DOI: 10.7274/28786112.v1
title: Advanced Computational Methods for Large-Scale Optimization Problems

description: 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.