Particle Swarm Optimization Algorithm

This text discusses the Particle Swarm Optimization function. Particle Swarm Optimization (PSO) is a population-based optimization technique inspired by collective animal behaviors such as bird flocking or fish schooling. In PSO implementations, each potential solution is represented as a particle possessing position and velocity vectors. These particles iteratively adjust their trajectories by exchanging information with neighboring particles, gradually converging toward optimal solutions. Key algorithmic components include: - **Initialization**: Randomly generating particle positions and velocities within search boundaries - **Fitness Evaluation**: Calculating objective function values for each particle's position - **Velocity Update**: Adjusting particle movement using personal best (pBest) and global best (gBest) positions according to the formula: v_i(t+1) = w*v_i(t) + c1*r1*(pBest_i - x_i(t)) + c2*r2*(gBest - x_i(t)) - **Position Update**: Moving particles based on updated velocities: x_i(t+1) = x_i(t) + v_i(t+1) PSO finds extensive applications in function optimization challenges, particularly in neural network training, image processing, machine learning model tuning, and other complex optimization domains where gradient-based methods face limitations.