QC-CCG：用于两阶段自适应鲁棒优化的量子-经典算法
QC-CCG: Quantum-Classical Algorithm for Two-stage Adaptive Robust Optimization
浏览论文内容
中文总结 AI 辅助
本文提出混合量子-经典列与约束生成框架，通过QUBO编码和边界调整求解两阶段自适应鲁棒优化，在保证解质量的同时降低计算负担。
中文摘要 AI 辅助
量子优化通过二次无约束二元优化（QUBO）公式为解决大规模组合问题提供了一种有前景的方法。然而，将基于QUBO的求解器集成到结构化优化框架中同时保持解保证仍然是一个基本挑战。本文开发了一种混合量子-经典列与约束生成（QCCG）框架，用于求解具有二元第一阶段决策和线性补偿（在多面体不确定性下）的两阶段自适应鲁棒优化问题。所提出的方法将受限主问题重新表述为QUBO，并使用量子优化器近似求解，同时保留经典对抗性子问题以计算最坏情况补偿并认证解质量。我们利用松弛变量和惩罚项为不等式约束的主问题构建了保约束的QUBO编码，使一般的混合整数结构能够映射到量子兼容的表示。为解决离散化、惩罚建模和量子优化带来的不精确性，我们引入了一种边界调整机制，该机制产生有效的下界和上界，并提供经过认证的停止准则。我们证明了所提出的框架推广了经典列与约束生成，并在主问题精确求解时保留其收敛性质。在两阶段鲁棒选址-运输问题上的数值实验表明，所提出的混合方法实现了与经典方法相当的解质量，同时减少了求解混合整数主问题相关的计算负担，突显了混合量子-经典优化在不确定性下可扩展决策中的潜力。
英文摘要
Quantum optimization provides a promising approach for solving large-scale combinatorial problems through quadratic unconstrained binary optimization (QUBO) formulations. However, integrating QUBO-based solvers into structured optimization frameworks while preserving solution guarantees remains a fundamental challenge. This paper develops a hybrid quantum-classical column-and-constraint generation (QCCG) framework for solving two-stage adaptive robust optimization problems with binary first-stage decisions and linear recourse under polyhedral uncertainty. The proposed approach reformulates the restricted master problem as a QUBO and solves it approximately using a quantum optimizer, while retaining a classical adversarial subproblem to compute worst-case recourse and certify solution quality. We construct a constraint-preserving QUBO encoding for inequality-constrained master problems using slack variables and penalty terms, enabling general mixed-integer structures to be mapped to quantum-compatible representations. To address inexactness arising from discretization, penalty modeling, and quantum optimization, we introduce a bound-adjustment mechanism that yields valid lower and upper bounds and provides a certified stopping criterion. We show that the proposed framework generalizes classical column-and-constraint generation and retains its convergence properties when the master problem is solved exactly. Numerical experiments on two-stage robust location-transportation problems demonstrate that the proposed hybrid approach achieves solution quality comparable to classical methods while reducing the computational burden associated with solving mixed-integer master problems, highlighting the potential of hybrid quantum-classical optimization for scalable decision-making under uncertainty.
发表机构
- School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）
机构由 AI 辅助整理，请以论文原文为准。
