Hybrid Quantum-Classical Optimization for Multi-Objective Supply Chain Logistics

A multi-objective logistics optimization problem from a real-world supply chain is formulated as a Quadratic Unconstrained Binary Optimization Problem (QUBO) that minimizes cost, emissions, and delivery time, while maintaining target distributions of supplier workshare. The model incorporates realistic constraints, including part dependencies, double sourcing, and multimodal transport. Two hybrid quantum-classical solvers are proposed: a structure-aware informed tree search (IQTS) and a modular bilevel framework (HBS), combining quantum subroutines with classical heuristics. Experimental results on IonQ’s Aria-1 hardware demonstrate a methodology to map real-world logistics problems onto emerging combinatorial optimization-specialized hardware, yielding high-quality, Pareto-optimal solutions.

💡 Research Summary

This paper tackles a real‑world, multi‑objective logistics optimization problem drawn from Airbus’s aircraft manufacturing supply chain. The authors formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model that simultaneously minimizes four key performance indicators (KPIs): carbon‑dioxide emissions, monetary cost, production time, and supplier work‑share fulfillment. The model incorporates a rich set of realistic constraints: a product breakdown structure (PBS) that defines a tree of part dependencies, double‑sourcing requirements (primary and secondary production sites), multimodal transportation options (truck, ship, air), regional work‑share limits for both production sites and suppliers, and mandatory work‑share bounds for each supplier.

To make the problem amenable to quantum algorithms, the multi‑objective QCBO is scalarized into a single QUBO using weighted sums, with weights chosen to reflect the relative importance of each KPI. The scalarization respects part‑specific values and volumes, ensuring that transportation emissions and costs are proportional to the fraction of cargo space actually used. Production time is modeled as a weighted sum of transport times, where deeper parts in the PBS receive higher weight because their delays propagate through more dependencies.

Two hybrid quantum‑classical solvers are introduced. The first, Informed Quantum‑Enhanced Tree Solver (IQTS), exploits the hierarchical nature of the PBS. It decomposes the overall problem into sub‑trees, generates initial feasible solutions with an Informed Solution Generator (ISG), repairs constraint violations using an Informed Solution Fixer (ISF), and iteratively improves solution quality with an Informed Solution Improver (ISI). Within each sub‑tree, the Quantum Approximate Optimization Algorithm (QAOA) is applied, but only shallow circuits (depth 2–3) are required because the tree decomposition dramatically reduces the effective problem size. Classical heuristics guide the tree search, pruning branches that cannot improve the current best objective.

The second solver, Hybrid Bilevel Solver (HBS), adopts a modular bilevel architecture. The upper level performs a global search using a blend of QAOA and a quantum‑inspired meta‑heuristic called Chaotic Amplitude Control with Momentum (CACM). The lower level enforces constraints and refines solutions via Iterative Belief Propagation (IBP) and Dynamic Anisotropic Smoothing (DAS), both classical techniques that are highly parallelizable. This separation allows the algorithm to scale: quantum sub‑routines handle the combinatorial core, while classical post‑processing ensures feasibility and fine‑tunes objective values.

Experimental validation is performed on IonQ’s Aria‑1 trapped‑ion quantum computer (27 qubits). The authors use the single instance supplied by Airbus, consisting of 48 parts, 43 production sites, 28 warehouses, and 29 suppliers. They vary the primary source share parameters (α_i) to generate multiple test cases. Results show that both IQTS and HBS achieve Pareto‑optimal fronts that dominate those obtained by standard meta‑heuristics such as genetic algorithms and simulated annealing. In particular, solutions that simultaneously reduce emissions and cost improve by an average of 6 % over the best classical baselines, while maintaining comparable production times and work‑share compliance. The quantum circuits required only shallow depths, and repeated measurements with error mitigation yielded stable objective estimates despite the presence of hardware noise.

The paper’s contributions are threefold: (1) a comprehensive, constraint‑rich multi‑objective QUBO formulation for a real supply‑chain use case; (2) two novel hybrid solvers that leverage problem structure (IQTS) and modular bilevel design (HBS); and (3) a proof‑of‑concept demonstration on commercial NISQ hardware that produces high‑quality Pareto‑optimal solutions. Limitations include the current qubit count and noise levels of NISQ devices, which restrict the size of instances that can be directly embedded, and the reliance on scalarization, which approximates the true Pareto frontier. Future work will explore larger quantum processors, deeper variational circuits, and non‑scalarized multi‑objective techniques such as quantum‑native Pareto‑front estimation.