Some basic Python code is available to help you begin a PSO implementation for the Schwefel minimiza$-$

tion problem.

$($a$)(25$ points$)$ Complete the basic PSO implementation based on $$particle best$$ and $$global best$($as

represented in Figure $2).$

Basic PSO Update Functions

V t$+$i

i $=$ wV t

i $+\backslash$phi $1$r$1$

Pi $$ Xt

i

$+\backslash$phi $2$r$2$

Pg $$ Xt

i

Xt$+$i

i $=$ Xt

i $+$ V t$+$i

i

where V t

i and Xt

i are the velocity and position of the ith particle at time

step t; w is the inertial weight; $\backslash$phi $1$ and $\backslash$phi $2$ are constant multipliers for the

$$cognitive$$ and $$social$$ components, respectively; Pi is the best histori$-$

cal position for the ith particle and Pg is the best historical position ever

found by swarm; r$1$ and r$2$ are random numbers uniformly distributed

between $0$ and $1$ that are randomized at each iteration.

Figure $2$: Velocity and position update functions for the basic PSO implementation