PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE

 PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE

PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration.

Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. - PART 2 [Example 2]

1.) Initialize Population [Current Iteration (t) = 0]

Population Size = 4;

𝑥𝑖 : (i = 1,2,3,4) and (t = 0)

𝑥1 =1.3;

𝑥2=4.3;

𝑥3=0.4;

𝑥4=−1.2

2.) Fitness Function used:

Compute Fitness Values for Each Particle using fitness function.

𝑓1=1.69;

𝑓2=18.49;

𝑓3=0.16;

𝑓4=1.44;

3.) Initialize Velocity for each particle in the current Population.

𝑣1=0;

𝑣2=0;

𝑣3=0;

𝑣4=0;

4.) Find Personal Best & Global Best (𝐺_𝐵𝑒𝑠𝑡=0.4;) for each Particle.

𝐺_𝐵𝑒𝑠𝑡=0.4;

5.) Calculate Velocity for each Particle.

Calculate Velocity by:

𝑣_1^(0+1)=1∗0 +1∗0.233(1.3 −1.3)+1∗0.801(0.4 −1.3) ;

𝑣_1^1=0.7209;

𝑣_2^1=−3.1229;

𝑣_3^1=0;

𝑣_4^1=1.2816;

6.) Calculate Position for each Particle.

Calculate Particles Position by : 

𝑥_1^(0+1)=1.3 +0.7209=2.0209 ;

𝑥_2^(0+1)=4.3 −3.1229=1.1771;

𝑥_3^(0+1)=0.4+0=0.4;

𝑥_4^(0+1)=−1.2+1.2816=0.0819 ;

7.) Calculate Fitness Values for each Particle (t = 1).

𝑓_1^1=4.084;

𝑓_2^1=1.3855;

𝑓_3^1=0.16;

𝑓_4^1=0.0067;

8.) Repeat Until Stopping Criteria is met.

(Output after 100 iterations )

For More details watch this video: 

Link: https://youtu.be/Dds5CQGwxlM