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

Raoul Heese, Timothée Leleu, Sam Reifenstein, Christian Nietner, Yoshihisa Yamamoto

TL;DR

This work develops a multi-objective logistics optimization framework tailored to real-world supply chains and cast as a QUBO/Ising problem. It introduces two hybrid solvers, IQTS and HBS, that fuse problem-structure exploitation, quantum subroutines (QAOA), and classical heuristics within a scalable architecture. Preprocessing via pathfinding and feasibility reduction drastically lowers the search space, enabling large-scale instances (e.g., 48 parts, 43 sites, 29 suppliers) to be handled with 2416 binary variables. Experimental evaluation on IonQ’s Aria-1 and simulators shows competitive Pareto frontier coverage against classical baselines, while highlighting that hardware advantages are not yet realized at this scale. The study outlines clear pathways to scale with larger quantum devices and to extend the model with additional real-world constraints and alternative non-classical platforms.

Abstract

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.

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

TL;DR

This work develops a multi-objective logistics optimization framework tailored to real-world supply chains and cast as a QUBO/Ising problem. It introduces two hybrid solvers, IQTS and HBS, that fuse problem-structure exploitation, quantum subroutines (QAOA), and classical heuristics within a scalable architecture. Preprocessing via pathfinding and feasibility reduction drastically lowers the search space, enabling large-scale instances (e.g., 48 parts, 43 sites, 29 suppliers) to be handled with 2416 binary variables. Experimental evaluation on IonQ’s Aria-1 and simulators shows competitive Pareto frontier coverage against classical baselines, while highlighting that hardware advantages are not yet realized at this scale. The study outlines clear pathways to scale with larger quantum devices and to extend the model with additional real-world constraints and alternative non-classical platforms.

Abstract

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.
Paper Structure (35 sections, 53 equations, 16 figures, 1 table, 1 algorithm)

This paper contains 35 sections, 53 equations, 16 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Use case
  4. Model
  5. Problem description
  6. Problem instances
  7. Multi-Objective QCBO Model
  8. QUBO Model
  9. Methods
  10. Solver Components
  11. Informed Solution Generator (ISG)
  12. Informed Solution Fixer (ISF)
  13. Informed Solution Improver (ISI)
  14. Quantum Approximate Optimization Algorithm (QAOA)
  15. Iterative Belief Propagation (IBP)
  16. ...and 20 more sections

Figures (16)

  • Figure 1: Problem sketch: (a) The showing dependencies of all 48.0 parts with the assembled product, an aircraft, as the root. (b) Supply chain sites comprised of 43.0 production sites and 28.0 warehouses. The shown positions do not reflect geographical locations.
  • Figure 2: Sketch of the algorithmic architecture. We propose two hybrid quantum-classical solvers, IQTS (\ref{['sec:iqts']}) and HBS (\ref{['sec:hbs']}), which make use of various components: ISG (\ref{['sec:isg']}), ISF (\ref{['sec:isf']}), ISI (\ref{['sec:isi']}), QAOA (\ref{['sec:qaoa']}), IBP (\ref{['sec:ibp']}), CACm (\ref{['sec:cacm']}), DAS (\ref{['sec:das']}).
  • Figure 3: Sketch of how combines Ising solvers (, , and ) with hyperparameter tuning ().
  • Figure 4: Solutions from \ref{['exp:1']}, shown as pairwise projections of the four . Pareto-optimal solutions are highlighted. We mark two solutions, A and B, which are visualized in \ref{['fig:examplesolutions']}. Each solution represents a supply chain configuration.
  • Figure 5: Visualization of two Pareto-optimal solutions from \ref{['exp:1']}, which we call solution A and solution B. In (a) and (b), we show routes between production sites and warehouses, the thickness and color indicate cumulative costs and emissions, respectively. In (c) and (d), we show workshare fulfillments for sites and suppliers (both on the same horizontal axis, suppliers are marked). The of the two solutions are shown in \ref{['fig:pareto-e1']}.
  • ...and 11 more figures