粒子群最佳化 PSO

import random, math

def pso(objective, bounds, n_particles=30, iterations=100):
    dim = len(bounds)
    particles = [[random.uniform(b[0], b[1]) for b in bounds] for _ in range(n_particles)]
    velocity = [[0]*dim for _ in range(n_particles)]
    pbest = [p[:] for p in particles]
    pbest_val = [objective(p) for p in particles]
    gbest = min(pbest, key=lambda p: objective(p))
    gbest_val = objective(gbest)
    
    w, c1, c2 = 0.7, 1.5, 1.5
    for _ in range(iterations):
        for i in range(n_particles):
            for d in range(dim):
                r1, r2 = random.random(), random.random()
                velocity[i][d] = (w * velocity[i][d] 
                    + c1 * r1 * (pbest[i][d] - particles[i][d])
                    + c2 * r2 * (gbest[d] - particles[i][d]))
                particles[i][d] += velocity[i][d]
                particles[i][d] = max(bounds[d][0], min(bounds[d][1], particles[i][d]))
            
            val = objective(particles[i])
            if val < pbest_val[i]:
                pbest[i] = particles[i][:]
                pbest_val[i] = val
                if val < gbest_val:
                    gbest = particles[i][:]
                    gbest_val = val
    return gbest, gbest_val

def sphere(x):
    return sum(v*v for v in x)

best, val = pso(sphere, [(-10,10)]*3)
print(f"PSO 找到: {best}, f(x)={val:.6f}")