The problem of packing unequal circles into a circular container is a classic and challenging optimization problem in the field of 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 on 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. Our algorithm demonstrates excellent performance over existing state-of-the-art methods through comprehensive computational experiments across various benchmark instances, showcasing quality applicability and versatility. Notably, our algorithm improves the best-known results for 116 out of 239 benchmark instances while achieving parity with the remaining instances.

中文翻译：

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基于布局图变换的不等圆填充解哈希搜索

将不相等的圆装入圆形容器中的问题是计算几何领域中一个经典且具有挑战性的优化问题。本研究介绍了一套创新和有效的方法来解决这个问题。首先，我们提出了一种新的布局图转换方法，将配置表示为图形，以及一种不精确的哈希方法，有助于快速比较同构或相似性的配置。利用这些进步，我们提出了一种迭代解决方案哈希搜索算法，擅长通过高效的配置记录来规避冗余探索。此外，我们还引入了一些增强功能来优化和搜索过程，包括自适应邻接维护方法、高效的空位检测技术和基于 Voronoi 的定位方法。我们的算法通过跨各种基准实例的综合计算实验，展示了优于现有最先进方法的出色性能，展示了质量的适用性和多功能性。值得注意的是，我们的算法改进了 239 个基准测试实例中 116 个的最知名结果，同时实现了与其余实例的同等结果。