Table 2 The setup of the parameters.

From: Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications

Algorithm

Parameters

Value

AHA

migration coefficient

2n

AO

 

\(G_1=2\times rand-1\) \(G_2=2\times (1-\frac{t}{T})\) \(QF\left( t\right) =t^\frac{2\times r a n d-1}{{(1-T)}^2}\)

quality function used to equilibrium

the search strategies QF the slope from the

first location (1) to the last location (t)

DA

inertia weight w

\(w=max+t\times \left( \frac{max-min}{T}\right)\)

\(min=0.4,\ max=0.9\)

separation weight s

\(s=2\times rand\times [0.1-t(\frac{0.1}{T/2})]\)

alignment weight a

\(a=2\times rand\times [0.1-t(\frac{0.1}{T/2})]\)

the cohesion weight c

\(c=2\times rand\times [0.1-t(\frac{0.1}{T/2})]\)

food factor f

\(f=2\times rand\)

enemy factor e

\(e=0.1-t(\frac{0.1}{{T/2}})\)

DMOA

convergence constant a

\(a={(1-\frac{t}{T})}^{2\times \frac{t}{T}}\)

GBO

\(\beta\) the most significant parameter

\(\beta =\beta _{min}+(\beta _{max}-\beta _{min})\times {(1-{(\frac{t}{T})}^3)}^2\)

in the GBO to balance the exploration

 

and exploitation searching processes

\(\beta _{min}=0.2,\beta _{max}=1.2,\ pr=0.5\)

HGS

convergence constant a

\(a=2\times (1-\frac{t}{T})\)

HHO

\(E_0\) is the initial state of its energy, E indicates the escaping energy of the prey.

\(E=2E_0\times (1-\frac{t}{T})\)

LFGOA

 

\(C=C_{max}-t\times \frac{C_{max}-C_{min}}{T}\)

 

convergence constant C

\(C_{max}=1, C_{min}=0.00001\)

MVO

travelling distance rate (TDR) \(\in {[}0.6 1{]}\)

\(TDR=1-\frac{t^{1/p}}{T^{1/p}},\ p=6\)

  1. t Current iteration, T The maximal iteration.