Table 3.

Benchmark functions used to validate the performance of ABSA

Label	Function name (type)	Function	Optimum value of F(x)	Range of solution space
FN01	Third-order polynomial with a single variable (Max)	$F(x)=x^3-5x^2-20x$	15.4564	$-65.12\le x\le 65.12$
FN02	Polynomial with two variables (Max)	$F(x_1,x_2)=x_1^3-5x_1^2-2.04x_2^2+4x_2$	1.9608	$-3\le (x_1,x_2)\le 3$
FN03	Exponential with two variables (Max)	$F(x_1,x_2)=x_1{exp}^{(-x_1^2-x_2^2)}$	0.4289	$-2\le (x_1,x_2)\le 2$
FN04	De Jong’s (Min)	$F(x)={\sum }_{i=1}^n{x}_i^2$	0.0000	$-5.12\le x_i\le 5.12,i=1,\dots ,N$
FN05	Weighted sphere model (Min)	$F(x)={\sum }_{i=1}^n(i·x_i^2)$	0.0000	$-5.12\le x_i\le 5.12,i=1,\dots ,N$
FN06	Shwefel’s (Min)	$F(x)={\sum }_{i=1}^n(i·x_i^2)$	0.0000	$-65.536\le x_i\le 65.536,i=1,\dots ,N$
FN07	Rosenbrock’s valley (Min)	$F(x)={\sum }_{i=1}^n[100{(x_{i+1}-x_i^2)}^2)+{(1-x_i)}^2]$	0.0000	$-2.048\le x_i\le 2.048,i=1,\dots ,N$
FN08	Easom’s (Min)	$F(x_1,x_2)=-cos{x}_{1}cos{x}_{2}exp(-{(x_1-\mathit{\pi })}^2-{(x_2-\mathit{\pi })}^2)$	−1.0000	$-100\le (x_1,x_2)\le 100$
FN09	Goldstein-Price’s (Min)	$F(x_1,x_2)=(1+{(x_1+x_2+1)}^2(19-14x_1+3x_1^2-14x_2+6x_1{x}_2+3x_2^2))(30+{(2x_1-3x_2)}^2(18-32x_1+12x_1^2+48x_2-36x_1{x}_2+27x_2^2))$	3.0000	$-2\le (x_1,x_2)\le 2$
FN10	Booth’s (Min)	$F(x_1,x_2)={(x_1+2x_2-7)}^2+{(2x_1+x_2-5)}^2$	0.0000	$-10\le (x_1,x_2)\le 10$