Wolf Pack Algorithm for Unconstrained Global Optimization

Table 1

Benchmark functions in experiments.

No.	Functions	Formulation	Global extremum	𝐷	C	Range
1	Rosenbrock	𝑓(𝑥)=100(𝑥2−𝑥^21)^2+(1−𝑥1)^2	𝑓min(𝑥)=0	2	UN	(−2.048, 2.048)
2	Colville	𝑓(𝑥)=100𝑥^21−𝑥2^2+𝑥1−1^2+𝑥3−1^2+90𝑥^23−𝑥4^2+10.1𝑥2−1^2+𝑥4−1^2+19.8(𝑥2−1)(𝑥4−1)	𝑓min(𝑥)=0	4	UN	(−10, 10)
3	Sphere	𝑓(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖	𝑓min(𝑥)=0	200	US	(−100, 100)
4	Sumsquares	𝑓(𝑥)=∑^𝐷𝑖=1𝑖𝑥^2𝑖	𝑓min(𝑥)=0	150	US	(−10, 10)
5	Booth	𝑓(𝑥)=(𝑥1+2𝑥2−7)^2+(2𝑥1+𝑥2−5)^2	𝑓min(𝑥)=0	2	MS	(−10, 10)
6	Bridge	𝑓(𝑥)=sin𝑥^21+𝑥^22𝑥^21+𝑥^22 +expcos2𝜋𝑥1+cos2𝜋𝑥22−0.7129	𝑓max(𝑥)=3.0054	2	MN	(−1.5, 1.5)
7	Ackley	𝑓(𝑥)=−20exp−0.21𝐷^𝐷𝑖∑=1𝑥^2𝑖1−exp𝐷^𝐷𝑖∑=1cos2𝜋𝑥𝑖+20+𝑒	𝑓min(𝑥)=0	50	MN	(−32, 32)
8	Griewank	1𝑓(𝑥)=4000^𝐷𝑖∑=1𝑥^2𝑖−∏^𝐷𝑖=1𝑥cos^𝑖√𝑖+1	𝑓min(𝑥)=0	100	MN	(−600, 600)

𝐷: dimension; C: characteristic; U: unimodal; M: multimodal; S: separable; N: nonseparable.