Swarm Intelligence Algorithms

252 Monarch Butterfly Optimization

flutter staying in region 1 and total number of monarch butterfly population

respectively. Similarly, the butterflies found in region 2 are considered to be

‘subpopulation 2’, P

n2

= P

n

− P

n1

.

This migration process of butterflies is mathematically expressed as

s

ij

(t + 1) = s

r

1

,j

(t) (19.1)

where, s

ij

(t + 1), represents the jth position element/variable of the ith but-

terfly in t + 1 generation, whereas, s

r

1

,j

(t), represents the jth element of s

r

1

which is the new position of monarch butterfly r

1

of current generation t. The

butterfly r

1

is randomly selected from subpopulation 1 or region 1.

For decision making, a random number