Enterprise AI Analysis

Quantum Reinforcement Learning (QRL) Foundations

QRL aims to enhance classical reinforcement learning by leveraging quantum mechanics (superposition, entanglement, unitary evolution) for improved representational capacity, exploration efficiency, and decision-making in high-dimensional environments. Traditional quantum approaches for VRP (e.g., VQAs, GAS) often treat it as a static problem, limited to single-vehicle scenarios, and lack dynamic decision-making capabilities.

QRL Advantages for CVRP:

• Dynamic Environments: QRL naturally accommodates changing states, like evolving customer demands after service.
• Enhanced Expressivity: Quantum representations can better capture complex dependencies and high-order correlations in combinatorial structures.
• Scalable Routing Policies: Hybrid architectures with attention mechanisms offer a promising direction for multi-vehicle interactions and dynamic constraints.

Transformer-Based Reinforcement Learning Architectures

This study implements an Advantage Actor-Critic (A2C) framework with transformer architectures, designed to capture complex relationships in the CVRP. Three variants are explored:

• Classical Pointer Network (CPN): A fully classical Transformer-based architecture using self-attention for customer context and cross-attention for vehicle-customer interactions.
• Hybrid Quantum Pointer Network (HQP): A hybrid architecture where quantum circuits (Variational Quantum Circuits - VQC) are used for encoder-decoder relational processing, while input embeddings and output layers remain classical. It uses multi-head quantum processing paths.
• Full Quantum Pointer Network (FQP): Maximizes quantum expressivity by implementing all encoder, decoder, and input embeddings via quantum circuits and amplitude encoding, allowing direct quantum-level cross-attention.

All models share the same RL formulation, environment, state representation, and reward structure, ensuring a fair comparison.

Extended Objective Functions for CVRP

Beyond minimizing total travel distance, our CVRP formulation incorporates additional components to encourage spatially coordinated and high-quality service, crucial for real-world enterprise deployment:

• Overlap Penalty: Discourages vehicles from serving customers too close to those served by others, penalizing route crossings between vehicles.
• Zone (Soft-Clustering) Penalty: Encourages each vehicle to remain close to its dynamic spatial anchor (centroid of already served customers), promoting geographically coherent service regions.
• Customer Service Reward: Provides a positive reward for successfully serving a customer, balancing distance with service quality.

This multi-objective approach biases the agents towards generating more interpretable, efficient, and robust routing solutions, essential for practical logistics operations.

Experimental Findings & Model Performance

Experiments were conducted on a CVRP instance with 20 clients and 4 vehicles over ten independent runs. Performance was assessed using three key metrics:

• Total Distance: Sum of all route distances.
• Compactness: Measure of geographical concentration of routes.
• Overlap: Degree of route intersection among vehicles.

Key Results: The Hybrid Quantum Pointer Network (HQP) demonstrated the best overall performance in minimizing total distance and significantly reducing route overlap. The Full Quantum Pointer Network (FQP) achieved the highest route compactness. While classical models showed more variability, quantum-enhanced models consistently produced more structured and coherent routing solutions, indicating a robust advantage for enterprise logistics.