The optimization of front-end crude oil scheduling is a critical determinant of refinery profitability and operational stability. However, the coupling of discrete logistics events (e.g., vessel berthing) with continuous material flows (e.g., pipeline transfers) renders this problem an NP-hard Mixed-Integer Linear Programming (MILP) challenge, often intractable for classical solvers at industrial scales. This study proposes a novel hybrid quantum-classical framework to address these computational bottlenecks. We employ Benders Decomposition to decouple the monolithic model into a discrete Master Problem (MP) and a continuous Subproblem (SP). To exploit the search capabilities of quantum computing, the MP is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved via a hybrid quantum solver, while the SP enforces mass balance and quality constraints through iterative optimality and feasibility cuts. Extensive experiments on 15 multi-scale instances demonstrate that the proposed framework significantly outperforms traditional metaheuristics (e.g., Genetic Algorithms, Tabu Search), reducing total operating costs by approximately 73--80% and achieving computational speeds comparable to state-of-the-art commercial solvers (Gurobi). By effectively leveraging global optimality cuts, the method overcomes the tendency of heuristic approaches to trap in local optima, providing a robust and scalable solution for complex refinery logistics.
The optimization of front-end crude oil scheduling is a critical determinant of refinery profitability and operational stability. However, the coupling of discrete logistics events (e.g., vessel berthing) with continuous material flows (e.g., pipeline transfers) renders this problem an NP-hard Mixed-Integer Linear Programming (MILP) challenge, often intractable for classical solvers at industrial scales. This study proposes a novel hybrid quantum-classical framework to address these computational bottlenecks. We employ Benders Decomposition to decouple the monolithic model into a discrete Master Problem (MP) and a continuous Subproblem (SP). To exploit the search capabilities of quantum computing, the MP is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved via a hybrid quantum solver, while the SP enforces mass balance and quality constraints through iterative optimality and feasibility cuts. Extensive experiments on 15 multi-scale instances demonstrate that the proposed framework significantly outperforms traditional metaheuristics (e.g., Genetic Algorithms, Tabu Search), reducing total operating costs by approximately 73--80% and achieving computational speeds comparable to state-of-the-art commercial solvers (Gurobi). By effectively leveraging global optimality cuts, the method overcomes the tendency of heuristic approaches to trap in local optima, providing a robust and scalable solution for complex refinery logistics.
• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.
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.
Abstract The selection of crude oil feedstock is a critical, high-impact optimization problem in the petrochemical industry, directly influencing refinery profitability and environmental footprint. Traditional optimization methods face scalability challenges as the complexity and number of constraints increase. This paper presents an initial study on the application of quantum computing to solve a binary feedstock optimization model. We formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and employ the Quantum Approximate Optimization Algorithm (QAOA) to find low-cost solutions. To manage the probabilistic nature of quantum results, we introduce Conditional Value at Risk (CVaR) as a post-processing technique to select robust, high-quality solutions. Our results on a representative small-scale problem demonstrate the viability of this hybrid quantum-classical approach, showing its potential to identify near-optimal solutions. We conclude with a discussion of current limitations and an open call for collaboration to further explore quantum computing applications in the energy sector.
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.
The Benders’ decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders’ decomposition can be described as a strategy of divide and conquer. The Benders’ decomposition algorithm has been employed in a variety of applications such as communication, networking, and machine learning. However, the master problem in Benders’ decomposition is still NP-hard, which motivates us to employ quantum computing. In the paper, we propose a hybrid quantum-classical Benders’ decomposition algorithm. We transfer the Benders’ decomposition’s master problem into the quadratic unconstrained binary optimization (QUBO) model and solve it by the state-of-the-art quantum annealer. Then, we analyze the computational results and discuss the feasibility of the proposed algorithm. Due to our reformulation in the master problem in Benders’ decomposition, our hybrid algorithm, which takes advantage of both classical and quantum computers, can guarantee the solution quality for solving MILP problems.
This paper presents a hybrid classical-quantum approach to solve mixed-integer linear programming (MILP) using neutral-atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a subproblem, where the MP is addressed using a neutral-atom device, after being transformed into a quadratic unconstrained binary optimization (QUBO) model, with an automatized procedure. Our MILP to QUBO conversion tightens the upper bounds of the continuous variables involved, positively impacting the required qubit count, and the convergence of the algorithm. To solve the QUBO, we develop a heuristic for atom register embedding and apply a variational algorithm for pulse shaping. In addition, we implement a proof of concept that outperforms existing solutions. We also conduct preliminary numerical results: In a series of small MILP instances our algorithm identifies over 95% of feasible solutions of high quality, outperforming classical BD approaches where the MP is solved using simulated annealing.