Basic Particle Swarm Optimization Algorithm Implementation

In this implementation, we utilize the basic Particle Swarm Optimization (PSO) algorithm to solve the Rastrigrin function using MATLAB. The Rastrigrin function is a commonly used benchmark in optimization problems, featuring multiple local minima that challenge optimization algorithms. The PSO algorithm mimics the social behavior of particle swarms in nature, where each particle represents a potential solution and adjusts its position based on personal best experience and global best knowledge from the swarm. Key implementation aspects include: - Initialization of particle positions and velocities within specified bounds - Fitness evaluation using the Rastrigrin function formula: f(x) = 10n + Σ[xi² - 10cos(2πxi)] - Updating particle velocities using cognitive and social components with inertia weight - Tracking personal best (pbest) and global best (gbest) positions - Iterative optimization process with convergence criteria The MATLAB implementation involves defining key parameters such as swarm size, maximum iterations, cognitive coefficient (c1), social coefficient (c2), and inertia weight. The algorithm efficiently navigates the solution space to locate the global minimum of the Rastrigrin function, demonstrating PSO's effectiveness in handling multimodal optimization problems.