Ant Colony Optimization for Social Utility Maximization in a Multiuser Communication System

Table 3

Comparisons of CPU time and social utility between the proposed SAACO approach and LINGO in large scale problem.

Test case (𝑚,𝑛)*	LINGO		SAACO		Differrence
	Sociall utility	CPU time (seconds)	Sociall utility	CPU time (seconds)	Difference_s^+	Difference_t^++
(10,100)	4.064655	238.333	4.054523	238.439	−0.00249	0.00044
(10,128)	4.122419	563.667	4.107250	362.911	−0.00368	−0.55318
(10,256)	4.162954	3906.667	4.217743	2835.007	0.01316	−0.37801
(20,100)	7.911308	3224.000	7.888093	1608.873	−0.00293	−1.00389
(20,128)	8.061679	4807.000	8.031333	3144.747	−0.00376	−0.52858
(20,256)	8.372676	45587.000	8.354917	21984.100	−0.00212	−1.07364

∗(𝑚,𝑛) = (number of users, number of channels).
⁺Difference_s = (socialutilitybySAACO−socialutilitybyLINGO)/socialutilitybyLINGO.
⁺⁺Difference_t = (CPUtimebySAACO−CPUtimebyLINGO)/CPUtimebyLINGO.