Genetic Algorithm

Reference: Holland J H. Genetic algorithms[J]. Scientific American, 1992, 267(1): 66-73.

The genetic algorithm (GA) with simulated binary crossover and polynomial mutation to solve real optimization problems.

Variables	Meaning
npop	population size
iter	iteration number
lb	lower bound
ub	upper bound
pc	crossover probability
eta_c	Spread factor distribution index
pm	mutation probability
eta_m	perturbance factor distribution index
dim	dimension
pop	population
objs	objectives
gbest	the global best
gbest_sol	the global best solution
iter_best	the global best of each iteration
con_iter	convergence iteration

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__':
    t_npop = 300
    t_iter = 1500
    t_lb = np.array([0, 0, 10, 10])
    t_ub = np.array([99, 99, 200, 200])
    print(main(t_npop, t_iter, t_lb, t_ub))

Output:

The GA converges at its 1,331-th iteration, and the global best value is 8051.400862765215.

{
  'gbest': 8051.400862765215, 
  'best solution': array([ 1.3005842 ,  0.64288936, 67.38671732, 10.        ]), 
  'convergence iteration': 1331
}