Harmony Search

Reference: A new heuristic optimization algorithm: Harmony search[J]. Simulation, 2001, 2(2):60-68

Variables	Meaning
hms	Harmony memory size
iter	The number of iterations
hmcr	Harmony memory consideration rate
par	Pitch adjustment rate
bw	Bandwidth
nnew	The number of new harmonies created in each iteration
lb	The lower bound (list)
ub	The upper bound (list)
pos	The set of harmonies (list)
score	The score of harmonies (list)
dim	Dimension (list)
new_pos	The set of newly created harmonies (list)
new_score	The score of newly created harmonies (list)
gbest	The score of the global best harmony
gbest_pos	The position of the global best harmony (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
    hms = 30
    iter = 1000
    hmcr = 0.9
    par = 0.1
    bw = 0.02
    nnew = 20
    lb = [0, 0, 10, 10]
    ub = [99, 99, 200, 200]
    print(main(hms, iter, hmcr, par, bw, nnew, lb, ub))

Output:

The HS converges at its 674-th iteration, and the global best value is 8114.787624542521.

{
    'best score': 8114.787624542521, 
    'best solution': [1.3078025478995294, 0.6468035853866221, 67.40186804119926, 10], 
    'convergence iteration': 674
}