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arXiv:2610.35478

Benchmarking quantum-annealing-based approaches for factory layout planning

Xiangqian Wu, Philipp Schworm, Marcel Wagner, Jan C. Aurich

quant-phmath.OCSubmitted Oct 26, 2026• Announced Oct 27, 2026• 0 citations
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Abstract

The earlystage of factory layout planning has a direct effect on the operating costs, efficiency, and productivity of manufacturing systems. Conventional automated planning approaches often face a trade-off between solution quality and computational effort. Recent studies have investigated the potential of quantum annealing (QA) for solving factory layout planning problems. However, existing studies have mainly focused on individual QA-based formulations, whereas current hybrid QA solvers support multiple model types that combine QA and classical methods. To explore the potential of QA for factory layout planning, this paper benchmarks four QA based approaches implemented with the corresponding solvers, including an iterative binary quadratic model (IBQM), a hybrid discrete quadratic model (HDQM), a hybrid constrained quadratic model (HCQM), and a hybrid nonlinear model (HNLM). To improve scalability, an iterative decomposition strategy is developed for IBQM, while a candidate selection procedure is introduced for HDQM. The approaches are benchmarked against genetic algorithm, particle swarm optimization, and a hybrid tabu search and simulated annealing approach on 14 layout instances with different layout sizes, geometric complexity, spatial restrictions, and transport route configurations. The comparative analysis considers solution quality, computation time, and scalability. The results show that QA-based approaches achieve competitive solution quality and substantial computational advantages, reducing computation time by up to 94.51% relative to the classical reference methods. Among them, IBQM obtains the best solution quality in 78.6% of the instances, with a maximum improvement of 17.41% associated with an 81.34% reduction in computation time. These findings provide a basis for their further application in industrial layout planning.

AI Summary

The paper asks how different quantum-annealing-based formulations perform on early-stage factory layout planning, where functional units must be positioned and oriented to minimize material-flow-weighted Manhattan distances subject to geometric and spacing constraints. It compares four approaches: an iterative binary quadratic model (IBQM), and discrete quadratic, constrained quadratic, and nonlinear models solved using D-Wave’s corresponding hybrid solvers. IBQM incorporates flow-based decomposition and progressively expanded search regions; the discrete model uses candidate selection to limit its size. The benchmark comprises 14 instances with 10–75 functional units, including unequal rectangles, composite shapes, obstacles, and different transport-route configurations. Comparators are genetic algorithms, particle swarm optimization, and a tabu-search/simulated-annealing method using the same iterative BQM formulation. Reported computation times include model generation, cloud submission, execution, and result transfer. IBQM achieves the lowest transport intensity in 11 of 14 instances. Its largest reported improvement is 17.41% relative to particle swarm optimization, with 81.34% less computation time. Against the matched classical BQM approach, IBQM improves transport intensity in 12 instances, by up to 4.51%, and reduces runtime in all instances, by up to 64.75%. All tested hybrid approaches finish within 15 minutes; the three direct hybrid approaches finish within three minutes. These are solver-level comparisons involving hybrid classical–quantum resources. Stated limitations include the growth of quadratic interactions in IBQM and the discrete model, and the latter’s candidate-selection trade-off between scalability and solution quality. The study considers static layouts and a single objective; dynamic inputs, multiple objectives, and broader manufacturing structures remain future work.

Little sign of AI-generated textOverclaimsIncrementalMissing comparisonPossible error

Central claim may not hold: The claimed common-problem benchmark uses generally different transport objectives for composite units: BQM, DQM and CQM sum over constituent rectangles, while NLM uses one designated transport-center rectangle, without an explained common evaluation. The reported computation-time reductions compare completed runs with different prescribed budgets and generally different solution qualities, so they establish configuration-specific runtime savings rather than an equivalent-quality computational advantage.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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The earlystage of factory layout planning has a direct effect on the operating costs, efficiency, and productivity of manufacturing systems. Conventional automated planning approaches often face a trade-off between solution quality and computational effort. Recent studies have investigated the potential of quantum annealing (QA) for solving factory layout planning problems. However, existing studies have mainly focused on individual QA-based formulations, whereas current hybrid QA solvers support multiple model types that combine QA and classical methods. To explore the potential of QA for factory layout planning, this paper benchmarks four QA based approaches implemented with the corresponding solvers, including an iterative binary quadratic model (IBQM), a hybrid discrete quadratic model (HDQM), a hybrid constrained quadratic model (HCQM), and a hybrid nonlinear model (HNLM). To improve scalability, an iterative decomposition strategy is developed for IBQM, while a candidate selection procedure is introduced for HDQM. The approaches are benchmarked against genetic algorithm, particle swarm optimization, and a hybrid tabu search and simulated annealing approach on 14 layout instances with different layout sizes, geometric complexity, spatial restrictions, and transport route configurations. The comparative analysis considers solution quality, computation time, and scalability. The results show that QA-based approaches achieve competitive solution quality and substantial computational advantages, reducing computation time by up to 94.51% relative to the classical reference methods. Among them, IBQM obtains the best solution quality in 78.6% of the instances, with a maximum improvement of 17.41% associated with an 81.34% reduction in computation time. These findings provide a basis for their further application in industrial layout planning.
The paper asks how different quantum-annealing-based formulations perform on early-stage factory layout planning, where functional units must be positioned and oriented to minimize material-flow-weighted Manhattan distances subject to geometric and spacing constraints. It compares four approaches: an iterative binary quadratic model (IBQM), and discrete quadratic, constrained quadratic, and nonlinear models solved using D-Wave’s corresponding hybrid solvers. IBQM incorporates flow-based decomposition and progressively expanded search regions; the discrete model uses candidate selection to limit its size.
The benchmark comprises 14 instances with 10–75 functional units, including unequal rectangles, composite shapes, obstacles, and different transport-route configurations. Comparators are genetic algorithms, particle swarm optimization, and a tabu-search/simulated-annealing method using the same iterative BQM formulation. Reported computation times include model generation, cloud submission, execution, and result transfer.
IBQM achieves the lowest transport intensity in 11 of 14 instances. Its largest reported improvement is 17.41% relative to particle swarm optimization, with 81.34% less computation time. Against the matched classical BQM approach, IBQM improves transport intensity in 12 instances, by up to 4.51%, and reduces runtime in all instances, by up to 64.75%. All tested hybrid approaches finish within 15 minutes; the three direct hybrid approaches finish within three minutes. These are solver-level comparisons involving hybrid classical–quantum resources.
Stated limitations include the growth of quadratic interactions in IBQM and the discrete model, and the latter’s candidate-selection trade-off between scalability and solution quality. The study considers static layouts and a single objective; dynamic inputs, multiple objectives, and broader manufacturing structures remain future work.
Inadequately planned factory layouts can lead to higher operational costs. The planning process is time-consuming and multiple planning parameters must be considered simultaneously, leading to large solution spaces. Automated planning approaches can support the planning team in the early phases of layout planning by generating layout variants that can afterwards be further specified. Recent studies from other disciplines have shown the potential of Quantum Annealing (QA) to solve complex assignment problems within seconds. Consequently, this paper presents a first implementation of a QA-based layout planning approach and demonstrates its advantages regarding scalability, solution quality, and computing time.
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.
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.
Abstract Layout optimization problems involve finding the optimal arrangement of elements in order to maximize efficiency. For instance, the wind farm layout optimization (WFLO) problem consists of the best turbine placement to maximize energy production while minimizing wake losses. As its nonlinear and combinatorial nature makes it challenging for traditional optimization methods, alternative approaches such as quantum annealing and quantum‐classical hybrid methods offer a promising alternative for tackling such complex problems. Here, WFLO is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem using the Jensen wake model. A quantum annealer is compared, the Gurobi solver, and the Quantum Approximate Optimization Algorithm (QAOA). The quantum annealer provides solutions one order of magnitude faster than Gurobi with at most 3% lower power output, making it suitable for rapid suboptimal approximations. These findings highlight the trade‐off between the quality of the solution and the computational time and demonstrate how quantum methods, especially when combined with classical solvers, can contribute to efficient renewable energy optimization.
This study evaluates a nonlinear model (NLM) formulation for flexible job shop scheduling problems (FJSSP) using a hybrid nonlinear solver and compares achieved makespan and computing times against established binary quadratic model (BQM) approaches. The NLM formulation enables non-iterative computation across all tested problem instances, eliminating the need for decomposition required by BQM-based methods. However, solution quality remains inferior to both iterative hybrid BQM and quantum processing unit (QPU) approaches. Computational analysis reveals that the NLM approach exhibits higher computation times for smaller instances compared to iterative hybrid BQM methods but demonstrates more favorable scaling behavior between smallest and largest instances. The results suggest potential application of NLM formulations for generating initial solutions in large-scale scheduling problems. Additional findings indicate that minimal BQM energy does not necessarily correspond to minimal makespan solutions, and chain breaks in QPU implementations can occasionally yield feasible solutions.
Abstract Disassembly is the core of sustainable recovery processes, enabling the reuse, remanufacturing, and recycling of end-of-life products. Disassembly Sequence Optimization (DSO) is the key to achieving practical and efficient disassembly applications in industrial scenarios. This study presents a novel approach to DSO by leveraging Quantum Annealing (QA) through Quadratic Unconstrained Binary Optimization (QUBO) and Constrained Quadratic Model (CQM) formulations integrated with CAD-based assembly designs. The proposed methods aim to address computational challenges in industrial disassembly applications. We evaluated these methods against classical heuristics using two distinct product designs. For a smaller, denser assembly, the hybrid CQM model demonstrated superior performance in terms of solution quality and computational time. Conversely, for a larger, sparser assembly, a classical heuristic achieved better results in solution quality when constraining computational time compared to the hybrid quantum approaches. The QUBO model, although did not overcome classical, showed promise in exploring solution spaces, obtaining better solution quality than CQM for the larger problem. These findings indicate that the current practical utility of quantum annealing for DSO is influenced by problem size, structure, and hybrid workflow efficiency. Future research should focus on optimizing the balance between classical and quantum resources to further enhance efficiency. As quantum hardware continues to advance, these formulations have the potential to revolutionize sustainable manufacturing by optimizing disassembly planning with greater efficiency and adaptability to large assemblies.