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

Table 2

Comparisons of CPU time and social utility between the proposed SAACO approach and LINGO.

Test case (𝑚,𝑛)*	LINGO		SAACO		Difference
	Social utility	CPU time (seconds)	Social utility	CPU time (seconds)	Difference_s^+	Difference_t^++
(10,10)	2.422536	1.0	2.418003	1.214600	−0.001871	0.214600
(10,20)	3.027710	4.0	3.029383	4.901600	0.000553	0.225400
(10,30)	3.454207	10.5	3.448223	15.805900	−0.001732	0.505324
(10,40)	3.665038	21.2	3.660824	22.857000	−0.001150	0.078160
(10,50)	3.737554	31.3	3.7343727	36.64825	−0.000851	0.171994
(20,10)	3.981162	5.6	3.998787	7.241300	0.004427	0.293089
(20,20)	5.575991	30.9	5.60343	26.974900	0.004921	−0.127026
(20,30)	6.447189	88.9	6.440597	79.355200	−0.001023	−0.107366
(20,40)	6.942952	215.7	6.943312	190.842300	0.000052	−0.115242
(20,50)	7.265195	375.3	7.250848	347.890200	−0.001975	−0.073034

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