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

Table 6

Basis functions of test 3 [10].

Function	Formula	Range	Optimum 𝑓(𝑥)
Easom	𝑓ES(𝑥^→)=−cos(𝑥1)cos(𝑥2)𝑒^−((𝑥1−𝜋)2+(𝑥2−𝜋)2)	𝑥^→∈[−100,100]^𝑛𝑛=2	−1
DeJong	𝑓DJ(𝑥^→)=𝑥^21+𝑥^22+𝑥^23	𝑥^→∈[−5.12,5.12]^𝑛𝑛=3	0
Zakharov	𝑓Zn(𝑥^→)=∑^𝑛𝑖=1𝑥^2𝑖+∑^𝑛𝑖=1𝑖𝑥𝑖2^2+∑^𝑛𝑖=1𝑖𝑥𝑖2^4	𝑥^→∈[−5,10]^𝑛𝑛=2.5	0