Advanced Computational Methods for Large-Scale Optimization Problems

With the development of science and technology, large-scale optimization tasks have become integral to cutting-edge engineering. The challenges of solving these problems arises from ever-growing system sizes, intricate physical space, and the computational cost required to accurately model and optimize target objectives. Taking the design of advanced functional materials as an example, the high-dimensional parameter space and high-fidelity physical simulations can demand immense computational resources for searching and iterations. Although emerging machine learning techniques have been combined with conventional experimental and simulation approaches to explore the design space and identify high-performance solutions, these methods are still limited to a small part of the design space around those materials have been well investigated. Over the past several decades, continuous development of both hardware and algorithms have addressed some of the challenges. High-performance computing (HPC) architectures and heterogeneous systems have greatly expanded the capacity to perform large-scale calculations and optimizations; On the other hand, the emergence of machine learning frameworks and algorithms have dramatically facilitated the development of advanced models and enable the integration of AI-driven techniques into traditional experiments and simulations more seamlessly. In recent years, quantum computing (QC) has received widespread attention due to its powerful performance on solving global optima and is regarded as a promising solution to large-scale and non-linear optimization problems in the future, and in the meantime, the quantum computing principles also expand the capacity of classical algorithms on exploring high-dimensional combinatorial spaces. In this dissertation, we will show the power of the integration of machine learning algorithms, quantum algorithms and HPC architectures on tackling the challenges of solving large-scale optimization problems. In the first part of this dissertation, we introduced an optimization algorithm based on a Quantum-inspired Genetic Algorithm (QGA) to design planar multilayer (PML) for transparent radiative cooler (TRC) applications. Results of numerical experiments showed that our QGA-facilitated optimization algorithm can converge to comparable solutions as quantum annealing (QA) and the QGA overperformed on classical genetic algorithm (CGA) on both convergence speed and global search capacity. Our work shows that quantum heuristic algorithms will become powerful tools for addressing the challenges traditional optimization algorithm faced when solving large-scale optimization problems with complex search space. In the second part of the dissertation, we proposed a quantum annealing-assisted lattice optimization (QALO) algorithm for high-entropy alloy (HEA) systems. The algorithm is developed based on the active learning framework that integrates the field-aware factorization machine (FFM), quantum annealing (QA) and machine learning potential (MLP). When applying to optimize the bulk grain configuration of the NbMoTaW alloy system, our algorithm can quickly obtain low-energy microstructures and the results successfully reproduce the Nb segregation and W enrichment in the bulk phase driven by thermodynamic driving force, which usually be observed in the experiments and MC/MD simulations. This work highlights the potential of quantum computing in exploring the large design space for HEA systems. In the third part of the dissertation, we employed the Distributed Quantum Approximate Optimization Algorithm (DQAOA) to address large-scale combinatorial optimization problems that exceed the limits of conventional computational resources. This was achieved through a divide-and-conquer strategy, in which the original problem is decomposed into smaller sub-tasks that are solved in parallel on a high-performance computing (HPC) system. To further enhance convergence efficiency, we introduced an Impact Factor Directed (IFD) decomposition method. By calculating impact factors and leveraging a targeted traversal strategy, IFD captures local structural features of the problem, making it effective for both dense and sparse instances. Finally, we explored the integration of DQAOA with the Quantum Framework (QFw) on the Frontier HPC system, demonstrating the potential for efficient management of large-scale circuit execution workloads across CPUs and GPUs.随着科学技术的发展，大规模优化任务已成为前沿工程领域的核心组成部分。此类问题的求解挑战源于不断扩张的系统规模、复杂的物理空间，以及精准建模与优化目标所需的高额计算成本。以先进功能材料的设计为例，高维参数空间与高保真物理模拟往往需要耗费海量计算资源以完成搜索与迭代过程。尽管新兴机器学习技术已与传统实验、模拟方法相结合，以探索设计空间并筛选高性能方案，但此类方法的应用范围仍局限于已被充分研究的材料周边的小部分设计空间内。过去数十年来，硬件与算法的持续发展已部分解决了上述挑战。高性能计算（High-performance Computing, HPC）架构与异构系统极大拓展了大规模计算与优化的能力；另一方面，机器学习框架与算法的涌现则大幅推动了先进模型的发展，使得AI驱动技术能够更顺畅地融入传统实验与模拟流程。近年来，量子计算（Quantum Computing, QC）凭借其求解全局最优解的优异性能受到广泛关注，被视为未来解决大规模非线性优化问题的极具潜力的方案；与此同时，量子计算原理也拓展了经典算法探索高维组合空间的能力。本学位论文将展示机器学习算法、量子算法与HPC架构的融合技术在应对大规模优化问题求解挑战中的效能。本论文的第一部分介绍了一种基于量子启发式遗传算法（Quantum-inspired Genetic Algorithm, QGA）的优化算法，用于面向透明辐射制冷器（Transparent Radiative Cooler, TRC）应用的平面多层结构（Planar Multilayer, PML）设计。数值实验结果表明，我们基于QGA的优化算法可收敛至与量子退火（Quantum Annealing, QA）相当的解，且QGA在收敛速度与全局搜索能力上均优于经典遗传算法（Classical Genetic Algorithm, CGA）。本研究表明，量子启发式算法将成为解决传统优化算法在求解复杂搜索空间下的大规模优化问题时所面临挑战的有力工具。论文第二部分针对高熵合金（High-entropy Alloy, HEA）体系，提出了一种量子退火辅助晶格优化（Quantum Annealing-assisted Lattice Optimization, QALO）算法。该算法基于主动学习框架构建，整合了场感知因子分解机（Field-aware Factorization Machine, FFM）、量子退火（QA）与机器学习势函数（Machine Learning Potential, MLP）。将其应用于优化NbMoTaW合金体系的块体晶粒构型时，本算法可快速获得低能量微观结构，且结果成功复现了热力学驱动力驱动下块体相中的铌（Nb）偏析与钨（W）富集现象——此类现象通常可在实验与蒙特卡洛/分子动力学（MC/MD）模拟中观测到。本研究凸显了量子计算在探索高熵合金体系广阔设计空间中的应用潜力。论文第三部分采用分布式量子近似优化算法（Distributed Quantum Approximate Optimization Algorithm, DQAOA），以解决超出传统计算资源限制的大规模组合优化问题。该方案通过分治策略实现：将原始问题分解为若干子任务，并在高性能计算（HPC）系统上并行求解。为进一步提升收敛效率，本文提出了一种影响因子导向（Impact Factor Directed, IFD）分解方法。该方法通过计算影响因子并采用针对性遍历策略，捕捉问题的局部结构特征，可同时有效处理稠密与稀疏实例。最后，本研究在Frontier超算系统上探索了DQAOA与量子框架（Quantum Framework, QFw）的集成，展示了跨CPU与GPU高效管理大规模电路执行工作负载的潜力。