MGPM Methods for Rectangular Single-Size Printed Circuit Board Orthogonal Packing Problems

Table 1

Statistics of 4 algorithms.

DS	MGPM-DP			MGPM-BC			Simplex method			Dynamic prog. Algorithm
	AUR (%)	AN (Ps)	ACT (S)	AUR (%)	AN (Ps)	ACT (S)	AUR (%)	AN (Ps)	ACT (S)	AUR (%)	AN (Ps)	ACT (S)
D1	97.78%	689	0.1584	97.47%	687	0.1240	97.41%	687	0.0193	97.51%	688	26.2678
D2	98.33%	577	0.0629	98.11%	576	0.0443	98%	575	0.0183	97.76%	574	23.8502
D3	98.23%	944	0.5587	98.04%	943	0.1517	97.96%	942	0.0186	97.75%	933	28.9502
D4	98.61%	1288	0.2691	98.49%	1287	0.1801	98.45%	1286	0.0186	97.97%	1280	29.1002
D5	98.91%	1607	0.5764	98.75%	1605	0.4251	98.68%	1604	0.0185	98.27%	1596	27.6002
D6	97.95%	2291	1.6091	97.80%	2289	1.2813	97.71%	2288	0.0185	97.59%	2280	21.0023

Note. Since the dynamic programming algorithm is very time-consuming, if no solutions are found in 30 seconds, AUR and AN is 0.