Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container

Table 1

Results of the numerical experiments.

Circle radius	Δ	Problem dimension	Circle number	Complete	Half	Compact	Compact half
0.625	0.15625	1403	10	6.4	125.5	144.8	110.6
0.5625	0.0703125	2449	13	50.4	647.0	5034.5	1890.6
0.5	0.125	697	18	2.6	3.2	5.2	24.1
0.4375	0.0546875	3666	21	849.2	310.8	7459.9	3690.5
0.375	0.046875	1425	32	50.0	21.4	3873.5	847.7
0.3125	0.078125	2139	45	403.8	183.9	6514.3	4451.8
0.275	0.06875	2880	61	1032.4	415.3	*	6985.4
0.25	0.0625	3649	74	1234.8	535.5	14645.9	7840.6
0.1875	0.046875	6897	140	1427.3	725.9	*	8765.2