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

Table 2

Basis functions of test 1 [10].

Function	Formula (𝑛=10)	Range	Optimum 𝑓(𝑥)
Plane (PL)	𝑓PL(𝑥^→)=𝑥1	𝑥^→∈[0.5,1.5]^𝑛	1.5
Diagonal; Plane (DP)	𝑓DP(𝑥^→1)=𝑛^𝑛𝑖∑=1𝑥𝑖	𝑥^→∈[0.5,1.5]^𝑛	1.5
Sphere (SP)	𝑓SP(𝑥^→)=∑^𝑛𝑖=1𝑥^2𝑖	𝑥^→∈[−3,7]^𝑛	0
Ellipsoid (EL)	𝑓EL(𝑥^→)=∑^𝑛𝑖=1100^(𝑖−1)/(𝑛−1)𝑥𝑖^2	𝑥^→∈[−3,7]^𝑛	0
Cigar (CG)	𝑓CG(𝑥^→)=𝑥^21+10∑^4𝑛𝑖=2𝑥^2𝑖	𝑥^→∈[−3,7]^𝑛	0
Tablet (TB)	𝑓TB(𝑥^→)=10^4𝑥^21+∑^𝑛𝑖=2𝑥^2𝑖	𝑥^→∈[−3,7]^𝑛	0
Rosenbrock (Rn)	𝑓Rn(𝑥^→)=∑^𝑛−1𝑖=1100(𝑥^2𝑖−𝑥𝑖+1)^2+(𝑥𝑖−1)^2	𝑥^→∈[−5,5]^𝑛	0