Particle Swarm Optimization

This project presents a simple implementation of the Particle Swarm Optimization (PSO) algorithm in MATLAB, applied to the Ackley benchmark function for testing global optimization.Standars Particle Swarm Optimization algorithm is defined as below :

$$ \mathbf{v}_i^{t+1} = w \mathbf{v}_i^{t} + c_1 r_1 (\mathbf{pbest}_i - \mathbf{x}_i^{t}) + c_2 r_2 (\mathbf{gbest} - \mathbf{x}_i^{t}) $$

$$ \mathbf{x}_i^{t+1} = \mathbf{x}_i^{t} + \mathbf{v}_i^{t+1} $$

The Ackley function is defined as:

$$ f(x) = -20 \cdot \exp\left( -0.2 \cdot \sqrt{ \frac{1}{n} \sum_{i=1}^{n} x_i^2 } \right) - \exp\left( \frac{1}{n} \sum_{i=1}^{n} \cos(2 \pi x_i) \right) + 20 + e $$

The results was visualized as below :

As shown in the plot, the swarm successfully converges to the global minimum of the Ackley function.

Repository Structure

The repository is organized as follows:

• Main/: Contains the main PSO algorithm and related scripts.
• ackley.m: Defines the Ackley test function used for optimization.
• plotPSO.m: Provides visualization of the PSO optimization process.
• pso.m: Implements the PSO algorithm.

How to Use This Repository

1. Clone the repository to your local machine using Git:

git clone https://github.com/zeniafragaki/Particle_Swarm_Optimization.git

2. Open MATLAB and change the working directory to the Main folder inside the cloned repo:

cd('path/to/Particle_Swarm_Optimization/Main')

*Check your path before running the algorithm

3. Run pso.m to start the PSO algorithm.

*4.If you use this algorithm, try changing the upper and lower bounds in the parameters section of pso.m, or replace Ackley’s benchmark function to observe how the PSO results change.