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NSGA-II

Reference: Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.

Nondominated sorting genetic algorithm II (NSGA-II) with simulated binary crossover (SBX) and polynomial mutation.

Variables Meaning
npop Population size
iter Iteration number
lb Lower bound
ub Upper bound
pc Crossover probability (default = 1)
eta_c The spread factor distribution index (default = 20)
pm Mutation probability (default = 0.1)
eta_m The perturbance factor distribution index (default = 20)
dim Dimension
pop Population
objs Objectives
pfs pfs[i] means the Pareto front which the i-th individual belongs to
rank The Pareto rank of all the individuals in the population
cd Crowding distance
mating_pool Mating pool
pf The obtained Pareto front

Test problem: ZDT3

$$ \left{ \begin{aligned} &f_1(x)=x_1\\ &f_2(x)=g(x)\left[1-\sqrt{x_1/g(x)}-\frac{x_1}{g(x)}\sin(10\pi x_1)\right]\\ &g(x)=1+9\left(\sum_{i=2}^nx_i\right)/(n-1)\\ &x_i\in[0, 1], \qquad i=1,\cdots,n \end{aligned} \right. $$

Example

if __name__ == '__main__':
    main(100, 300, np.array([0] * 10), np.array([1] * 10))
Output:

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