Optimization

159Guided Random Search Methods

TABLE 5.7

Algorithm for Particle Swarm Optimization

Step 1: Initialize i

max

, w

1

, ϕ

1

, ϕ

2

, n (population size), x

i,min

, and x

i,max

.

Step 2: Initialize the starting position and velocities of the variables as

x

i,k

= x

i,min

+ (x

i,max

− x

i,min

)u

i

k = 1 ⋯ n

v

i,k

= 0

Step 3: Compute p

i,k

= f(x

i,k

) k = 1 ⋯ n

Step 4: Compute pbest

i,k

= p

i,k

and gbest

i

= minimum(pbest

i,k

)

The location of pbest

k

and gbest is given by p

xik

and g

ix

.

Step 5: Update velocity

v

i+1,k

= w

1

v

i,k

+ ϕ

1

(p

xik

− x

i,k

)u

i

+ ϕ

2

(g

ix

− x

i,k

)u

i

Step 6: Update position x

i+1,k

= x

i,k

+ v

i+1,k

Step 7: Update tness p

i+1,k

= f(x

i+1,k

)

Step 8: If p

i+1,k

< pbest

i,k

then ...