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 |      5 |  3.0138058941 |  3.7176787630 |  0.000000E+00
     2 |      400 |      6 |  3.0138058941 |  3.6427723242 |  0.000000E+00
     3 |      500 |      8 |  3.0138058941 |  3.4364790298 |  0.000000E+00
     4 |      600 |     11 |  3.0138058941 |  3.4386766063 |  0.000000E+00
     5 |      700 |     15 |  2.8667629021 |  3.3320777680 |  0.000000E+00
     6 |      800 |      4 |  2.5658326517 |  2.8253961582 |  0.000000E+00
     7 |      900 |      8 |  2.4141409799 |  2.6622877311 |  0.000000E+00
     8 |     1000 |      8 |  2.1928645655 |  2.4698842478 |  0.000000E+00
     9 |     1100 |      7 |  2.1863131225 |  2.4396968173 |  0.000000E+00
    10 |     1200 |      9 |  2.0191938459 |  2.1108713214 |  0.000000E+00

[1]:

<pymoo.core.result.Result at 0x104ed8b30>

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 |      7 |  3.3187610973 |  3.9446592819 |  0.000000E+00
     2 |      100 |      7 |  3.3187610973 |  3.6947717967 |  0.000000E+00
     3 |      200 |      6 |  2.9518388038 |  3.6145482342 |  0.000000E+00
     4 |      300 |      7 |  2.9518388038 |  3.5043045355 |  0.000000E+00
     5 |      400 |      5 |  2.9432434290 |  3.3264026468 |  0.000000E+00
     6 |      500 |      8 |  2.8173758892 |  2.8948286380 |  0.000000E+00
     7 |      600 |      5 |  2.4927446235 |  2.6612847083 |  0.000000E+00
     8 |      700 |      4 |  2.4859345973 |  2.6081961608 |  0.000000E+00
     9 |      800 |      5 |  2.3022041851 |  2.4928715407 |  0.000000E+00
    10 |      900 |      8 |  2.3022041851 |  2.2670321519 |  0.000000E+00

[2]:

<pymoo.core.result.Result at 0x104f0d640>