基于布局图变换的不等圆装填解哈希搜索
Solution-Hashing Search Based on Layout-Graph Transformation for Unequal Circle Packing
AI总结：
针对不等圆装填优化难题，提出布局图变换与非精确哈希方法，构建迭代解哈希搜索算法并辅以多项优化技术，在多数基准实例上达到或超越现有最优结果。
摘要：
将不等圆装入圆形容器的问题是计算几何中经典且具有挑战性的优化问题。本研究提出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，同时提出了一种非精确哈希方法，可快速比较构型的同构性或相似性。借助这些进展，我们提出了迭代解哈希搜索算法，该算法能够通过高效的构型记录来规避冗余探索。此外，我们还引入了若干改进措施来优化优化与搜索过程，包括自适应邻接维护方法、高效空位检测技术以及基于Voronoi的定位方法。通过在各类基准实例上开展的全面计算实验，我们的算法性能优于现有最先进方法，展现出显著的适用性与通用性。值得注意的是，我们的算法在179个基准实例中有56个超越了已知最优结果，其余实例则与已知最优结果持平。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
