Biased Initialization

One way of customizing an algorithm is a biased initial population. This can be very helpful if expert knowledge already exists, and known solutions should be improved. In the following, two different ways of initialization are provided: a) just providing the design space of the variables and b) a Population object where the objectives and constraints are provided and are not needed to be calculated again.

NOTE: This works with all population-based algorithms in pymoo. Technically speaking, all algorithms which inherit from GeneticAlgorithm. For local-search based algorithm, the initial solution can be provided by setting x0 instead of sampling.

By Array

[1]:

import numpy as np

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.problems import get_problem
from pymoo.optimize import minimize

problem = get_problem("zdt2")

X = np.random.random((300, problem.n_var))

algorithm = NSGA2(pop_size=100, sampling=X)

minimize(problem,
         algorithm,
         ('n_gen', 10),
         seed=1,
         verbose=True)

==========================================================================
n_gen  |  n_eval  | n_nds  |      igd      |       gd      |       hv
==========================================================================
     1 |      300 |      3 |  3.1420452829 |  3.1994780681 |  0.000000E+00
     2 |      400 |      5 |  3.0414757847 |  3.4436017730 |  0.000000E+00
     3 |      500 |      5 |  2.6567210587 |  3.3254690927 |  0.000000E+00
     4 |      600 |      5 |  2.3229724294 |  2.6825979150 |  0.000000E+00
     5 |      700 |      8 |  1.7015039477 |  2.3511355341 |  0.000000E+00
     6 |      800 |      7 |  1.6630101217 |  1.7968312673 |  0.000000E+00
     7 |      900 |      6 |  1.3226871000 |  1.9917156630 |  0.000000E+00
     8 |     1000 |      4 |  1.3226871000 |  1.1836092686 |  0.000000E+00
     9 |     1100 |      5 |  1.2824360868 |  1.4520198639 |  0.000000E+00
    10 |     1200 |      9 |  1.1338264126 |  1.1647797734 |  0.000000E+00

[1]:

<pymoo.core.result.Result at 0x7f7f0a318fd0>

By Population (pre-evaluated)

[2]:

import numpy as np

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.problems import get_problem
from pymoo.core.evaluator import Evaluator
from pymoo.core.population import Population
from pymoo.optimize import minimize

problem = get_problem("zdt2")

# create initial data and set to the population object
X = np.random.random((300, problem.n_var))
pop = Population.new("X", X)
Evaluator().eval(problem, pop)

algorithm = NSGA2(pop_size=100, sampling=pop)

minimize(problem,
         algorithm,
         ('n_gen', 10),
         seed=1,
         verbose=True)

==========================================================================
n_gen  |  n_eval  | n_nds  |      igd      |       gd      |       hv
==========================================================================
     1 |        0 |     10 |  3.7658693587 |  3.9065078970 |  0.000000E+00
     2 |      100 |      4 |  3.1955011925 |  3.3561578888 |  0.000000E+00
     3 |      200 |      3 |  2.6711445903 |  2.9717542152 |  0.000000E+00
     4 |      300 |      4 |  2.5318797772 |  2.7706347082 |  0.000000E+00
     5 |      400 |      5 |  2.0923789500 |  2.1824969365 |  0.000000E+00
     6 |      500 |      4 |  1.7572820023 |  1.9821361334 |  0.000000E+00
     7 |      600 |      8 |  1.5130224748 |  2.0044436873 |  0.000000E+00
     8 |      700 |     10 |  1.3591191014 |  1.8476065358 |  0.000000E+00
     9 |      800 |     11 |  1.3214394872 |  1.6207413422 |  0.000000E+00
    10 |      900 |      4 |  1.1839834216 |  0.9601325831 |  0.000000E+00

[2]:

<pymoo.core.result.Result at 0x7f7f0a172070>