Solving a Real-World Package Delivery Routing Problem Using Quantum Annealers

TL;DR

A quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages.

Abstract

Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations.The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.

Figures (9)

• Figure 1: A graphical step-by-step resolution of an instance composed of 14 different deliveries (D14_P1), being one of them a TP (surrounded by a red circle).
• Figure 2: General workflow of Q4RPD.
• Figure 4: A SRP instance composed of five delivery locations, and a tentative solution. Delivery location with $ID$=0 represents the starting point of the route. Delivery location with $ID$=1 represents the destination, that is, the delivery location that must be reached before a certain restricted time.
• Figure 5: General scheme of LeapCQMHybrid solver. CH = Classical Heuristic Module. QM = Quantum Module.
• Figure 6: Step-by-step resolution of D16_P1, consisting of non-priority 15 deliveries and one TP (surrounded by a red circle). Two non-priority demands belong to the same client (surrounded by a green circle), which are served by the same truck.