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Expert Systems with Applications

Quantum modeling of the dynamic ride-sharing problem: Development of quantum benders decomposition methods

Erfan Amani Bani, Kourosh Eshghi

Published Jan 27, 2026• 0 citations
Publisher
DOI
10.1016/j.eswa.2026.131320

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Scheduling multiple federated learning (FL) models within a distributed network, especially in large-scale scenarios, poses significant challenges since it involves solving NP-hard mixed-integer nonlinear programming (MINLP) problems. However, it's imperative to optimize participant selection and learning rate determination for these FL models to avoid excessive training costs and prevent resource contention. While some existing methods focus solely on optimizing a single global FL model, others struggle to achieve optimal solutions as the problem grows more complex. In this paper, exploiting the potential of quantum computing, we introduce the Hybrid Quantum-Classical Benders' Decomposition (HQCBD) algorithm to effectively tackle the joint MINLP optimization problem for multi-model FL training. HQCBD combines quantum and classical computing to solve the joint participant selection and learning scheduling problem. It decomposes the optimization problem into a master problem with binary variables and small subproblems with continuous variables, then leverages the strengths of both quantum and classical computing to solve them respectively and iteratively. Furthermore, we propose the Hybrid Quantum-Classical Multiple-cuts Benders' Decomposition (MBD) algorithm, which utilizes the inherent capabilities of quantum algorithms to produce multiple cuts in each round, to speed up the proposed HQCBD algorithm. Extensive simulation on the commercial quantum annealing machine demonstrates the effectiveness and robustness of the proposed methods (both HQCBD and MBD), with improvements of up to 70.3% in iterations and 81% in computation time over the classical Benders' decomposition algorithm on classical CPUs, even at modest scales.
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.
The scheduling problem for federated learning (FL) with multiple models in a distributed network is challenging, as it involves NP-hard mixed-integer nonlinear programming. Moreover, it requires optimal participant selection and learning rate determination among multiple FL models to avoid high training costs and resource competition. To overcome those chal-lenges, in literature the Benders' decomposition algorithm (BD) can deal with mixed integer problems, however, it still suffers from limited scalability. To address this issue, in this paper, we present the Hybrid Quantum-Classical Benders' Decomposition (HQCBD) algorithm, which combines the power of quantum and classical computing to solve the joint participant selection and learning scheduling problem in multi-model FL. HQCBD decomposes the optimization problem into a master problem with binary variables and small subproblems with continuous variables. This collaboration maximizes the potential of both quantum and classical computing, and optimizes the complex joint optimization problem. Simulation on the commercial D-Wave quantum annealing machine demonstrates the effectiveness and robustness of the proposed method, with up to 18% improvement of iterations and 81% improvement of computation time over BD algorithm on classical CPUs even at small scales.