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

Table 8

Case results for small-scale order sizes (comparison with Gurobi).

Number	Number of orders	Optimal solution	Optimal value	Gurobi			LNSGA			Time limit (s)
				Solution	Objective value:	GAP (%)	Solution	Objective value:	GAP (%)
1	2	(29, 20, 8)	4640	(29, 26, 10)	7540	38.46	(29, 20, 8)	4640	0.00	25.53
2	2	(30, 19, 9)	5130	(46, 28, 9)	11592	55.75	(30, 19, 9)	5130	0.00	36.72
3	2	(30, 18, 7)	3780	(30, 21, 14)	8820	57.14	(30, 18, 7)	3780	0.00	21.7
4	4	(30, 19, 10)	5800	(33, 17, 30)	20097	71.14	(30, 20, 10)	6000	3.33	68.1
5	4	(29, 20, 9)	5130	(33, 17, 30)	16830	69.52	(30, 20, 9)	5400	5.00	81.93
6	4	(28, 20, 10)	5600	(35, 30, 16)	16800	66.67	(30, 20, 10)	6000	6.67	72.96
7	6	(29, 18, 10)	5880	(30, 24, 21)	15120	61.11	(30, 20, 10)	6000	2.00	89.98
8	6	(32, 19, 10)	7000	(34, 30, 11)	11220	37.61	(37, 20, 10)	7400	5.41	107.78
9	6	(28, 18, 10)	5510	(30, 24, 20)	14400	61.74	(30, 20, 10)	6000	8.17	107.88
10	8	(28, 19, 10)	6200	(38, 30, 20)	22800	72.81	(32, 20, 10)	6400	3.13	168.41
11	8	(52, 17, 9)	9405	(47, 24, 20)	22560	58.31	(57, 20, 10)	11400	17.50	120.61
12	8	(27, 18, 10)	5040	(30, 25, 19)	14250	64.63	(30, 20, 10)	6000	16.00	127.33
Average		—	5760	—	15169	59.57	—	6179	5.60	85.74