Constrained Quadratic Model Formulations for MDCVRPTW: Quantum Vs Classical

The Vehicle Routing Problem is a combinatorial optimization problem of immense practical importance, and has been studied extensively in the past. In this paper, we discuss classical and quantum approaches to the Multi-Depot Capacitated Vehicle Routing Problem with Time Windows (MDCVRPTW) using node based and time expanded formulations. The MD-CVRPTW that we study has additional features like multiple pairs of depots for different vehicles and non-overlapping routes. We pose this problem as Constrained Quadratic Model problem and use CPLEX for the classical approach and DWave's hybrid quantum-classical solver for the quantum approach. Initial empirical results suggest that the quantum approach outperforms the classical approach in terms of quality of solution for comparable running times.