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The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem(NPO) that arises in various fields including transportation and logistics. TheCVRP extends from the Vehicle Routing Problem (VRP), aiming to determine themost efficient plan for a fleet of vehicles to deliver goods to a set ofcustomers, subject to the limited carrying capacity of each vehicle. As thenumber of possible solutions skyrockets when the number of customers increases,finding the optimal solution remains a significant challenge. Recently, aquantum-classical hybrid algorithm known as Quantum Approximate OptimizationAlgorithm (QAOA) can provide better solutions in some cases of combinatorialoptimization problems, compared to classical heuristics. However, the QAOAexhibits a diminished ability to produce high-quality solutions for someconstrained optimization problems including the CVRP. One potential approachfor improvement involves a variation of the QAOA known as the Grover-MixerQuantum Alternating Operator Ansatz (GM-QAOA). In this work, we attempt to useGM-QAOA to solve the CVRP. We present a new binary encoding for the CVRP, withan alternative objective function of minimizing the shortest path that bypassesthe vehicle capacity constraint of the CVRP. The search space is furtherrestricted by the Grover-Mixer. We examine and discuss the effectiveness of theproposed solver through its application to several illustrative examples.

A Feasibility-Preserved Quantum Approximate Solver for the Capacitated Vehicle Routing Problem