Solution-hashing search based on layout-graph transformation for unequal circle packing

Abstract

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.