We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To separate inequality constraints that are difficult for quantum routines we use a decomposition in master and pricing problems: the former targets the assignment of vehicles to reservations and the latter suggests vehicle exploitation plans that respect the battery state-of-charge constraints. The master problem is equivalent to the search for an optimal set partition. In our hybrid scheme, the master problem is reformulated in a quadratic unconstrained binary optimization problem which can be solved with quantum annealing on the DWave Advantage system. On large instances, we benchmark the performance of the decomposition technique with classical and quantum-inspired metaheuristics: simulated annealing, tabu search, and vector annealing by NEC. The numerical results with purely classical solvers are comparable to the solutions from the traditional mixed integer linear programming approaches in terms of solution quality while being faster. In addition, it scales better to larger instances. The major advantage of the proposed approach is that it enables quantum-based methods for this realistic problem with many inequality constraints. We show this by initial studies on DWave hardware where optimal solutions can be found for small instances.
We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To separate inequality constraints that are difficult for quantum routines we use a decomposition in master and pricing problems: the former targets the assignment of vehicles to reservations and the latter suggests vehicle exploitation plans that respect the battery state-of-charge constraints. The master problem is equivalent to the search for an optimal set partition. In our hybrid scheme, the master problem is reformulated in a quadratic unconstrained binary optimization problem which can be solved with quantum annealing on the DWave Advantage system. On large instances, we benchmark the performance of the decomposition technique with classical and quantum-inspired metaheuristics: simulated annealing, tabu search, and vector annealing by NEC. The numerical results with purely classical solvers are comparable to the solutions from the traditional mixed integer linear programming approaches in terms of solution quality while being faster. In addition, it scales better to larger instances. The major advantage of the proposed approach is that it enables quantum-based methods for this realistic problem with many inequality constraints. We show this by initial studies on DWave hardware where optimal solutions can be found for small instances.
The rapid deployment of electric vehicles (EVs) in public parking facilities and fleet operations raises challenging intra-day charging scheduling problems under tight charger capacity and limited dwell times. We model this problem as a variant of the Partition Coloring Problem (PCP), where each vehicle defines a partition, its candidate charging intervals are vertices, and temporal and resource conflicts are represented as edges in a conflict graph. On this basis, we design a branch-and-price algorithm in which the restricted master problem selects feasible combinations of intervals, and the pricing subproblem is a maximum independent set problem. The latter is reformulated as a quadratic unconstrained binary optimization (QUBO) model and solved by quantum-annealing-inspired algorithms (QAIA) implemented in the MindQuantum framework, specifically the ballistic simulated branching (BSB) and simulated coherent Ising machine (SimCIM) methods, while the master problem is solved by Gurobi. Computational experiments on a family of synthetic EV charging instances show that the QAIA-enhanced algorithms match the pure Gurobi-based branch-and-price baseline on small and medium instances, and clearly outperform it on large and hard instances. In several cases where the baseline reaches the time limit with non-zero optimality gaps, the QAIA-based variants close the gap and prove optimality within the same time budget. These results indicate that integrating QAIA into classical decomposition schemes are a promising direction for large-scale EV charging scheduling and related PCP applications.
• 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.
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 logistical management of urban hydrogen fuel cell electric bus (FCEB) fleets presents a computationally complex scheduling problem, especially under dynamic conditions. This paper compares a classical global Mixed-Integer Linear Programming (MILP) baseline with a sequential hybrid quantum–classical model for real-time decision-making (and includes a monolithic quantum comparator for completeness). The hybrid approach employs a classical director to maintain fleet state and, hour by hour, formulates a Quadratic Unconstrained Binary Optimization (QUBO) over candidate actions that is mapped to Ising and solved via the Quantum Approximate Optimization Algorithm (QAOA); the MILP decision is replaced only if the QAOA proposal is feasible and value-improving. Simulation results on a 24-hour, 5-vehicle scenario show that while MILP finds a globally consistent plan, the hybrid method captures short-term opportunities through windowed variational refinement, yielding higher total value; the monolithic quantum solution remains competitive but does not surpass the classical baseline at this scale. The advantage of the hybrid model thus arises from locality and adaptive refinement rather than a Grover-type N bound, offering a pragmatic path to dynamic fleet management under realistic SOC and capacity constraints.
Motivated by recent progress in quantum hardware and algorithms, researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and limited in size such that quantum heuristics cannot be scaled to relevant problem sizes and are often outperformed by their classical counterparts. Moreover, if provably optimal solutions are desired, one has to resort to classical exact methods. As, however, quantum technologies may improve considerably in future, we demonstrate in this work how quantum heuristics with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems. To this end, we consider vehicle routing as a prototypical NP-hard problem. We model the pricing and separation subproblems arising in a branch-price-and-cut algorithm as quadratic unconstrained binary optimization problems. This allows to use established quantum heuristics like quantum annealing or the quantum approximate optimization algorithm for their solution. A key feature of our algorithm is that it profits not only from the best solution returned by the quantum heuristic but from all solutions below a certain cost threshold, thereby exploiting the inherent randomness is quantum algorithms. Moreover, we reduce the requirements on quantum hardware since the subproblems, which are solved via quantum heuristics, are smaller than the original problem. We provide a proof-of-concept experimental study comparing quantum annealing to simulated annealing and to established classical algorithms in our framework. While our hybrid quantum-classical approach is still outperformed by purely classical methods, our results reveal that both pricing and separation may be well suited for quantum heuristics if quantum hardware improves.