Quantum-Efficient Reinforcement Learning Solutions for Last-Mile On-Demand Delivery

Quantum computation has demonstrated a promising alternative to solving the NP-hard combinatorial problems. Specifically, when it comes to optimization, classical approaches become intractable to account for large-scale solutions. Specifically, we investigate quantum computing to solve the large-scale Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW). In this regard, a Reinforcement Learning (RL) framework augmented with a Parametrized Quantum Circuit (PQC) is designed to minimize the travel time in a realistic last-mile on-demand delivery. A novel problem-specific encoding quantum circuit with an entangling and variational layer is proposed. Moreover, Proximal Policy Optimization (PPO) and Quantum Singular Value Transformation (QSVT) are designed for comparison through numerical experiments, highlighting the superiority of the proposed method in terms of the scale of the solution and training complexity while incorporating the real-world constraints.