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 |  3.3964081538 |  3.6259891178 |  0.000000E+00
     2 |      400 |      6 |  3.1097757797 |  3.6194649000 |  0.000000E+00
     3 |      500 |      7 |  2.5086266661 |  3.0300779266 |  0.000000E+00
     4 |      600 |      8 |  2.4924464817 |  2.8454565056 |  0.000000E+00
     5 |      700 |      7 |  2.1828638281 |  2.6355705446 |  0.000000E+00
     6 |      800 |     10 |  1.9559331968 |  2.8513196787 |  0.000000E+00
     7 |      900 |      5 |  1.6050907669 |  2.1003702004 |  0.000000E+00
     8 |     1000 |      8 |  1.5079232696 |  2.1068711721 |  0.000000E+00
     9 |     1100 |      5 |  1.3825471777 |  1.8258211682 |  0.000000E+00
    10 |     1200 |      9 |  0.9505397695 |  1.3279334785 |  0.000000E+00
[1]:
<pymoo.core.result.Result at 0x7fb8cac8afd0>

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 |      9 |  3.3815805339 |  3.8812224224 |  0.000000E+00
     2 |      100 |      5 |  3.3815805339 |  3.2191629500 |  0.000000E+00
     3 |      200 |      4 |  2.1685470597 |  2.6570874278 |  0.000000E+00
     4 |      300 |      5 |  1.9735924562 |  2.1336859663 |  0.000000E+00
     5 |      400 |      6 |  1.5130978941 |  1.8369989439 |  0.000000E+00
     6 |      500 |      3 |  1.5130978941 |  1.6175725573 |  0.000000E+00
     7 |      600 |      7 |  1.4299626763 |  1.4248231870 |  0.000000E+00
     8 |      700 |      6 |  1.1522367478 |  1.2460282461 |  0.000000E+00
     9 |      800 |      8 |  1.1522367478 |  1.3090562172 |  0.000000E+00
    10 |      900 |      6 |  0.9918438754 |  0.8925696618 |  0.000000E+00
[2]:
<pymoo.core.result.Result at 0x7fb8cadf6eb0>