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"""
Optimization using dlib
=======================
"""
# %%
# In this example we are going to explore optimization using the interface to the `dlib <http://dlib.net/>`_ library.
# %%
import openturns as ot
import openturns.viewer as otv
# %%
# List available algorithms
for algo in ot.Dlib.GetAlgorithmNames():
print(algo)
# %%
# More details on dlib algorithms are available `here <http://dlib.net/optimization.html>`_ .
# %%
# Solving an unconstrained problem with conjugate gradient algorithm
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# The following example will demonstrate the use of dlib conjugate gradient algorithm to find the minimum of `Rosenbrock function <https://en.wikipedia.org/wiki/Rosenbrock_function>`_.
# The optimal point can be computed analytically, and its value is [1.0, 1.0].
# %%
# Define the problem based on Rosebrock function
rosenbrock = ot.SymbolicFunction(["x1", "x2"], ["(1-x1)^2+(x2-x1^2)^2"])
problem = ot.OptimizationProblem(rosenbrock)
# %%
# The optimization algorithm is instantiated from the problem to solve and the name of the algorithm
algo = ot.Dlib(problem, "cg")
print("Dlib algorithm, type ", algo.getAlgorithmName())
print("Maximum iteration number: ", algo.getMaximumIterationNumber())
print("Maximum evaluation number: ", algo.getMaximumCallsNumber())
print("Maximum absolute error: ", algo.getMaximumAbsoluteError())
print("Maximum relative error: ", algo.getMaximumRelativeError())
print("Maximum residual error: ", algo.getMaximumResidualError())
print("Maximum constraint error: ", algo.getMaximumConstraintError())
# %%
# When using conjugate gradient, BFGS/LBFGS, Newton, least squares or trust region methods, optimization proceeds until one of the following criteria is met:
#
# - the errors (absolute, relative, residual, constraint) are all below the limits set by the user ;
# - the process reaches the maximum number of iterations or function evaluations.
# %%
# Adjust number of iterations/evaluations
algo.setMaximumIterationNumber(1000)
algo.setMaximumCallsNumber(10000)
algo.setMaximumAbsoluteError(1e-3)
algo.setMaximumRelativeError(1e-3)
algo.setMaximumResidualError(1e-3)
# %%
# Solve the problem
startingPoint = [1.5, 0.5]
algo.setStartingPoint(startingPoint)
algo.run()
# %%
# Retrieve results
result = algo.getResult()
print("x^ = ", result.getOptimalPoint())
print("f(x^) = ", result.getOptimalValue())
print("Iteration number: ", result.getIterationNumber())
print("Evaluation number: ", result.getCallsNumber())
print("Absolute error: ", result.getAbsoluteError())
print("Relative error: ", result.getRelativeError())
print("Residual error: ", result.getResidualError())
print("Constraint error: ", result.getConstraintError())
# %%
# Solving problem with bounds, using LBFGS strategy
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# In the following example, the input variables will be bounded so the function global optimal point is not included in the search interval.
#
# The problem will be solved using LBFGS strategy, which allows the user to limit the amount of memory used by the optimization process.
# %%
# Define the bounds and the problem
bounds = ot.Interval([0.0, 0.0], [0.8, 2.0])
boundedProblem = ot.OptimizationProblem(
rosenbrock, ot.Function(), ot.Function(), bounds
)
# %%
# Define the Dlib algorithm
boundedAlgo = ot.Dlib(boundedProblem, "lbfgs")
boundedAlgo.setMaxSize(15) # Default value for LBFGS' maxSize parameter is 10
startingPoint = [0.5, 1.5]
boundedAlgo.setStartingPoint(startingPoint)
boundedAlgo.run()
# %%
# Retrieve results
result = boundedAlgo.getResult()
print("x^ = ", result.getOptimalPoint())
print("f(x^) = ", result.getOptimalValue())
print("Iteration number: ", result.getIterationNumber())
print("Evaluation number: ", result.getCallsNumber())
print("Absolute error: ", result.getAbsoluteError())
print("Relative error: ", result.getRelativeError())
print("Residual error: ", result.getResidualError())
print("Constraint error: ", result.getConstraintError())
# %%
# **Remark:**
# The bounds defined for input variables are always strictly respected when using dlib algorithms. Consequently, the constraint error is always 0.
# %%
# Draw optimal value history
graph = result.drawOptimalValueHistory()
view = otv.View(graph)
# %%
# Solving least squares problem
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# In least squares problem, the user provides the residual function to minimize.
# Here the underlying OptimizationProblem is defined as a LeastSquaresProblem.
#
# dlib least squares algorithms use the same stop criteria as CG, BFGS/LBFGS and Newton algorithms.
# However, optimization will stop earlier if no significant improvement can be achieved during the process.
# %%
# Define residual function
n = 3
m = 20
x = [[0.5 + 0.1 * i] for i in range(m)]
model = ot.SymbolicFunction(["a", "b", "c", "x"], ["a + b * exp(-c *x^2)"])
p_ref = [2.8, 1.2, 0.5] # Reference a, b, c
modelx = ot.ParametricFunction(model, [0, 1, 2], p_ref)
# Generate reference sample (with normal noise)
x00 = modelx(x[0])[0]
y = [x00 * ot.Normal(1.0, 0.05).getRealization()[0] for i in range(m)]
def residualFunction(params):
modelx = ot.ParametricFunction(model, [0, 1, 2], params)
return [modelx(x[i])[0] - y[i] for i in range(m)]
# %%
# Definition of residual as ot.PythonFunction and optimization problem
residual = ot.PythonFunction(n, m, residualFunction)
lsqProblem = ot.LeastSquaresProblem(residual)
# %%
# Definition of Dlib solver, setting starting point
lsqAlgo = ot.Dlib(lsqProblem, "least_squares")
lsqAlgo.setStartingPoint([0.0, 0.0, 0.0])
lsqAlgo.run()
# %%
# Retrieve results
result = lsqAlgo.getResult()
print("x^ = ", result.getOptimalPoint())
print("f(x^) = ", result.getOptimalValue())
print("Iteration number: ", result.getIterationNumber())
print("Evaluation number: ", result.getCallsNumber())
print("Absolute error: ", result.getAbsoluteError())
print("Relative error: ", result.getRelativeError())
print("Residual error: ", result.getResidualError())
print("Constraint error: ", result.getConstraintError())
# %%
# Draw errors history
graph = result.drawErrorHistory()
view = otv.View(graph)
# %%
# Draw optimal value history
graph = result.drawOptimalValueHistory()
view = otv.View(graph)
otv.View.ShowAll()
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