Biased Initialization

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 do not need 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 |      7 |  3.4498120761 |  3.5720363508 |  0.000000E+00
     2 |      400 |     10 |  3.4498120761 |  3.6900721146 |  0.000000E+00
     3 |      500 |      8 |  3.3156556714 |  3.6739753199 |  0.000000E+00
     4 |      600 |      6 |  3.1791347805 |  3.3565188180 |  0.000000E+00
     5 |      700 |      6 |  3.0018445382 |  3.1936330666 |  0.000000E+00
     6 |      800 |      7 |  2.7697440492 |  3.0296347551 |  0.000000E+00
     7 |      900 |      5 |  2.6794514616 |  2.8805573058 |  0.000000E+00
     8 |     1000 |      6 |  2.5320222264 |  2.6748708277 |  0.000000E+00
     9 |     1100 |      8 |  2.2682622087 |  2.3985960717 |  0.000000E+00
    10 |     1200 |     12 |  2.1003467070 |  2.4401607727 |  0.000000E+00

[1]:

<pymoo.core.result.Result at 0x107731090>

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 |  3.0731111570 |  3.5509953393 |  0.000000E+00
     2 |      100 |     11 |  2.9880803008 |  3.6187327244 |  0.000000E+00
     3 |      200 |     12 |  2.9880803008 |  3.3645507936 |  0.000000E+00
     4 |      300 |      7 |  2.5790751253 |  3.2335589851 |  0.000000E+00
     5 |      400 |     12 |  2.3565452599 |  3.0401088150 |  0.000000E+00
     6 |      500 |      9 |  2.2763320737 |  2.6122510588 |  0.000000E+00
     7 |      600 |      8 |  2.2509934597 |  2.4301576015 |  0.000000E+00
     8 |      700 |     10 |  1.9639887257 |  2.3668197539 |  0.000000E+00
     9 |      800 |      8 |  1.4716815079 |  1.9850583407 |  0.000000E+00
    10 |      900 |      9 |  1.4716815079 |  1.8232881293 |  0.000000E+00

[2]:

<pymoo.core.result.Result at 0x11a450d00>
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