Loading is the Key: A Novel Genetic Quantum Algorithm for SDVRP

This paper solves Split Demand Vehicle Routing Problem with minimal vehicles and controlled task splits. Our algorithm encodes the mapping between task splits and vehicles into a binary matrix and uses Genetic Quantum Algorithm to control the evolvement process. To convert the binary matrix solution into task loading schemes, we design a novel cost function and successfully convert task assignment problem to Transportation Problem which can be solved by Transportation Simplex Method. Our algorithm uses a simple nearest-neighborhood based heuristic to generate vehicle routes and adopts a local search method tailored for SDVRP to improve solution quality. The experimental results show that our algorithm splits few tasks and can obtain many solutions better than CVRP best-known in TSPLIB 95. Further analysis reveals that savings of SDVRP mostly come from CVRP’s failure to combine tasks geographically close into one route, when the number of vehicles are restricted to minimum.