Hybrid intelligence approach for multi-load level reactive power planning using VAR compensator in power transmission network

Protection and Control of Modern Power Systems

Table 3 Details of benchmark-test-functions [39]

Benchmarks	Range	Functions	Type
Sphere	[− 100, 100]	\( f(u)=\sum \limits_{i=1}^d{u}_i^2 \)	UM
Step	[−100, 100]	\( f(u)=\sum \limits_{i=1}^d{\left({u}_i+0.5\right)}^2 \)	UM
Dejong’s	[−1.28, 1.28]	\( f(u)=\sum \limits_{i=1}^d\left[{iu}_i^4+\mathit{\operatorname{rand}}\left(0,1\right)\right] \)	UM
Ackley’s	[−32, 32]	\( f(u)=-20\exp \left(-0.2\sqrt{\frac{1}{d}\sum \limits_{i=1}^d{u}_i^2}\right)-\exp \left(\frac{1}{d}\sum \limits_{i=1}^d\cos \left(2\pi {u}_i\right)\right)+20+e \)	MM
Griwank	[−600, 600]	\( f(u)=\sum \limits_{i=1}^d\frac{u_i^2}{4000}-\prod \limits_{i=1}^d\cos \left(\frac{u_i}{\sqrt{i}}\right)+1 \)	MM
Schwefel’s	[− 500, 500]	\( f(u)=\sum \limits_{i=1}^d\left[100{\left({x}_{i+1}-{x}_i^2\right)}^2+{\left({x}_i-1\right)}^2\right] \)	MM