The problem of packing unequal circles into a circular container stands as a classic and challenging optimization problem in computational geometry. This study introduces a suite of innovative and efficient methods to tackle this problem. Firstly, we present a novel layout-graph transformation method that represents configurations as graphs, together with an inexact hash method facilitating fast comparison of configurations for isomorphism or similarity. Leveraging these advancements, we propose an Iterative Solution-Hashing Search algorithm adept at circumventing redundant exploration through efficient configuration recording. Additionally, we introduce several enhancements to refine the optimization and search processes, including an adaptive adjacency maintenance method, an efficient vacancy detection technique, and a Voronoi-based locating method. Through comprehensive computational experiments across various benchmark instances, our algorithm demonstrates superior performance over existing state-of-the-art methods, showcasing remarkable applicability and versatility. Notably, our algorithm surpasses the best-known results for 56 out of 179 benchmark instances while achieving parity with the remaining instances.

翻译：将不等圆装入圆形容器是计算几何中一个经典且富有挑战性的优化问题。本研究引入了一套创新且高效的方法来解决该问题。首先，我们提出了一种新颖的布局图变换方法，将构型表示为图结构，并配合一种非精确哈希方法，以快速比较构型的同构性或相似性。基于这些进展，我们提出了一种迭代解哈希搜索算法，通过高效的构型记录避免冗余探索。此外，我们引入了多项改进措施以优化搜索与优化流程，包括一种自适应邻接维护方法、一种高效的空缺检测技术以及一种基于Voronoi的定位方法。通过在多个基准实例上的计算实验，我们的算法在性能上超越了现有最先进方法，展现出卓越的适用性与通用性。值得注意的是，在179个基准实例中，我们的算法在56个实例上超越了已知最优结果，并在其余实例上与其持平。