Investigating the use of metaheuristics for solving single vehicle routing problems with time‐varying traversal costs

Metaheuristic algorithms, such as simulated annealing and tabu search, are popular solution techniques for vehicle routing problems (VRPs). These approaches rely on iterative improvements to a starting solution, involving slight alterations to the routes (ie, neighbourhood moves), moving a node to a different part of a solution, swapping nodes or inverting sections of a tour, for example. When working with standard VRPs, where the costs of the arcs do not vary with advancing time, evaluating changes to the total cost following a neighbourhood move is a simple process: simply subtract the cost of the links removed from the solution and add the costs for the new links. When a time‐varying aspect (eg, congestion) is included in the costs, these calculations become estimations rather than exact values. This paper focuses on a single vehicle routing problem, similar to the Travelling Salesman Problem, and investigates the potential for using estimation methods on simple models with time‐variant costs, mimicking the effects of road congestion.