Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Solving the resource constrained project scheduling problem with quantum annealing

Luis Fernando Pérez Armas, Stefan Creemers, Samuel Deleplanque

Published Jul 22, 2024• 30 citations
Publisher

Abstract

Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research.

DOI
10.1038/s41598-024-67168-6

Related papers

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

Kenta Sawamura, Kensuke Araki, Naoki Maruyama +2 more

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.

quant-pharXiv:2511.03257•Nov 6, 2025•0 citations

Quantum solution for solving the Bin Packing problem

Samuel Deleplanque, Amélia Durbec, Amina El Yaagoubi

Quantum optimization shows significant potential in tackling complex combinatorial challenges, prompting our research exploration into the domain of quantum computing to address the Bin Packing Problem (BPP) through Quadratic Unconstrained Binary Optimization (QUBO) formulations. This work-in-progress paper outlines our proposal for a thorough study that encompasses classical bin packing formulations, initiating with the Mixed Integer Linear Program, followed by a comparative analysis of the corresponding QUBO representations, and adopting a structured approach of Quantum Annealing on the D-Wave machine. While our work is still in progress, continuous comparative analyses are being conducted to evaluate various QUBO formulations, derived from diverse classical bin packing models, aiming to identify the most efficient QUBO for addressing the BPP. On another front, efforts are dedicated to refining the solution process further, with a focus on enhancing the precision of the selected QUBO formulation.

International Conference on Control, Decision and Information Technologies (CoDIT)•Jul 1, 2024•1 citation

Formulations for Quantum Annealed Project Scheduling

U Kanade

Resource constrained project scheduling and related allocation tasks can be expressed as Quadratic Unconstrained Binary Optimization (QUBO) models and submitted to quantum annealers. This paper develops the QUBO formulation in detail: choice of binary variables, linear and quadratic objective terms, conversion of precedence and resource constraints into penalty functions, and calibration of penalty weights. The resulting Hamiltonian is embedded onto quantum hardware, annealed, and post-processed. Hybrid classical–quantum workflows that wrap the QUBO solver inside Monte Carlo risk analysis or a digital twin are examined. Supporting process flowcharts and energy-landscape figures illustrate every stage. The treatment remains grounded in construction and logistics applications while remaining transferable to other combinatorial domains such as ULD configuration. Keywords: QUBO formulation; quantum annealing; Ising model; penalty methods; resource-constrained project scheduling; hybrid quantum-classical; minor embedding; Monte Carlo; digital twin.

International Journal of Creative and Open Research in Engineering and Management•Aug 22, 2026•0 citations

Quantum Annealing Combinatorial Optimization (QACO)

Jincheng Zhang

This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.

•Sep 3, 2026•0 citations

Performance enhancing of hybrid quantum-classical Benders approach for MILP optimization

Sergio López-Baños, Elisabeth Lobe, Ontje Lünsdorf +1 more

Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.

quant-pharXiv:2601.14024•Jan 21, 2026•0 citations

Constraint Embedding for Solving Optimization Problems on Quantum Annealers

Tomáš Vyskočil, Hristo N. Djidjev

Quantum annealers such as the commercially available D-Wave machines are designed to natively solve quadratic unconstrained binary optimization (QUBO) problems. While most of the well-known NP-hard optimization problems can easily be formulated as quadratic binary problems, such formulations also contain constraints, which commonly are added to the objective function in the form of penalties to obtain a QUBO version. However, the standard method for defining such penalties leads to QUBOs that are dense and therefore take too much of the resources of the quantum annealer. In this paper, we describe an alternative approach to the constraint embedding problem that uses mixed-integer linear programming (MILP) and is scalable to problems of arbitrary number of variables.

IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum•May 1, 2019•2 citations
Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research.
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 optimization shows significant potential in tackling complex combinatorial challenges, prompting our research exploration into the domain of quantum computing to address the Bin Packing Problem (BPP) through Quadratic Unconstrained Binary Optimization (QUBO) formulations. This work-in-progress paper outlines our proposal for a thorough study that encompasses classical bin packing formulations, initiating with the Mixed Integer Linear Program, followed by a comparative analysis of the corresponding QUBO representations, and adopting a structured approach of Quantum Annealing on the D-Wave machine. While our work is still in progress, continuous comparative analyses are being conducted to evaluate various QUBO formulations, derived from diverse classical bin packing models, aiming to identify the most efficient QUBO for addressing the BPP. On another front, efforts are dedicated to refining the solution process further, with a focus on enhancing the precision of the selected QUBO formulation.
Resource constrained project scheduling and related allocation tasks can be expressed as Quadratic Unconstrained Binary Optimization (QUBO) models and submitted to quantum annealers. This paper develops the QUBO formulation in detail: choice of binary variables, linear and quadratic objective terms, conversion of precedence and resource constraints into penalty functions, and calibration of penalty weights. The resulting Hamiltonian is embedded onto quantum hardware, annealed, and post-processed. Hybrid classical–quantum workflows that wrap the QUBO solver inside Monte Carlo risk analysis or a digital twin are examined. Supporting process flowcharts and energy-landscape figures illustrate every stage. The treatment remains grounded in construction and logistics applications while remaining transferable to other combinatorial domains such as ULD configuration. Keywords: QUBO formulation; quantum annealing; Ising model; penalty methods; resource-constrained project scheduling; hybrid quantum-classical; minor embedding; Monte Carlo; digital twin.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.
Quantum annealers such as the commercially available D-Wave machines are designed to natively solve quadratic unconstrained binary optimization (QUBO) problems. While most of the well-known NP-hard optimization problems can easily be formulated as quadratic binary problems, such formulations also contain constraints, which commonly are added to the objective function in the form of penalties to obtain a QUBO version. However, the standard method for defining such penalties leads to QUBOs that are dense and therefore take too much of the resources of the quantum annealer. In this paper, we describe an alternative approach to the constraint embedding problem that uses mixed-integer linear programming (MILP) and is scalable to problems of arbitrary number of variables.