Packing Unequal Circles into a Square Container by Partitioning Narrow Action Spaces and Circle Items

We address the NP-hard problem of finding a non-overlapping dense packing pattern for n Unequal Circle items in a two-dimensional Square Container (PUC-SC) such that the size of the container is minimized. Based on our previous work on Action Space-based Global Optimization (ASGO) that approximates each circle item as a square item to find large unoccupied spaces efficiently, we propose an optimization algorithm based on the Partitioned Action Space and Partitioned Circle Items (PAS-PCI). The PAS is used to partition the narrow action space on the long side to find two equal action spaces to fully utilize the unoccupied spaces. The PCI are used to partition the circle items into four groups based on item sizes for the basin-hopping strategy. Experiments on two sets of benchmark instances show the effectiveness of the proposed method. In comparison with our previous ASGO algorithm on the 68 tested instances published with ASGO, PAS-PCI not only achieves smaller containers in 64 instances and matches the other 4 but also runs faster in most instances. In comparison with the best record of the Packomania website for 94 instances, PAS-PCI finds smaller containers for 82 and matches the other 12. Note that we updated 19 records (47-48, 51-54, 57, 61-72) that had remained unchanged since 2013. K. He Department of Computer Science and Technology, Huazhong University of Science & Technology, Wuhan 430074, China. E-mail: [email protected] M. Dosh ? Department of Computer Science and Technology, Huazhong University of Science & Technology, Wuhan 430074, China. Faculty of education for girls, Kufa University, Najaf, Iraq. E-mail: [email protected], [email protected] S. Zou Department of Computer Science and Technology, Huazhong University of Science & Technology, Wuhan 430074, China. E-mail: [email protected] ar X iv :1 70 1. 00 54 1v 2 [ cs .C G ] 2 7 Fe b 20 17