Metaheuristics for the vehicle routing problem with stochastic demands

In the vehicle routing problem with stochastic demands a vehicle has to serve a set of customers whose exact demand is known only upon arrival at the customer's location. The objective is to find a permutation of the customers (an a priori tour) that minimizes the expected distance traveled by the vehicle. Since the objective function is computationally demanding, effective approximations of it could improve the algorithms' performance. We show that a good choice is using the length of the a priori tour as a fast approximation of the objective, to be used in the local search of the several metaheuristics analyzed. We also show that for the instances tested, our metaheuristics find better solutions with respect to a known effective heuristic and with respect to solving the problem as two related deterministic problems.