Particle Swarm Optimization Algorithm for Solving Function Extremum Problems

The Particle Swarm Optimization (PSO) algorithm is an intelligent algorithm commonly used for solving extremum problems in function optimization. This algorithm mimics the collective behavior of bird flocks to search for optimal solutions. In this program, we can observe in detail the optimization process of PSO, including key steps such as particle position updates using the formula x_i(t+1) = x_i(t) + v_i(t+1), velocity adjustments governed by v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t)), and fitness evaluation through objective function calculations. Through this implementation, we gain deeper insights into the working mechanism and advantages of PSO, such as its global search capability and parallel computation efficiency. The code typically involves initializing particle positions/velocities, defining inertia weight (w) and acceleration constants (c1, c2), and implementing iteration loops with convergence checks.