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Version: 0.6.1

Mixed Variable Problem

In some cases, variables might have different types; some might be real, discrete (choice), binary, or integer-valued. For those cases, different evolutionary operators must be applied to different types of variables. In pymoo this is supported by defining a MixedVariableProblem where the vars values are set. For example, let us consider the following optimization problem:

from pymoo.core.problem import ElementwiseProblem
from pymoo.core.variable import Real, Integer, Choice, Binary


class MixedVariableProblem(ElementwiseProblem):

    def __init__(self, **kwargs):
        vars = {
            "b": Binary(),
            "x": Choice(options=["nothing", "multiply"]),
            "y": Integer(bounds=(0, 2)),
            "z": Real(bounds=(0, 5)),
        }
        super().__init__(vars=vars, n_obj=1, **kwargs)

    def _evaluate(self, X, out, *args, **kwargs):
        b, x, z, y = X["b"], X["x"], X["z"], X["y"]

        f = z + y
        if b:
            f = 100 * f

        if x == "multiply":
            f = 10 * f

        out["F"] = f

In order to solve such a problem, pymoo offers MixedVariableGA, which defines different operators for each variable type. For more details, please look at the implementation itself.

from pymoo.core.mixed import MixedVariableGA
from pymoo.core.variable import Real, Integer
from pymoo.optimize import minimize

problem = MixedVariableProblem()

algorithm = MixedVariableGA(pop=10)

res = minimize(problem,
               algorithm,
               termination=('n_evals', 1000),
               seed=1,
               verbose=False)

print("Best solution found: \nX = %s\nF = %s" % (res.X, res.F))

Best solution found:
X = {'b': False, 'x': 'nothing', 'y': 0, 'z': 1.5582963983665096e-05}
F = [1.5582964e-05]

Moreover, for single-objective optimization, the well-known Hyperparameter optimization framework Optuna can be used (pymoo only wraps to their interface here. Congrats on their excellent work!).

from pymoo.algorithms.soo.nonconvex.optuna import Optuna
from pymoo.core.variable import Real, Integer
from pymoo.optimize import minimize

problem = MixedVariableProblem()

algorithm = Optuna()

res = minimize(problem,
               algorithm,
               termination=('n_evals', 300),
               seed=1,
               verbose=False)

print("Best solution found: \nX = %s\nF = %s" % (res.X, res.F))

Best solution found:
X = {'b': False, 'x': 'nothing', 'y': 0, 'z': 1.2059959575777589e-05}
F = [1.20599596e-05]

Moreover, if you intend to solve a multi-objective optimization problem, you can either instantiate existing algorithms with MixedVariableMating or add a multi-objective survival to MixedVariableGA. The latter can be realized, for instance by:

class MultiObjectiveMixedVariableProblem(ElementwiseProblem):

    def __init__(self, **kwargs):
        vars = {
            "b": Binary(),
            "x": Choice(options=["nothing", "multiply"]),
            "y": Integer(bounds=(-2, 2)),
            "z": Real(bounds=(-5, 5)),
        }
        super().__init__(vars=vars, n_obj=2, n_ieq_constr=0, **kwargs)

    def _evaluate(self, X, out, *args, **kwargs):
        b, x, z, y = X["b"], X["x"], X["z"], X["y"]

        f1 = z ** 2 + y ** 2
        f2 = (z+2) ** 2 + (y-1) ** 2

        if b:
            f2 = 100 * f2

        if x == "multiply":
            f2 = 10 * f2

        out["F"] = [f1, f2]

from pymoo.visualization.scatter import Scatter
from pymoo.algorithms.moo.nsga2 import RankAndCrowdingSurvival
from pymoo.core.mixed import MixedVariableGA
from pymoo.optimize import minimize

problem = MultiObjectiveMixedVariableProblem()

algorithm = MixedVariableGA(pop_size=20, survival=RankAndCrowdingSurvival())

res = minimize(problem,
               algorithm,
               ('n_gen', 50),
               seed=1,
               verbose=False)

plot = Scatter()
plot.add(problem.pareto_front(), plot_type="line", color="black", alpha=0.7)
plot.add(res.F, facecolor="none", edgecolor="red")
plot.show()

/var/folders/dp/fdf8szyn3zd4kcyh18gxsyvm0000gn/T/ipykernel_98481/3314106399.py:8: DeprecationWarning: RankAndCrowdingSurvival is deprecated and will be removed in version 0.8.*; use RankAndCrowding operator instead, which supports several and custom crowding diversity metrics.
  algorithm = MixedVariableGA(pop_size=20, survival=RankAndCrowdingSurvival())

<pymoo.visualization.scatter.Scatter at 0x7f8bc822c550>

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