An Auxiliary Function Method for Global Minimization in Integer Programming

Table 3

Numerical results of Problem 5 (𝑀=10⁸).

Algorithm	𝑥0	𝑥^∗	𝐸𝑓+𝑔
AFM	[2,−2]^𝑇	[0,−1]^𝑇	118743
	[0,−1]^𝑇	[0,−1]^𝑇	83181
	[−2,−2]^𝑇	[0,−1]^𝑇	91850
	[−0.5,−1]^𝑇	[0,−1]^𝑇	86024
	[1,−1.5]^𝑇	[0,−1]^𝑇	113741
	[1,−1]^𝑇	[0,−1]^𝑇	91698
DFMA	[2,−2]^𝑇	[0,−1]^𝑇	268489
	[0,−1]^𝑇	[0,−1]^𝑇	254444
	[−2,−2]^𝑇	[0,−1]^𝑇	270930
	[−0.5,−1]^𝑇	[0,−1]^𝑇	254444
	[1,−1.5]^𝑇	[0,−1]^𝑇	267978
	[1,−1]^𝑇	[0,−1]^𝑇	254444
DFMB	[2,−2]^𝑇	[0,−1]^𝑇	176397
	[0,−1]^𝑇	[0,−1]^𝑇	170351
	[−2,−2]^𝑇	[0,−1]^𝑇	175828
	[−0.5,−1]^𝑇	[0,−1]^𝑇	171831
	[1,−1.5]^𝑇	[0,−1]^𝑇	173889
	[1,−1]^𝑇	[0,−1]^𝑇	173334