An Auxiliary Function Method for Global Minimization in Integer Programming

Table 2

Numerical results of Problem 4 (𝑀=10⁸).

Algorithm	𝑥0	𝑥^∗	𝐸𝑓+𝑔
AFM	[1,1,0,0]^𝑇	[1,1,1,1]^𝑇	3936
	[1,1,1,1]^𝑇	[1,1,1,1]^𝑇	3324
	[−10,10,−10,10]^𝑇	[1,1,1,1]^𝑇	4977
	[−10,−5,0,5]^𝑇	[1,1,1,1]^𝑇	3454
	[−10,0,0,−10]^𝑇	[1,1,1,1]^𝑇	3571
	[0,0,0,0]^𝑇	[1,1,1,1]^𝑇	3539
DFMA	[1,1,0,0]^𝑇	[1,1,1,1]^𝑇	9153
	[1,1,1,1]^𝑇	[1,1,1,1]^𝑇	9123
	[−10,10,−10,10]^𝑇	[1,1,1,1]^𝑇	14543
	[−10,−5,0,5]^𝑇	[1,1,1,1]^𝑇	9248
	[−10,0,0,−10]^𝑇	[1,1,1,1]^𝑇	9285
	[0,0,0,0]^𝑇	[1,1,1,1]^𝑇	9162
DFMB	[1,1,0,0]^𝑇	[1,1,1,1]^𝑇	6523
	[1,1,1,1]^𝑇	[1,1,1,1]^𝑇	6498
	[−10,10,−10,10]^𝑇	[1,1,1,1]^𝑇	8553
	[−10,−5,0,5]^𝑇	[1,1,1,1]^𝑇	6701
	[−10,0,0,−10]^𝑇	[1,1,1,1]^𝑇	6655
	[0,0,0,0]^𝑇	[1,1,1,1]^𝑇	6530