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

arXiv:2603.18038

Advanced Quantum Annealing for the Bi-Objective Traveling Thief Problem: An $\varepsilon$-Constraint-based Approach

Nguyen Hoang Viet, Nguyen Xuan Tung, Trinh Van Chien, Won-Joo Hwang

quant-phcs.ITSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
arXivHTMLPDF

Abstract

This paper addresses the Bi-Objective Traveling Thief Problem (BI-TTP), a challenging multi-objective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the $\varepsilon$-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable $\varepsilon$-levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting $\varepsilon$ parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.

Comments
14 pages, 5 figures, and 3 tables. Accepted by IEEE Transactions on Quantum Engineering

Related papers

Advanced Quantum Annealing for the Biobjective Traveling Thief Problem: An $\varepsilon$-Constraint-Based Approach

Nguyen Hoang Viet, Nguyen Xuan Tung, Trinh Van Chien +1 more

This article addresses the biobjective traveling thief problem (BI-TTP), a challenging multiobjective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the $\varepsilon$ -constraint method. Specifically, we reformulate the biobjective problem into a single-objective formulation by restricting the second objective through adjustable $\varepsilon$ -levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a quadratic unconstrained binary optimization model, enabling direct solution via a QA solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance the overall performance. By leveraging the flexibility in selecting $\varepsilon$ parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.

IEEE Transactions on Quantum Engineering•Jan 1, 2026•0 citations

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 Annealing for Bi-objective Weighted Portfolio Optimization in Real-world Financial Markets

Shu–Yu Kuo, Kun-Lin Lee, Yao–Hsin Chou +2 more

Quantum computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.

Genetic and Evolutionary Computation Conference Companion (GECCO Companion)•Jul 14, 2025•1 citation

Advancing Bi-Objective Weighted Portfolio Optimization Across International Markets via Quantum Annealing

Shu–Yu Kuo, Kun-Lin Lee, Jyun–Yi Shen +1 more

Quantum finance has emerged as a key research area as interest grows in leveraging quantum computing for solving complex optimization problems in financial technology. Quantum annealing (QA), which leverages quantum tunneling effects, presents a promising method for tackling portfolio optimization challenges that primarily involve balancing risk and return. Traditional single-solution optimization approaches often fail to accommodate diverse investor preferences regarding risk tolerance and expected returns. To bridge this gap, we propose a novel bi-objective weighted portfolio optimization framework based on the trend ratio (TR) model. Our approach integrates D-Wave's advanced constrained quadratic model (CQM) hybrid solver with QA and employs scalarization-based non-dominated analysis, enabling multiple runs with different weights between risk and return to effectively achieve bi-objective optimization. This flexible strategy generates a diverse set of high-quality solutions tailored to different investor profiles. In our experiments, we investigate the interaction between two well-known international stock indices, DJI and Nikkei, to gain insights into cross-market dynamics and enhance portfolio diversification. Experimental results show that the proposed approach consistently demonstrates strong potential compared to conventional multi-objective optimization algorithms, delivering solutions with improved quality and computational efficiency. These findings highlight the potential of quantum computing in advancing financial decision-making and portfolio optimization.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•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

Towards scalable quantum annealing for pooling and blending problems: A methodological proof-of-concept

Vasileios K. Mappas, Bogdan Dorneanu, Eduardo Nolasco +2 more

Industrial optimization challenges, such as the pooling and blending problem (PBP), require advanced computational methods to address non-convexity and scalability limitations in classical solvers. This work introduces a novel methodological framework for solving PBPs using quantum annealing (QA) that transforms the PBP into quadratic unconstrained binary optimization (QUBO) formulations at two resolution levels, enabling direct deployment on quantum annealers. Key innovations include a discretization technique tailored for PBP’s bilinear constraints and an embedding method optimized for current quantum hardware. Benchmarking against classical solvers focuses on Haverly’s classical three-stream PBP, enabling transparent comparison and development of quantum embedding and solution techniques. The proposed framework offers a scalable template for adapting similar engineering systems to quantum annealing architectures. Addressing genuine industrial-scale instances will require future advances in quantum hardware and embedding algorithms. The results demonstrate that QA exhibits the best performance among the examined alternatives, provide foundational insights towards leveraging QA in Process Systems Engineering.

Process Safety and Environmental Protection•Aug 24, 2025•1 citation
Advanced Quantum Annealing for the Bi-Objective Traveling Thief Problem: An ε\varepsilonε-Constraint-based Approach
This paper addresses the Bi-Objective Traveling Thief Problem (BI-TTP), a challenging multi-objective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the ε\varepsilonε-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable ε\varepsilonε-levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting ε\varepsilonε parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.
Advanced Quantum Annealing for the Biobjective Traveling Thief Problem: An ε\varepsilonε-Constraint-Based Approach
This article addresses the biobjective traveling thief problem (BI-TTP), a challenging multiobjective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the ε\varepsilonε -constraint method. Specifically, we reformulate the biobjective problem into a single-objective formulation by restricting the second objective through adjustable ε\varepsilonε -levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a quadratic unconstrained binary optimization model, enabling direct solution via a QA solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance the overall performance. By leveraging the flexibility in selecting ε\varepsilonε parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.
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 computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.
Quantum finance has emerged as a key research area as interest grows in leveraging quantum computing for solving complex optimization problems in financial technology. Quantum annealing (QA), which leverages quantum tunneling effects, presents a promising method for tackling portfolio optimization challenges that primarily involve balancing risk and return. Traditional single-solution optimization approaches often fail to accommodate diverse investor preferences regarding risk tolerance and expected returns. To bridge this gap, we propose a novel bi-objective weighted portfolio optimization framework based on the trend ratio (TR) model. Our approach integrates D-Wave's advanced constrained quadratic model (CQM) hybrid solver with QA and employs scalarization-based non-dominated analysis, enabling multiple runs with different weights between risk and return to effectively achieve bi-objective optimization. This flexible strategy generates a diverse set of high-quality solutions tailored to different investor profiles. In our experiments, we investigate the interaction between two well-known international stock indices, DJI and Nikkei, to gain insights into cross-market dynamics and enhance portfolio diversification. Experimental results show that the proposed approach consistently demonstrates strong potential compared to conventional multi-objective optimization algorithms, delivering solutions with improved quality and computational efficiency. These findings highlight the potential of quantum computing in advancing financial decision-making and portfolio optimization.
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.
Industrial optimization challenges, such as the pooling and blending problem (PBP), require advanced computational methods to address non-convexity and scalability limitations in classical solvers. This work introduces a novel methodological framework for solving PBPs using quantum annealing (QA) that transforms the PBP into quadratic unconstrained binary optimization (QUBO) formulations at two resolution levels, enabling direct deployment on quantum annealers. Key innovations include a discretization technique tailored for PBP’s bilinear constraints and an embedding method optimized for current quantum hardware. Benchmarking against classical solvers focuses on Haverly’s classical three-stream PBP, enabling transparent comparison and development of quantum embedding and solution techniques. The proposed framework offers a scalable template for adapting similar engineering systems to quantum annealing architectures. Addressing genuine industrial-scale instances will require future advances in quantum hardware and embedding algorithms. The results demonstrate that QA exhibits the best performance among the examined alternatives, provide foundational insights towards leveraging QA in Process Systems Engineering.