Research into the development of special-purpose computing architectures designed to solve quadratic unconstrained binary optimization (QUBO) problems has flourished in recent years. It has been demonstrated in the literature that such special-purpose solvers can outperform traditional CMOS architectures by orders of magnitude with respect to timing metrics on synthetic problems. However, they face challenges with constrained problems such as the quadratic assignment problem (QAP), where mapping to binary formulations such as QUBO introduces overhead and limits parallelism. In-memory computing (IMC) devices, such as memristor-based analog Ising machines, offer significant speedups and efficiency gains over traditional CPU-based solvers, particularly for solving combinatorial optimization problems. In this work, we present a novel local search heuristic designed for IMC hardware to tackle the QAP. Our approach enables massive parallelism that allows for computing of full neighbourhoods simultaneously to make update decisions. We ensure binary solutions remain feasible by selecting local moves that lead to neighbouring feasible solutions, leveraging feasible-space search heuristics and the underlying structure of a given problem. Our approach is compatible with both digital computers and analog hardware. We demonstrate its effectiveness in CPU implementations by comparing it with state-of-the-art heuristics for solving the QAP.

翻译：近年来，专门用于求解二次无约束二进制优化（QUBO）问题的专用计算架构研究蓬勃发展。文献表明，在合成问题上，此类专用求解器在时间指标上可以比传统CMOS架构快数个数量级。然而，它们在处理约束问题（如二次分配问题（QAP））时面临挑战，因为映射到QUBO等二进制表述会引入开销并限制并行性。内存计算（IMC）设备（如基于忆阻器的模拟伊辛机）相比传统的基于CPU的求解器，在求解组合优化问题时能提供显著的加速和效率提升。本文提出了一种专为IMC硬件设计的新型局部搜索启发式算法以求解QAP。我们的方法支持大规模并行性，可同时计算完整邻域以做出更新决策。通过选择导向相邻可行解的局部移动，并利用可行空间搜索启发式算法及给定问题的底层结构，我们确保二进制解始终保持可行性。该方法兼容数字计算机和模拟硬件。我们通过将其与求解QAP的先进启发式算法进行对比，在CPU实现中验证了其有效性。