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 |      9 |  3.4263166968 |  3.6065637248 |  0.000000E+00
     2 |      400 |      9 |  3.4263166968 |  3.6065637248 |  0.000000E+00
     3 |      500 |      9 |  3.1254966147 |  3.5042317638 |  0.000000E+00
     4 |      600 |      8 |  3.1254966147 |  3.3424242973 |  0.000000E+00
     5 |      700 |      9 |  2.7730924862 |  2.9476011711 |  0.000000E+00
     6 |      800 |      6 |  2.7651185744 |  3.0604868293 |  0.000000E+00
     7 |      900 |      6 |  2.7204373268 |  2.5981733455 |  0.000000E+00
     8 |     1000 |      9 |  2.4744829151 |  2.6817757290 |  0.000000E+00
     9 |     1100 |     10 |  2.0338516500 |  2.3534914670 |  0.000000E+00
    10 |     1200 |     11 |  1.6560598627 |  2.2848483862 |  0.000000E+00

[1]:

<pymoo.core.result.Result at 0x109b9c3b0>

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 |     12 |  3.2297464619 |  3.6925488405 |  0.000000E+00
     2 |      100 |     11 |  3.2297464619 |  3.5903848768 |  0.000000E+00
     3 |      200 |      7 |  3.0523599646 |  3.4791563522 |  0.000000E+00
     4 |      300 |      8 |  2.6639663788 |  3.1920129823 |  0.000000E+00
     5 |      400 |     10 |  2.6165004620 |  3.1022423363 |  0.000000E+00
     6 |      500 |      2 |  2.5960444794 |  2.4970731136 |  0.000000E+00
     7 |      600 |      9 |  2.4282609218 |  2.5870466534 |  0.000000E+00
     8 |      700 |      8 |  2.1444465512 |  2.4875942051 |  0.000000E+00
     9 |      800 |      9 |  2.1444465512 |  2.3615570636 |  0.000000E+00
    10 |      900 |      9 |  1.9416099053 |  2.6063042431 |  0.000000E+00

[2]:

<pymoo.core.result.Result at 0x10c931550>