An Empirical Analysis of Time-window Relaxations in Vehicle Routing Heuristics

The contribution of infeasible solutions in heuristic searches for vehicle routing problems does not make, up to date, a consensus in the metaheuristics community. In one hand, infeasible solutions may allow to transition between structurally different feasible solutions, thus enhancing the search. In the other hand they also lead to more complex move evaluation procedures and in wider search spaces. Choices of constraint relaxations may this dramatically impact the method performance, both in terms of speed and solution quality. This paper analyzes the impact of infeasible solutions on heuristic searches through various empirical studies on local search improvement procedures for the vehicle routing problem with time windows (VRPTW). As a result of these analyses, relaxations appear clearly to have a positive impact on the solution quality. Especially, the time-window relaxation scheme of Nagata et al. (2010) clearly contributes to increase the performance of neighborhood searches for this problem.