A Genetic Algorithm with Lower Neighborhood Search for the Three-Dimensional Multiorder Open-Size Rectangular Packing Problem

Table 10

Case results for small-scale order sizes (comparison with VNS and GA).

Number	Number of orders	GA			VNS			LNSGA
		Solution	Objective value: LWH	CPU time (s)	Solution ()	Objective value:	CPU time (s)	Solution	Objective value:	CPU time (s)
1	2	(8, 26, 29)	6032	60.76	(9, 25, 29)	6525	24.61	(8, 20, 29)	4640	25.53
2	2	(9, 22, 30)	5940	92.58	(10, 21, 31)	6510	29.92	(9, 19, 30)	5130	36.72
3	2	(7, 28, 30)	5880	43.83	(8, 27, 30)	6480	28.25	(7, 18, 30)	3780	21.7
4	4	(10, 21, 30)	6300	157.01	(10, 20, 29)	5800	49.96	(10, 20, 30)	6000	68.1
5	4	(9, 20, 30)	5400	190.5	(10, 21, 29)	6090	25.43	(9, 20, 30)	5400	81.93
6	4	(10, 20, 30)	6000	167.44	(10, 20, 30)	6000	52.53	(10, 20, 30)	6000	72.96
7	6	(10, 20, 30)	6000	198.16	(10, 20, 31)	6200	64.82	(10, 20, 30)	6000	89.98
8	6	(10, 28, 30)	8400	283.27	(10, 22, 32)	7040	58.74	(10, 20, 37)	7400	107.78
9	6	(10, 20, 30)	6000	296.28	(11, 20, 29)	6380	78.4	(10, 20, 30)	6000	107.88
10	8	(10, 20, 31)	6200	444.52	(12, 20, 30)	7200	66.49	(10, 20, 32)	6400	168.41
11	8	(10, 20, 52)	10400	264.08	(13, 19, 55)	11495	61.54	(10, 20, 57)	11400	120.61
12	8	(10, 25, 30)	7500	274.55	(11, 20, 29)	6380	67.91	(10, 20, 30)	6000	127.33
Average		—	6671	206.08	—	6842	50.72	—	6179	85.74