An Adaptive Bacterial Foraging Optimization Algorithm with Lifecycle and Social Learning

Table 1

Benchmark functions used in the experiment.

	Function	Formulation	Variable ranges	𝑓(𝑥^∗)
𝑓1	Sphere	𝑓(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖	[−5.12,5.12]	0
𝑓2	Rosenbrock	𝑓(𝑥)=∑^𝐷−1𝑖=1100𝑥^2𝑖−𝑥𝑖+1^2+1−𝑥𝑖^2	[−15,15]	0
𝑓3	Rastrigin	𝑓(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖−10cos(2𝜋𝑥𝑖)+10	[−10,10]	0
𝑓4	Ackley	𝑓(𝑥)=20+𝑒−20𝑒^(−0.2(1/𝐷)∑𝐷𝑖=1𝑥2𝑖)−𝑒^((1/𝐷)∑𝐷𝑖=1cos(2𝜋𝑥𝑖))	[−32.768,32.768]	0
𝑓5	Griewank	1𝑓(𝑥)=4000^𝐷𝑖∑=1𝑥^2𝑖−∏^𝐷𝑖=1𝑥cos^𝑖√𝑖+1	[−600,600]	0
𝑓6	Schwefel2.22	𝑓(𝑥)=∑^𝐷𝑖=1𝑥𝑖+∏^𝐷𝑖=1𝑥𝑖	[−10,10]	0
𝑓7	Shifted sphere	𝑓(𝑥)=∑^𝐷𝑖=1𝑧^2𝑖+𝑓bias1,𝑧=𝑥−𝑜	[−100,100]	−450
𝑓8	Shifted Schwefel1.2	𝑓(𝑥)=∑^𝐷∑𝑖=1^𝑖𝑗=1𝑧𝑗^2+𝑓bias2,𝑧=𝑥−𝑜	[−100,100]	−450
𝑓9	Shifted Rosenbrock	𝑓(𝑥)=∑^𝐷−1𝑖=1(100(𝑧^2𝑖−𝑧𝑖+1)^2+(𝑧𝑖−1)^2)+𝑓_bias6,	[−100,100]	390
		𝑧=𝑥−𝑜
𝑓10	Shifted rotated Griewank	𝑓(𝑥)=∑^𝐷𝑖=1𝑧^2𝑖−4000^𝐷∏𝑖=1𝑧cos^𝑖√𝑖+1+𝑓_bias7,	No bounds	−180
		𝑧=(𝑥−𝑜)∗𝑀
		𝑓(𝑥)=−20exp−0.21𝐷^𝐷𝑖∑=1𝑧^2𝑖
𝑓11	Shifted rotated Ackley	1−exp𝐷^𝐷𝑖∑=1cos2𝜋𝑧𝑖+20+𝑒+𝑓_bias8,	[−32,32]	−140
		𝑧=(𝑥−𝑜)∗𝑀
𝑓12	Shifted Rastrigin	𝑓(𝑥)=∑^𝐷𝑖=1𝑧^2𝑖−10cos2𝜋𝑧𝑖+10+𝑓_bias9,	[−5,5]	−330
		𝑧=(𝑥−𝑜)
𝑓13	Shifted rotated Rastrigin	𝑓(𝑥)=∑^𝐷𝑖=1𝑧^2𝑖−10cos2𝜋𝑧𝑖+10+𝑓_bias10,	[−5,5]	−330
		𝑧=(𝑥−𝑜)∗𝑀
		𝑓(𝑥)=∑^𝐷∑𝑖=1^𝑘max𝑘=0𝑎^𝑘cos2𝜋𝑏^𝑘𝑧𝑖+0.5
𝑓14	Shifted rotated Weierstrass	−𝐷∑^𝑘max𝑘=0𝑎^𝑘cos2𝜋𝑏^𝑘⋅0.5+𝑓_bias11,	[−0.5,0.5]	90
		𝑧=(𝑥−𝑜)∗𝑀