xavier-mayiming / chaotic-particle-swarm-optimization

Chaotic Particle Swarm Optimization

Reference: Liu, B., Wang, L., Jin, Y.-H., Tang, F., & Huang, D.-X. (2005). Improved particle swarm optimization combined with chaos. Chaos, Solitons & Fractals, 25(5), 1261–1271.

Variables	Meaning
pop	The number of particles
iter	The number of iterations
iter_chaos	The iteration number of chaotic local search
lbound	List, the lower bound
ubound	List, the upper bound
vmin	List, the minimum velocity
vmax	List, the maximum velocity
c1	The acceleration coefficient of exploitation
c2	The acceleration coefficient of exploration
omega_min	The minimum value of inertia weight
omega_max	The maximum value of inertia weight
dim	The number of dimensions
score	List, the score of the i-th particle is score[i]
position	List, the position of the i-th particle is position[i]
velocity	List, the velocity of the i-th particle is velocity[i]
g_best	The global best score
g_best_location	The position of the global best particle
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_location[i]
iter_best	List, the best-so-far score of each iteration
omega	The inertia weight with Adaptive Inertia Weight Factor (AIWF)

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__':
    # Parameter settings
    pop = 50
    iter = 100
    iter_chaos = 300
    c1 = 2
    c2 = 2
    omega_min = 0.2
    omega_max = 1.2
    lbound = [0, 0, 10, 10]
    ubound = [100, 100, 100, 100]
    vmin = [-2, -2, -2, -2]
    vmax = [2, 2, 2, 2]
    print(main(pop, iter, iter_chaos, lbound, ubound, vmin, vmax, c1, c2, omega_min, omega_max))

Output:

This comparative figure indicates that the CPSO finds a better solution compared to the PSO.

{
    'best solution': [1.3553460966593345, 0.6489113019601358, 67.41527440529954, 15.750952463723596], 
    'best score': 8688.271882233967
}