A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands

The multi-compartment vehicle routing problem (MC-VRP) consists of designing transportation routes to satisfy the demands of a set of customers for several products that, because of incompatibility constraints, must be loaded in independent vehicle compartments. Despite its wide practical applicability the MC-VRP has not received much attention in the literature, and the few existing methods assume perfect knowledge of the customer demands, regardless of their stochastic nature. This paper extends the MC-VRP by introducing uncertainty on what it is known as the MC-VRP with stochastic demands (MC-VRPSD). The MC-VRPSD is modeled as a stochastic program with recourse and solved by means of a memetic algorithm. The proposed memetic algorithm couples genetic operators and local search procedures proven to be effective on deterministic routing problems with a novel individual evaluation and reparation strategy that accounts for the stochastic nature of the problem. The algorithm was tested on instances of up to 484 customers, and its results were compared to those obtained by a savings-based heuristic and a memetic algorithm (MA/SCS) for the MC-VRP that uses a spare capacity strategy to handle demand fluctuations. In addition to effectively solve the MC-VRPSD, the proposed MA/SCS also improved 14 best known solutions in a 40-problem testbed for the MC-VRP.