Algorithm 1: The pseudo-code of IBWOA

Initializing populations using Gauss chaos mapping

Calculate the fitness value of each spider

Record the current worst fitness value, the best fitness value and its location information

while $t<T_{\max }$

initialize random parameters $m,\beta ,p,l_1,l_2,l_3,l_4$

for $i=1:N$

if random ≤ 0.3

the spider moves and update its location information using Equation (1)

or else

the spider moves and update its location information using Equation (2)

end if

calculating the pheromone value of the spider using Equation (3)

update the spider with low pheromone values using Equation (13)

if random ≤ $p$

h = 0

if ≤ 0.5

update the spider location information using Equation (7)

or else

update the spider location information using Equation (8)

end if

or else

h = 1

end if

calculate the fitness value of the spider

if the fitness value of the spider ≤ the best fitness value,

update the best fitness value and its location information

end if

end for

if h == 1

Obtain opposition solutions using Equation (11)

Retaining spiders with higher fitness values

end if

$t=t+1$

end while

Output the best fitness value