Bare-Bones Teaching-Learning-Based Optimization

Table 1

Details of numerical benchmarks used.

Function	Formula	𝐷	Range	Optima
Sphere	𝐹1(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖	30	[−100, 100]	0
Sum Square	𝐹2(𝑥)=∑^𝐷𝑖=1𝑖𝑥^2𝑖	30	[−100, 100]	0
Quadric	𝐹3(𝑥)=∑^𝐷𝑖=1𝑖𝑥^4𝑖+random(0,1)	30	[−1.28, 1.28]	0
Step	𝐹4(𝑥)=∑^𝐷𝑖=1𝑥𝑖+0.5^2	30	[−100, 100]	0
Schwefel 1.2	𝐹5(𝑥)=∑^𝐷∑𝑖=1^𝑖𝑗=1𝑥𝑗^2	30	[−100, 100]	0
Schwefel 2.21	𝐹6(𝑥)=max𝑥𝑖,1≤𝑖≤𝐷	30	[−100, 100]	0
Schwefel 2.22	𝐹7(𝑥)=∑^𝐷𝑖=1𝑥𝑖+∏^𝐷𝑖=1𝑥𝑖	30	[−10, 10]	0
Zakharov	𝐹8(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖+∑^𝐷𝑖=10.5𝑖𝑥𝑖^2+∑^𝐷𝑖=10.5𝑖𝑥𝑖^4	30	[−100, 100]	0
Rosenbrock	𝐹9(𝑥)=∑^𝐷−1𝑖=1100𝑥^2𝑖−𝑥𝑖+1^2+𝑥𝑖−1^2	30	[−2.048, 2.048]	0
Ackley	𝐹10−1(𝑥)=20−20exp51𝐷^𝐷𝑖∑=1𝑥^2𝑖1−exp𝐷^𝐷𝑖∑=1cos2𝜋𝑥𝑖+𝑒	30	[−32, 32]	0
Rastrigin	𝐹11(𝑥)=∑^𝐷𝑖=1(𝑥^2𝑖−10cos2𝜋𝑥𝑖+10)	30	[−5.12, 5.12]	0
Weierstrass	𝐹12(𝑥)=∑^𝐷∑𝑖=1^𝑘𝑚𝑎𝑥𝑘=0𝑎^𝑘𝑐𝑜𝑠2𝜋𝑏^𝑘𝑥𝑖+0.5−𝐷∑^𝑘max𝑘=0𝑎^𝑘cos2𝜋𝑏^𝑘×0.5𝑎=0.5𝑏=3𝑘max=20	30	[−0.5, 0.5]	0
Griewank	𝐹13(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖−4000^𝑛∏𝑖=1𝑥cos^𝑖√𝑖+1	30	[−600, 600]	0
Schwefel	𝐹14(𝑥)=418.9829𝐷+∑^𝐷𝑖=1−𝑥𝑖sinabs𝑥𝑖	30	[−500, 500]	0
Bohachevsky1	𝐹15(𝑥)=𝑥^21+2𝑥^22−0.3cos3𝜋𝑥1−0.4cos4𝜋𝑥2+0.7	2	[−100, 100]	0
Bohachevsky2	𝐹16(𝑥)=𝑥^21+2𝑥^22−0.3cos3𝜋𝑥1∗cos4𝜋𝑥2+0.3	2	[−100, 100]	0
Bohachevsky3	𝐹17(𝑥)=𝑥^21+2𝑥^22−0.3cos(3𝜋𝑥1+(4𝜋𝑥2)+0.3	2	[−100, 100]	0
Shekel5	𝐹18(𝑥)=−∑^5𝑖=1(𝑥−𝑎𝑖)(𝑥−𝑎𝑖)^𝑇+𝑐𝑖^−1	4	[0, 10]	−10.1532
Shekel7	𝐹19(𝑥)=−∑^7𝑖=1(𝑥−𝑎𝑖)(𝑥−𝑎𝑖)^𝑇+𝑐𝑖^−1	4	[0, 10]	−10.4029
Shekel10	𝐹20(𝑥)=−∑^10𝑖=1(𝑥−𝑎𝑖)(𝑥−𝑎𝑖)^𝑇+𝑐𝑖^−1	4	[0, 10]	−10.5364