U-NSGA-III

The algorithm is implemented based on [30]. NSGA-III selects parents randomly for mating. It has been shown that tournament selection performs better than random selection. The U stands for unified and increases NSGA-III’s performance by introducing tournament pressure.

The mating selection works as follows:

Example

import numpy as np

from pymoo.algorithms.moo.nsga3 import NSGA3
from pymoo.algorithms.moo.unsga3 import UNSGA3
from pymoo.problems import get_problem
from pymoo.optimize import minimize

problem = get_problem("ackley", n_var=30)

# create the reference directions to be used for the optimization - just a single one here
ref_dirs = np.array([[1.0]])

# create the algorithm object
algorithm = UNSGA3(ref_dirs, pop_size=100)

# execute the optimization
res = minimize(problem,
               algorithm,
               termination=('n_gen', 150),
               save_history=True,
               seed=1)

print("UNSGA3: Best solution found: \nX = %s\nF = %s" % (res.X, res.F))

UNSGA3: Best solution found:
X = [-0.01452247  0.10488671 -0.05554308 -0.15282582  0.07108663 -0.00474762
  0.03998208 -0.16357624 -0.03409419 -0.034674   -0.05350105 -0.07683928
 -0.0294493   0.03797795 -0.03061699 -0.02951845 -0.03778558 -0.02335115
  0.07986168 -0.04592675 -0.01191177 -0.02108846  0.03165472 -0.1141958
  0.00033753 -0.04114211 -0.00800433  0.09807808 -0.00910689 -0.01033059]
F = [0.45634742]

U-NSGA-III has for single- and bi-objective problems a tournament pressure which is known to be useful. In the following, we provide a quick comparison (here just one run, so not a valid experiment) to see the difference in convergence.

_res = minimize(problem,
                NSGA3(ref_dirs, pop_size=100),
                termination=('n_gen', 150),
                save_history=True,
                seed=1)
print("NSGA3: Best solution found: \nX = %s\nF = %s" % (res.X, res.F))

NSGA3: Best solution found:
X = [-0.01452247  0.10488671 -0.05554308 -0.15282582  0.07108663 -0.00474762
  0.03998208 -0.16357624 -0.03409419 -0.034674   -0.05350105 -0.07683928
 -0.0294493   0.03797795 -0.03061699 -0.02951845 -0.03778558 -0.02335115
  0.07986168 -0.04592675 -0.01191177 -0.02108846  0.03165472 -0.1141958
  0.00033753 -0.04114211 -0.00800433  0.09807808 -0.00910689 -0.01033059]
F = [0.45634742]

import numpy as np
import matplotlib.pyplot as plt

ret = [np.min(e.pop.get("F")) for e in res.history]
_ret = [np.min(e.pop.get("F")) for e in _res.history]

plt.plot(np.arange(len(ret)), ret, label="unsga3")
plt.plot(np.arange(len(_ret)), _ret, label="nsga3")
plt.title("Convergence")
plt.xlabel("Generation")
plt.ylabel("F")
plt.legend()
plt.show()

API