A Crossover Bacterial Foraging Optimization Algorithm

Table 1

Description of benchmark functions used.

Function	Mathematical representation	Range of search	Theoretical optima
	𝑓1^→𝑥=−20exp−0.21𝑛^𝑛𝑖∑=1𝑥^2𝑖
Ackley	1−exp𝑛^𝑛𝑖∑=1cos2𝜋𝑥𝑖	(−5,5)^𝑛	𝑓1^→0=0
	+20+𝑒
Griewank	𝑓2^→𝑥=14000^𝑛𝑖∑=1𝑥^2𝑖−∏^𝑛𝑖=1𝑥cos^𝑖√𝑖+1	(−10,10)^𝑛	𝑓2^→0=0
Rastrigin	𝑓3^→𝑥=∑^𝑛𝑖=1𝑥^2𝑖−10cos2𝜋𝑥𝑖+10	(−5,5)^𝑛	𝑓3^→0=0
Rosenbrock	𝑓4^→𝑥=∑^𝑛−1𝑖=1100𝑥𝑖+1−𝑥^2𝑖^2+1−𝑥𝑖^2	(−2,2)^𝑛	𝑓4^→0=0
Rotated hyperellipsoid	𝑓5^→𝑥=∑^𝑛𝑖𝑖=1∑𝑗=1𝑥^2𝑗	(−5,5)^𝑛	𝑓5^→0=0
De Jong’s	𝑓6^→𝑥=∑^𝑛𝑖=1𝑥^2𝑖	(−5,5)^𝑛	𝑓6^→0=0
Weighted sphere model	𝑓7^→𝑥=∑^𝑛𝑖=1𝑖⋅𝑥^2𝑖	(−5,5)^𝑛	𝑓6^→0=0