## Iterated dynamic thresholding search for packing equal circles into a circular container.(English)Zbl 07479785

Summary: Packing equal circles in a circle is a classic global optimization problem that has a rich research history and a number of relevant applications. The problem is computationally challenging due to the fact that the number of possible packing configurations grows exponentially with the number of circles. In this work, we propose a highly effective iterated dynamic thresholding search algorithm for solving this difficult problem. The algorithm integrates several features including a two-phase local optimization method, a dynamic thresholding search and a container adjustment procedure. Computational experiments on popular benchmark instances with up to $$N=320$$ circles show that the algorithm outperforms significantly the state-of-the-art algorithms. In particular, it improves the best-known results for 136 instances, while matching the best-known results for other 175 instances.

### MSC:

 90Bxx Operations research and management science

### Keywords:

packing; thresholding search; global optimization; heuristics

### Software:

Packmol; L-BFGS; packomania
Full Text:

### References:

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