Enhanced Self-adaptive Global-best Harmony Search

Reference: Kaiping Luo, Jie Ma, Qiuhong Zhao. Enhanced self-adaptive global-best harmony search without any extra statistic and external archive. Information Sciences, 2019. 482: 228-247.

Variables	Meaning
hms	Harmony memory size
ni	The number of improvisations (iterations)
hmcr	Harmony memory consideration rate
par	Pitch adjustment rate
bw	Bandwidth
lb	The lower bound (list)
ub	The upper bound (list)
pos	The set of harmonies (list)
score	The score of harmonies (list)
dim	Dimension
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 = 10
    lb = [0, 0, 10, 10]
    ub = [99, 99, 200, 200]
    ni = 10000 * len(lb)
    print(main(hms, ni, lb, ub))

Output:

The ESGHS converges at its 14,294-th iteration, and the global best value is 8050.914044830637.

{
    'best score': 8050.914044830637, 
    'best solution': [1.3005502310626382, 0.6428626530744853, 67.38602233485172, 10.000000182456352], 
    'convergence iteration': 14294
}