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"""
Optimization using bonmin
=========================
"""
# %%
# %%
# In this example we are going to explore mixed-integer non linear problems
# optimization using the `bonmin <https://www.coin-or.org/Bonmin/index.html>`_
# interface.
# %%
import openturns as ot
# %%
# List available algorithms
for algo in ot.Bonmin.GetAlgorithmNames():
print(algo)
# %%
# Details and references on bonmin algorithms are available
# `here <https://projects.coin-or.org/Bonmin>`_ .
# %%
# Setting up and solving a simple problem
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# The following example will demonstrate the use of bonmin "BB" algorithm to
# solve the following problem:
#
# .. math::
# \min - x_0 - x_1 - x_2
#
# such that:
#
# .. math::
# \begin{array}{l}
# (x_1 - \frac{1}{2})^2 + (x_2 - \frac{1}{2})^2 \leq \frac{1}{4} \\
# x_0 - x_1 \leq 0 \\
# x_0 + x_2 + x_3 \leq 2\\
# x_0 \in \{0,1\}^n\\
# (x_1, x_2) \in \mathbb{R}^2\\
# x_3 \in \mathbb{N}
# \end{array}
#
# The theoretical minimum is reached for :math:`x = [1,1,0.5,0]`.
# At this point, the objective function value is :math:`-2.5`
#
# N.B.: equality and inequality constraints are required to be stated as
# :math:`g(x) = 0` and :math:`h(x) \geq 0`, respectively. Thus the inequalities
# above will have to be restated to match this requirement:
#
# .. math::
# \begin{array}{l}
# -(x_1 - \frac{1}{2})^2 - (x_2 - \frac{1}{2})^2 + \frac{1}{4} \geq 0\\
# -x_0 + x_1 \geq 0 \\
# -x_0 - x_2 - x_3 + 2 \geq 0\\
# \end{array}
# %%
# Definition of objective function
objectiveFunction = ot.SymbolicFunction(["x0", "x1", "x2", "x3"], ["-x0 -x1 -x2"])
# Definition of variables bounds
bounds = ot.Interval([0.0] * 4, [1, 1e6, 1e6, 5])
# Definition of constraints
# Constraints are defined as g(x) = 0 and h(x) >= 0
# No equality constraint -> nothing to do
# Inequality constraints:
h = ot.SymbolicFunction(
["x0", "x1", "x2", "x3"],
["-(x1-0.5)^2 - (x2-0.5)^2 + 0.25", "x1 - x0", "-x0 - x2 - x3 + 2"],
)
# Definition of variables types
CONTINUOUS = ot.OptimizationProblemImplementation.CONTINUOUS
BINARY = ot.OptimizationProblemImplementation.BINARY
INTEGER = ot.OptimizationProblemImplementation.INTEGER
variablesType = [BINARY, CONTINUOUS, CONTINUOUS, INTEGER]
# Setting up Bonmin problem
problem = ot.OptimizationProblem(objectiveFunction)
problem.setBounds(bounds)
problem.setVariablesType(variablesType)
problem.setInequalityConstraint(h)
bonminAlgorithm = ot.Bonmin(problem, "B-BB")
bonminAlgorithm.setMaximumCallsNumber(10000)
bonminAlgorithm.setMaximumIterationNumber(1000)
bonminAlgorithm.setStartingPoint([0.0] * 4)
# %%
# Running the solver
bonminAlgorithm.run()
# Retrieving the results
result = bonminAlgorithm.getResult()
print(" -- Optimal point = " + str(result.getOptimalPoint()))
print(" -- Optimal value = " + str(result.getOptimalValue()))
print(" -- Evaluation number = " + str(result.getInputSample().getSize()))
|
