Efficient feasibility checks and an adaptive large neighborhood search algorithm for the time-dependent green vehicle routing problem with time windows

In recent years, reducing emissions has been important for mitigating global warming and the effects of traffic congestion. As a variant of the green vehicle routing problem (GVRP), the time-dependent GVRP with time windows (TDGVRPTW) accounts for both time-dependent travel times and time window constraints and integrates the minimization of carbon emissions. Therefore, the TDGVRPTW is of great practical interest. In this paper, we design an effective adaptive large neighborhood search (ALNS) algorithm for solving the TDGVRPTW. The proposed algorithm uses a time discretization search (TDS) method to determine the departure time from each customer node, together with efficient feasibility checking procedures. The ALNS algorithm has been extensively tested on benchmark instances derived from the literature. The results show that, for small-size instances for which optimal solutions are known, the proposed algorithm can solve several instances to optimality and that high-quality solutions can be obtained for the instances that are not solved to optimality. For large-size instances involving up to 1000 customers, ALNS is particularly effective in computing solutions using a very limited amount of computing time.