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.