Tree Seed Algorithm

Reference: Mustafa Servet Kiran. TSA: Tree-seed algorithm for continuous optimization[J]. Expert Systems with Applications, 2015, 6686-6698.

Variables	Meaning
pop	The number of trees
iter	The number of iterations
lb	The lower bound (list)
ub	The upper bound (list)
ST	Search tendency
pos	The position of all trees (list)
score	The score of all trees (list)
dim	Dimension
gbest	The score of the global best tree
gbest_pos	The position of the global best tree (list)
seed_pos	The position of the seeds of the ith tree (list)
seed_score	The score of the seeds of the ith tree (list)
iter_best	The global best score of each iteration (list)
con_iter	The last iteration number when "gbest" 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 = 10
    iter = 1000
    lb = [0, 0, 10, 10]
    ub = [99, 99, 200, 200]
    ST = 0.1
    print(main(pop, iter, lb, ub, ST))

Output:

The TSA converges at its 442-th iteration, and the global best value is 8050.913534658795.

{
    'best score': 8050.913534658795, 
    'best solution': [1.3005502034963052, 0.6428626394484327, 67.3860209065443, 10.000000000000004], 
    'convergence iteration': 442
}