Swarm Intelligence Algorithms

Original bat algorithm 45

This frequency variation is then used for updating the velocity of each bat

v

t+1

i

= v

t

i

+ (x

t

i

− x

∗

)f

i

, (4.3)

where x

∗

is the best solution found at iteration t.

The position or solution vector x

i

is updated by

x

t+1

i

= x

t

i

+ (∆t)v

t+1

i

, (4.4)

where ∆t is the iteration or time increment. As all iterative algorithms are

updated in a discrete manner, we usually set ∆t = 1. Thus, we can simply

consider the vectors without any physical units, and then write the update

equation as

x

t+1

i

= x

t

i

+ v

t+1

i

. (4.5)

The pulse emission rate r

i

can monotonically increase from a lower value

r

(0)

i

, while the loudness can reduce from a higher value A

(0)

= 1. We have

A

t+1

i

= αA

t

i

, r

t+1

i

= r

(0)

i

[1 − exp(−γt)], (4.6)

where 0 < α < 1 and γ > 0 are constants. When