A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems

Algorithm 1

Butterfly optimization algorithm.

	Generate initial population of NP butterflies
	Initialize parameters c, a, p
	While t < tmax
	For each butterfly do
	Calculate the fragrance using equation (1)
	End for
	Find the best butterfly
	For each butterfly Xi do
	Generate a random number r from [0,1]
	If p < r
	Calculate the position using equation (2)
	Else
	Calculate the position using equation (3)
	End if
	Calculate the fitness and select the better one from [, Xi]
	End for
	Update parameter c
	End while
	Output the best position and fitness