| 王炎,杨迪雄,雷振增,陈国海.量子退火驱动的桁架结构拓扑优化设计方法[J].计算力学学报,2025,42(3):339~345,361 |
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| 量子退火驱动的桁架结构拓扑优化设计方法 |
| Quantum annealing-driven topology optimization design method for truss structures |
| 投稿时间：2025-03-27 修订日期：2025-05-08 |
| DOI：10.7511/jslx20250326002 |
| 中文关键词: 桁架结构 拓扑优化设计 量子退火算法 量子计算 二次无约束二进制优化问题 |
| 英文关键词:truss structures topology optimal design quantum annealing algorithm quantum computing quadratic unconstrained binary optimization problem |
| 基金项目:国家自然科学基金(12032008;52378484)资助项目. |
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| 摘要点击次数: 33 |
| 全文下载次数: 11 |
| 中文摘要: |
| 为克服桁架结构传统拓扑优化方法面临的计算效率低、易陷入局部最优等局限,本文基于桁架基结构思想,提出了一种量子退火驱动的桁架结构刚度优化设计方法。首先,选取桁架结构的弹性应变能作为目标函数,将体积约束表达成惩罚项形式嵌入结构优化问题的哈密顿量中,形成无约束优化问题。然后,通过构造杆件截面积的增量与编码量子比特的指数型映射关系,同时引入辅助量子比特,并以量子退火算法驱动其变化来实现增量正负方向的调整,从而将体积约束下的桁架刚度最大化问题转化为量子退火机能够求解的二次无约束二进制优化问题。使用经典计算机执行有限元分析,在专用量子退火机上实现优化求解,发展了经典与量子计算混合优化框架。两个桁架拓扑优化算例验证了本文提出的算法的稳定收敛性,并展示了量子退火算法在结构优化领域的可行性与应用潜力,为工程优化设计提供了一种融合经典计算与量子算法的创新范式。 |
| 英文摘要: |
| To address the limitations of computational inefficiency and ease to fall into local optima in traditional topology optimization methods for a truss structures,this paper proposes a quantum annealing-driven stiffness optimization design method based on the idea of a truss ground structure.Firstly,the elastic strain energy of the truss structure is selected as the objective function,while volume constraints are formulated as penalty terms embedded into the Hamiltonian of the truss system,thereby forming the problem of an unconstrained optimization.Subsequently,by constructing the exponential mapping relationship between the increment of the cross-sectional area of the bars and the encoded qubit,introducing auxiliary qubits and driving them by a quantum annealing algorithm,the adjustment of the positive and negative directions of the increment is realized.The volume-constrained truss stiffness optimization problem is transformed into a quadratic unconstrained binary optimization problem which is solvable by a quantum annealing machine.The hybrid optimization framework incorporating classical-quantum computing is developed,where classical finite element analysis is executed on a conventional computer and the optimization task is implemented on the special quantum annealer.Two examples of truss topology optimization indicate the stable convergence of the proposed algorithm of this paper.This work demonstrates the feasibility and application potential of the quantum annealing algorithm in structural optimization,offering an innovative paradigm for engineering design optimization that integrates classical computing with quantum algorithms. |
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