PSO for Solving Two-Objective Function Extremum Problems

PSO (Particle Swarm Optimization) is an optimization algorithm designed to solve extremum problems in multi-objective functions, particularly suitable for beginners learning multi-objective optimization. The algorithm mimics birds' foraging behavior to search for optimal solutions by treating particles as candidate solutions and iteratively updating their positions and velocities to improve solution quality. In code implementation, each particle maintains position (x) and velocity (v) vectors, updated using personal best (pbest) and global best (gbest) positions through velocity update equations like v = w*v + c1*rand()*(pbest-x) + c2*rand()*(gbest-x). PSO's simplicity and efficiency—achieved through parallel search mechanisms and minimal parameter tuning—make it a popular choice for multi-objective optimization problems. By applying PSO, learners can better understand the nature of multi-objective optimization problems while gaining practical experience in handling objective conflicts and Pareto front approximation through swarm intelligence techniques.