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"""
Optimize an LHS design of experiments
=====================================
"""
# %%
# This examples show how to generate optimized LHS experiments according to the different criteria.
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
# %%
# **LHS and space filling**
# %%
N = 100
# Considering independent Uniform distributions of dimension 3
# Bounds are (-1,1), (0,2) and (0, 0.5)
distribution = ot.JointDistribution(
[ot.Uniform(-1.0, 1.0), ot.Uniform(0.0, 2.0), ot.Uniform(0.0, 0.5)]
)
# Random LHS
lhs = ot.LHSExperiment(distribution, N)
lhs.setAlwaysShuffle(True) # randomized
design = lhs.generate()
# C2
c2 = ot.SpaceFillingC2().evaluate(design)
# PhiP with default p
phip = ot.SpaceFillingPhiP().evaluate(design)
# mindist
mindist = ot.SpaceFillingMinDist().evaluate(design)
# For p->infinity
phip_inf = ot.SpaceFillingPhiP(100).evaluate(design)
print(phip, mindist, phip_inf)
# %%
# **Optimized LHS using Monte Carlo**
# %%
# As with Monte Carlo, user decides of a fixed number of iterations,
# but this time this number is part of the temperature profile.
#
# Two profiles are currently provided:
# - Linear profile: :math:`T_i = T_0 (1-\frac{1}{n_{iter}})`
# - Geometric profile: :math:`T_i = T_O c^i, 0<c<1`
#
# Starting from an LHS design, a new design is built by permuting a random coordinate of two randomly chosen sample points;
# this new design is also an LHS, but not necessarily a more efficient design.
#
# A comparison of criteria of the two designs is done, and the new LHS is accepted with probability
#
# .. math::
# min\left(exp{\left[-\frac{\Phi(LHS_{new}) - \Phi(LHS)}{T_i}\right]}, 1\right)
#
# %%
# Considering independent Uniform(0,1) distributions of dimension 3
distribution = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * 3)
# Random LHS
lhs = ot.LHSExperiment(distribution, N)
lhs.setAlwaysShuffle(True) # randomized
algo = ot.SimulatedAnnealingLHS(lhs)
design = algo.generate()
# %%
# One could also fix the criterion, the temperature profile and get more results.
# Considering independent Uniform distributions of dimension 3
# Bounds are (-1,1), (0,2) and (0, 0.5)
distribution = ot.JointDistribution(
[ot.Uniform(-1.0, 1.0), ot.Uniform(0.0, 2.0), ot.Uniform(0.0, 0.5)]
)
# Random LHS
lhs = ot.LHSExperiment(distribution, N)
lhs.setAlwaysShuffle(True) # randomized
# Fixing C2 crit
space_filling = ot.SpaceFillingC2()
# Defining a temperature profile
# A geometric profile seems accurate with default parameters
# e.g. T0=10, c=0.95, iMax=2000
temperatureProfile = ot.GeometricProfile()
algo = ot.SimulatedAnnealingLHS(lhs, space_filling, temperatureProfile)
# optimal design
design = algo.generate()
result = algo.getResult()
# Criteria for the optimal design
crit_c2 = result.getC2()
crit_phip = result.getPhiP()
crit_mindist = result.getMinDist()
# History of the criterion used for optimization
history = result.getAlgoHistory()
criterion_hist = history[:, 0]
# Additional results
temperature_hist = history[:, 1]
probability_hist = history[:, 2]
# %%
# It is also possible to chain several iterations of the whole process with different starting points.
N = 10
# Considering independent Uniform distributions of dimension 3
# Bounds are (-1,1), (0,2) and (0, 0.5)
distribution = ot.JointDistribution(
[ot.Uniform(-1.0, 1.0), ot.Uniform(0.0, 2.0), ot.Uniform(0.0, 0.5)]
)
# Random LHS
lhs = ot.LHSExperiment(distribution, N)
lhs.setAlwaysShuffle(True) # randomized
# Fixing PhiP crit
space_filling = ot.SpaceFillingPhiP()
# Defining a temperature profile
# T0=10, iMax=3000
temperatureProfile = ot.LinearProfile(10.0, 3000)
algo = ot.SimulatedAnnealingLHS(lhs, space_filling, temperatureProfile)
restart = 50
design = algo.generateWithRestart(restart)
# Retrieve all optimal designs
result = algo.getResult()
designs = [result.getOptimalDesign(i) for i in range(restart)]
# %%
# Finally, we could start the optimization process of LHS using a precomputed LHS design.
# Considering independent Uniform distributions of dimension 3
# Bounds are (0,1)^3
distribution = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * 3)
# Random LHS
lhs = ot.LHSExperiment(distribution, N)
lhs.setAlwaysShuffle(True) # randomized
# Fixing C2 crit for example
space_filling = ot.SpaceFillingC2()
# Defining a temperature profile
# T0=10, iMax=3000
temperatureProfile = ot.LinearProfile(10.0, 3000)
algo = ot.SimulatedAnnealingLHS(lhs, space_filling, temperatureProfile)
design = algo.generate()
result = algo.getResult()
# check history ==> draw criterion
graph = result.drawHistoryCriterion()
view = viewer.View(graph)
# %%
# Convergence needs to be performed
# New algo starting from this design
algo = ot.SimulatedAnnealingLHS(design, distribution, space_filling, temperatureProfile)
design = algo.generate()
plt.show()
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