Water Flow Optimizer

Reference: Luo K. Water flow optimizer: a nature-inspired evolutionary algorithm for global optimization[J]. IEEE Transactions on Cybernetics, 2021.

Variables	Meaning
pop	The number of water particles
iter	The number of iterations
pl	The laminar probability
pe	The eddying probability
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]
best_score	The global best score
best_location	The position of the global best particle
possible_position	List, the possible movements of water particles
possible_score	List, the score of possible movements
iter_best	List, the best-so-far score of each iteration
con_iter	The last iteration number when the best_score is updated

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 = 3000
    pl = 0.3
    pe = 0.7
    lbound = [0, 0, 10, 10]
    ubound = [99, 99, 200, 200]
    print(main(pop, iter, pl, pe, lbound, ubound))

Output:

The upper figure is the convergence curve, and the lower figure is the enlarged view. The WFO converges at its 1250-th iteration.

{
    'best solution': [1.3005502034963052, 0.6428626394484327, 67.3860209065443, 10.000000000000005], 
    'best score': 8050.913534658795, 
    'convergence iteration': 1250
}