Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

Table 1

Comparison results of Examples 1–10.

Example; ()	Methods	Time (s)	Iter	Optimal solution	Optimal value
1 (min); ()	[13]	5.0780	48	(2.0, 8.0)	10
	[14]	0.3	53	(2.0, 8.0)	10
	[15]	10.83	27	(2.0003, 7.9999)	10.0042
	Ours	0.062	1	(2.0, 8.0)	10
2 (min); ()	[13]	0.2030	2	(0.0, 4.0)	3
	[16]	—	3	(0.0, 4.0)	3
	Ours	0.086	1	(0.0, 4.0)	3
3 (min); ()	[13]	0.1880	1	(1.3148, 0.1396, 0.0, 0.4233)	0.8902
	[17]	—	6	(1.3148, 0.1396, 0.0, 0.4233)	0.8902
	Ours	0.093	1	(1.3148, 0.1396, 0.0, 0.4233)	0.8902
4 (min); ()	[8]	—	—	(0.0, 4.0)	3
	[18]	—	—	(0.0, 4.0)	3
	Ours	0.0842	1	(0.0, 4.0)	3
5 (min); ()	[19]	—	—	(1.0, 3.0)	−13
	Ours	0.0150	1	(1.0, 3.0)	−13
6 (min); ()	[19]	—	—	(1.0, 4.0)	−22
	Ours	0.0160	1	(1.0, 4.0)	−22
7 (min); ()	[20]	—	57	(5.5556, 1.7778, 2.6667)	−112.754
	Ours	1.5930	34	(5.5556, 1.7778, 2.6667)	−112.7531
8 (max); ()	[21]	—	13	(0.74984, 0.74984)	−38.87628
	Ours	0.5	16	(0.75, 0.75)	−38.8750
9 (min); ()	[22]	—	7	(1.547, 2.421)	−16.2837
	Ours	0.659	23	(1.5480, 2.4152)	−16.2893
10 (min); ()	[22]	—	29	(1.5549, 0.7561)	10.6756
	Ours	0.7662	27	(1.5568, 0.7545)	10.6753