Particle Swarm Optimization

Reference: Kennedy J, Eberhart R. Particle swarm optimization[C]//Proceedings of ICNN'95-International Conference on Neural Networks. IEEE, 1995, 4: 1942-1948.

Variables	Meaning
pop	The number of population
u_bound	List, the upper bound of the i-th dimension is u_bound[i]
l_bound	List, the lower bound of the i-th dimension is l_bound[i]
vmin	List, the minimum velocity of the particle on the i-th dimension is vmin[i]
vmax	List, the maximum velocity of the particle on the i-th dimension is vmax[i]
iter	The maximum number of iterations
omega	The inertia weight to control the influence of the previous velocity value on the updated velocity
phi1	The cognitive weight
phi2	The social weight
dim	The number of dimensions
position	List, the position of the i-th particle is position[i]
fitness	List, the score of the i-th particle is fitness[i]
velocity	List, the velocity of the i-th particle is velocity[i]
g_best	The global best score
g_best_location	The global best position
p_best	List, the personal best score of the i-th particle is p_best[i]
p_best_location	List, the personal best position of the i-th particle is p_best[i]
iter_best	List, the best so-far score of each iteration

Test problem: Pressure vessel design

$$ \begin{align} &\text{min}\ f(x)=0.6224x_1x_3x_4+1.7781x_2x_3^2+3.1661x_1^2x_4+19.84x_1^2x_3,\\ &\text{s.t.} \\ &-x_1+0.0193x_3\leq0,\\ &-x_3+0.0095x_3\leq0,\\ &-\pi x_3^2x_4-\frac{4}{3}\pi x_3^3+1296000\leq0,\\ &x_4-240\leq0,\\ &0\leq x_1\leq99,\\ &0\leq x_2 \leq99,\\ &10\leq x_3 \leq 200,\\ &10\leq x_4 \leq 200. \end{align} $$

Example

if __name__ == '__main__':
    pop = 50
    iter = 500
    vmin = [-2, -2, -2, -2]
    vmax = [2, 2, 2, 2]
    print(main(pop, iter, vmin, vmax))

Output:

{
    'best solution': [1.300568607387978, 0.6431938035005514, 67.38697386901593, 10.0], 
    'best score': 8053.847210456193,
}