Use Particle Swarm Optimizer to Optimize a Non-convex Function

In this project, we will use the Particle Swarm Optimizer (PSO) to optimize a non-convex function. We will implement PSO from scratch and observe its performance on a non-convex function.

You will learn to:

Implement the Particle Swarm Optimizer algorithm using Python.

Use an optimization algorithm to find the global minima of a non-convex function.

Visualize the performance of Particle Swarm Optimizer.

Plot data using Python libraries.

Skills

Optimization

Data Plotting

Prerequisites

Basic knowledge of optimization

Experience with Python

Technologies

NumPy

Python

Matplotlib

Project Description

Particle Swarm Optimizer (PSO) is a type of bio-inspired optimizationBio-inspired algorithms are a type of optimization algorithm which are modeled on biological systems. algorithm that models animal swarms like fish and flies to find the global minimum of a given optimization problem. Different agents are randomly scattered across the solution space that gradually convergeIn optimization, convergence means that the solutions returned by the algorithm start to get closer with successive iterations. Convergence is an indication that the algorithm is able to find an optimal solution for the given problem. around the optimal solution.

This algorithm is well-suited for optimizing a non-convex function that has multiple local minima. For such functions, local optimization algorithms like gradient descent optimizer will not perform very well as the optimal solution is highly dependent on the starting point.

In this project, we will implement PSO and apply it to a non-convex function.

Project Tasks

Implementing the Algorithm

Task 0: Introduction

Task 1: Import Libraries

Task 2: Create Data Arrays

Task 3: Instantiate the Agents and Their Personal Bests

Task 4: Instantiate the Velocities of the Agents

Task 5: Update the Global Best Agent

Task 6: Update the Positions of the Agents

Task 7: Update the Data Arrays

Applying PSO to the Non-convex Function

Task 8: Define the Cost Function

Task 9: Optimize the Cost Function

Task 10: Plot the Results

Task 11: Visualize the Swarm Motion

Congratulations!

Relevant Courses

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