Ant Colony Optimization Algorithm for Continuous Domains Based on Position Distribution Model of Ant Colony Foraging

Table 4

Basis functions of test 2 [10].

Function	Formula	Range	Optimum 𝑓(𝑥)
𝐵2	𝑓𝐵2(𝑥^→)=𝑥^21+2𝑥^22−0.3cos(3𝜋𝑥1)−0.4cos(4𝜋𝑥2)+0.7	𝑥^→∈[−100,100]^𝑛𝑛=2	0
Goldstein and Price	𝑓𝑥GP^→=1+𝑥1+𝑥2+1^219−14𝑥1+3𝑥^21−14𝑥2+6𝑥1𝑥2+3𝑥^22×30+2𝑥1−3𝑥2^218−32𝑥1+12𝑥^21+48𝑥2−36𝑥1𝑥2+27𝑥^22	𝑥^→∈[0.5,1.5]^𝑛𝑛=2	3
Sphere model	𝑓SM(𝑥^→)=∑^𝑛𝑖=1𝑥^2𝑖	𝑥^→∈[−5.12,5.12]^𝑛𝑛=6	0
Martin and Gaddy	𝑓MG(𝑥)=(𝑥1−𝑥2)^2+𝑥1+𝑥2−103^2	𝑥^→∈[−20,20]^𝑛𝑛=2	0
Rosenbrock	𝑓Rn(𝑥^→)=∑^𝑛−1𝑖=1100(𝑥^2𝑖−𝑥𝑖+1)^2+(𝑥𝑖−1)^2	𝑥^→∈[−5,10]^𝑛; 𝑛=2.5	0