions obtained.