Mixed-Variable Optimization#

Layer 1: Use

Solve problems that include not only continuous variables but also integer and categorical variables, using saealib.

With minimize(), you can specify strings or instances for the algorithm, surrogate model, and evaluation strategy. The examples on this page add only problem-specific settings and use defaults for everything else.

What you’ll be able to do

By the end of this page, you’ll be able to define continuous, integer, and categorical variables in a Problem and run type-aware search.

For ordinary continuous variables, use the high-level API; to add custom variables or operators, see Custom components. This page defines variable types in a Problem and runs search with type-aware built-in operators.

Set up the problem#

Assume an objective function where each design variable is one of three types: continuous, integer, or categorical.

def func(x):
    # x[0]: continuous, x[1]: integer, x[2]: categorical index
    return x[0] ** 2 + (x[1] - 3) ** 2 + (0.0 if x[2] == 1 else 5.0)

x[2] represents one of three categories (0, 1, 2), and no penalty is applied only when 1 is chosen.

Define variables#

Each dimension’s type is specified with a subclass of Variable, passed to Problem’s variables argument.

Class	Meaning
`ContinuousVariable(lb, ub)`	Continuous value. A regular `Problem` with `lb`/`ub` omitted is treated as this type
`IntegerVariable(lb, ub)`	Integer value
`CategoricalVariable(categories)`	Selects one from a list of categories

import numpy as np
from saealib import Problem, ContinuousVariable, IntegerVariable, CategoricalVariable

variables = [
    ContinuousVariable(-5.0, 5.0),
    IntegerVariable(0, 10),
    CategoricalVariable([0, 1, 2]),
]

problem = Problem(
    func=func,
    dim=3,
    n_obj=1,
    direction=np.array([-1.0]),
    variables=variables,
)

Passing variables automatically derives Problem.lb/Problem.ub from each element’s lb/ub, so you don’t specify the lb/ub arguments.

Run minimize#

from saealib import minimize

result = minimize(problem, max_fe=500, seed=0)
print(result.x, result.f)

GA comes with dedicated crossover and mutation operators for each variable type by default (CrossoverIntegerSBX/MutationIntegerUniform for integers, CrossoverCategorical/MutationCategorical for categorical variables), so passing variables alone gives you type-aware search.

PSO is a velocity-based update scheme and cannot correctly handle integer and categorical variables.

For mixed-variable problems, stick with algorithm='GA' (the default).

Customize operators#

The operators for integer and categorical variables can also be specified individually via GA’s keyword arguments.

from saealib import (
    GA,
    CrossoverBLXAlpha,
    MutationUniform,
    SequentialSelection,
    TruncationSelection,
    CrossoverIntegerSBX,
    CrossoverCategorical,
    MutationIntegerUniform,
    MutationCategorical,
)

ga = GA(
    crossover=CrossoverBLXAlpha(0.7, 0.4),
    mutation=MutationUniform(0.3),
    parent_selection=SequentialSelection(),
    survivor_selection=TruncationSelection(),
    integer_crossover=CrossoverIntegerSBX(0.7, eta=15.0),
    integer_mutation=MutationIntegerUniform(0.3),
    categorical_crossover=CrossoverCategorical(0.7),
    categorical_mutation=MutationCategorical(0.3),
)

result = minimize(problem, algorithm=ga, max_fe=500, seed=0)

See Algorithm for details on each operator.