An Auxiliary Function Method for Global Minimization in Integer Programming

Table 5

Numerical results of Problem 7 (𝑀=10⁶).

Algorithm	𝑥0	𝑥^∗	𝐸𝑓+𝑔
AFM	[0,…,0]^𝑇	[1,…,1]^𝑇	873553
	[3,…,3]^𝑇	[1,…,1]^𝑇	557111
	[−5,…,−5]^𝑇	[1,…,1]^𝑇	463176
	[2,−2,…,2,−2,2]^𝑇	[1,…,1]^𝑇	576770
	[3,−3,…,3,−3,3]^𝑇	[1,…,1]^𝑇	794156
	[5,−5,…,5,−5,5]^𝑇	[1,…,1]^𝑇	581242
DFMA	[0,…,0]^𝑇	[1,…,1]^𝑇	893881
	[3,…,3]^𝑇	[1,…,1]^𝑇	1317062
	[−5,…,−5]^𝑇	[1,…,1]^𝑇	899485
	[2,−2,…,2,−2,2]^𝑇	[1,…,1]^𝑇	896281
	[3,−3,…,3,−3,3]^𝑇	[1,…,1]^𝑇	1516925
	[5,−5,…,5,−5,5]^𝑇	[1,…,1]^𝑇	1518820
DFMB	[0,…,0]^𝑇	[1,…,1]^𝑇	615173
	[3,…,3]^𝑇	[1,…,1]^𝑇	956979
	[−5,…,−5]^𝑇	[1,…,1]^𝑇	620725
	[2,−2,…,2,−2,2]^𝑇	[1,…,1]^𝑇	617573
	[3,−3,…,3,−3,3]^𝑇	[1,…,1]^𝑇	655048
	[5,−5,…,5,−5,5]^𝑇	[1,…,1]^𝑇	756943