An effective approach to solving complex problems is to decompose them and integrate dedicated solvers for those subproblems. We introduce a hybrid decomposition that incorporates: (1) a quantum annealer that samples from the configuration space of a relaxed problem to obtain strong candidate solutions, and (2) a classical processor that maintains a global search tree and enforces constraints on the relaxed components of the problem. Our framework is the first to use quantum annealing as part of a complete search. We consider variants of our approach with differing amounts of guidance from the quantum annealer. We empirically test our algorithm and compare the variants on problems from three scheduling domains: graph-coloring-type scheduling, simplified Mars Lander task scheduling, and airport runway scheduling. While we were only able to test on problems of small sizes, due to the limitation of currently available quantum annealing hardware, the empirical results show that results obtained from the quantum annealer can be used for more effective search node pruning and to improve node selection heuristics when compared to a standard classical approach.
An effective approach to solving complex problems is to decompose them and integrate dedicated solvers for those subproblems. We introduce a hybrid decomposition that incorporates: (1) a quantum annealer that samples from the configuration space of a relaxed problem to obtain strong candidate solutions, and (2) a classical processor that maintains a global search tree and enforces constraints on the relaxed components of the problem. Our framework is the first to use quantum annealing as part of a complete search. We consider variants of our approach with differing amounts of guidance from the quantum annealer. We empirically test our algorithm and compare the variants on problems from three scheduling domains: graph-coloring-type scheduling, simplified Mars Lander task scheduling, and airport runway scheduling. While we were only able to test on problems of small sizes, due to the limitation of currently available quantum annealing hardware, the empirical results show that results obtained from the quantum annealer can be used for more effective search node pruning and to improve node selection heuristics when compared to a standard classical approach.
An effective approach to solving problems involving mixed (continuous and discrete) variables and constraints, such as hybrid systems, is to decompose them into subproblems and integrate dedicated solvers geared toward those subproblems. Here, we introduce a new framework based on a tree search algorithm to solve hybrid discrete-continuous problems that incorporates: (1) a quantum annealer that samples from the configuration space for the discrete portion and provides information about the quality of the samples, and (2) a classical computer that makes use of information from the quantum annealer to prune and focus the search as well as check a continuous constraint. We consider four variants of our algorithm, each with progressively more guidance from the results provided by the quantum annealer. We empirically test our algorithm and compare the variants on a simplified Mars Lander task scheduling problem. Variants with more guidance from the quantum annealer have better performance.
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.
A promising use of quantum computers lies in the logistics and scheduling of industrial problems, such as space mission planning, maritime management, and many others. This field is expected to provide useful applications for quantum computing at the current stage of hardware development. Quantum annealing techniques have been proposed to solve scheduling problems, along with many other optimization problems. In this work, we test quantum annealing and hybrid techniques based on the D-Wave hardware to solve scheduling problems in the framework of job shop scheduling (JSP), which consists of optimally assigning operations to certain resources, while satisfying specific constraints and minimizing the total scheduling time, known as timespan. We devised an iterative algorithm that produces valid schedules for decreasing timespan values. We implemented a refined iterative variable pruning technique, which significantly reduces the number of spin variables in the corresponding Ising model, whose low-energy configurations are sampled by using the D-Wave Hybrid Solver Service. Our novel iterative algorithm leverages a directed acyclic graph (DAG) representation of partial or complete solutions of the JSP instance, which enables an efficient update of the feasible processing time windows for each operation. This approach leads to significantly improved results compared to the standard state-of-the-art applications of quantum annealing for the JSP. Remarkably, we can often prove the absolute optimality of the obtained solution, namely that a more efficient schedule within a shorter timespan can not exist.
Airline and space mission scheduling present complex combinatorial optimization challenges, requiring sophisticated coordination of multiple resources under stringent operational constraints. This paper introduces a novel hybrid quantum-classical framework for scheduling optimization, the Quantum Scheduling Optimization Algorithm (QSOA), addressing crew assignment, gate allocation, and trajectory planning through advanced quantum machine learning techniques. We formulate the scheduling problems as stochastic multi-objective optimization and propose three integrated solution approaches: (1) hybrid quantum optimization via QAOA with constraint-aware loss functions and problem decomposition strategies, (2) classical-quantum integration using graph partitioning and variational circuit optimization, and (3) comprehensive baselines including mixed-integer programming, genetic algorithms, and reinforcement learning formulations. For multi-objective handling, we develop Pareto-optimal sampling techniques combining quantum superposition with classical post-processing for constraint repair and solution refinement. Our experimental evaluation on realistic airline crew scheduling benchmarks and space mission simulators demonstrates significant improvements: the hybrid QSOA achieves 19.2\% cost reduction in airline scheduling compared to classical heuristics, while quantum methods provide competitive solutions for moderate-sized space mission subproblems with 15-18\% improvement in multi-objective trade-offs. The framework shows promise for scalable deployment in real-world transportation networks, with practical implications for next-generation scheduling optimization in complex operational environments.
I present a hybrid quantum-classical framework for constrained combinatorialoptimization based on fixed-schedule Trotterized Quantum Annealing (TQA). Theproposed approach combines Lagrangian-inspired penalty encoding, linearprogramming (LP)-guided problem decomposition, and static interaction pruning toimprove the sampling of high-quality feasible solutions while limiting quantum circuitcomplexity. Unlike conventional variational approaches that rely on iterative classical optimization ofcircuit parameters, my method employs a predetermined annealing schedule and penaltycoefficients determined during classical preprocessing. The constrained objective isencoded using a linear weight term and a quadratic penalty on deviations from theassigned capacity. LP relaxation guides the allocation of the global capacity betweenindependent problem groups, while static pruning reduces the number of pairwiseinteractions in the problem Hamiltonian. The resulting Trotterized evolution isimplemented without iterative optimization of quantum circuit angles. The framework is investigated on a 24-item knapsack problem, decomposed into twoindependent 12-variable subproblems and executed on quantum hardware. It builds onmy earlier experiments with ungrouped TQA on knapsack instances of 10 to 15 items, inwhich I used a sampling budget of 10 × 2^N shots. Because the fixed, coarse Trotterizedschedule spreads the probability over many configurations, the best solutions have smallindividual probabilities: with smaller budgets their position in the frequency ranking wasdominated by sampling noise and they could remain far down the list, whereas at 10 ×2^N shots they moved towards the front. In several runs on 15 items the optimalsolution was found within the top 1 % of the most frequently sampled configurations.These observations are empirical, drawn from a large number of runs rather than acontrolled scaling study. They suggest that the method may offer an effective way ofaccessing near-optimal solutions without relying on repeated variational parameteroptimization, although it requires a higher sampling budget in the experimentsconsidered. For the 24-item problem, a classical reconstruction procedure combinesindependently sampled group configurations to recover globally feasible solutions,including the exact optimum, even when the complete optimal bitstring is not observedin a single quantum measurement. These results motivate further investigation of fixed-schedule, penalty-based TQA as ahardware-oriented alternative to variational quantum optimization for constrained problems.In particular, the observed sampling behavior, feasibility-quality trade-off, andresource requirements provide a basis for systematic comparisons with CVaR-based andoptimizer-driven approaches.
Quantum computing (QC) holds great promise to open up a new era of computing and has been receiving significant attention recently. To overcome the performance limitations of near-term QC, utilizing the current quantum computers to complement classical techniques for solving real-world problems is of utmost importance. In this paper, we develop QC-based solution strategies that exploit quantum annealing and classical optimization techniques for solving large-scale scheduling problems in manufacturing systems. The applications of the proposed algorithms are illustrated through two case studies in production scheduling. First, we present a hybrid QC-based solution approach for the job-shop scheduling problem. Second, we propose a hybrid QC-based parametric method for the multi-purpose batch scheduling problem with a fractional objective. The proposed hybrid algorithms can tackle optimization problems formulated as mixed-integer linear and mixed-integer fractional programs, respectively, and provide feasibility guarantees. Performance comparison between state-of-the-art exact and heuristic solvers and the proposed QC-based hybrid solution techniques is presented for both job-shop and batch scheduling problems. Unlike conventional classical solution techniques, the proposed hybrid frameworks harness quantum annealing to supplement established deterministic optimization algorithms and demonstrate performance efficiency over standard off-the-shelf optimization solvers.