Quantum-classical hybrid algorithm using quantum annealing for multi-objective job shop scheduling

TL;DR

The paper tackles multi-objective production planning for large-scale job shop scheduling, where scalarization often misses important Pareto regions. It proposes a quantum–classical hybrid that decomposes the problem into resource allocation, formulated as a QUBO solvable by quantum annealing or simulated annealing, and scheduling, solved via MILP to enforce detailed constraints. The resource-allocation QUBO uses penalties to encode objectives and constraints, while scheduling optimizes lead time through a MILP with sequencing variables and Big-$M$ linearization. Experiments on casting-inspired benchmarks show the hybrid approach yields broader, higher-quality Pareto fronts (as measured by hypervolume) than a monolithic method, with insights into robustness across annealing methods and practical implications for industrial deployment.

Abstract

Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.

Figures (6)

• Figure 1: Two modeling approaches for production planning. (a) Non-separation method and (b) separation method.
• Figure 2: Conceptual diagram of Pareto optimal set and hypervolume metric. (a) Parato solutions and (b) hypervolume.
• Figure 3: Comparison of hypervolume between the separation method and the non-separation method. Horizontal axis is the number of orders (problem size) and vertical axis is hypervolume. (a) Separation method using SA and (b) separation method using QA.
• Figure 4: Improvement rate of the separation method and the non-separation method. Horizontal axis is the number of orders (problem size) and vertical axis is the improvement rate of hypervolume.
• Figure 5: Comparison of robustness in the separation method. Horizontal axis is the number of orders (problem size) and vertical axis is hypervolume. Preturbation is the result of recalculating the schedule by replacing part of the resource allocation. (a) Separation method using SA and (b) separation method using QA.