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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
# Defining parameters
dimension = 3
bounds = ot.Interval(dimension)
size = 25
# Build standard LHS algorithm
distribution = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * dimension)
distribution.setDescription(["U" + str(i) for i in range(dimension)])
lhs = ot.LHSExperiment(distribution, size)
lhs.setRandomShift(False) # centered
lhs.setAlwaysShuffle(True) # randomized
# print the object
print("lhs=", lhs)
print("Bounds of uniform distributions=", distribution.getRange())
# Generate design without optimization
design = lhs.generate()
print("design=", design)
# Defining space fillings
spaceFillingC2 = ot.SpaceFillingC2()
spaceFillingPhiP = ot.SpaceFillingPhiP(10)
spaceFillingMinDist = ot.SpaceFillingMinDist()
# print the criteria on this design
print(
"PhiP=%f, C2=%f"
% (ot.SpaceFillingPhiP().evaluate(design), ot.SpaceFillingC2().evaluate(design))
)
# --------------------------------------------------#
# ------------- Simulated annealing ------------- #
# --------------------------------------------------#
# Geometric profile
T0 = 10.0
iMax = 2000
c = 0.95
geomProfile = ot.GeometricProfile(T0, c, iMax)
# 1) Simulated Annealing LHS with geometric temperature profile, C2
# optimization
optimalLHSAlgorithm = ot.SimulatedAnnealingLHS(lhs, spaceFillingC2, geomProfile)
print("lhs=", optimalLHSAlgorithm)
design = optimalLHSAlgorithm.generate()
print("Generating design using geometric temperature profile & C2 criterion=", design)
result = optimalLHSAlgorithm.getResult()
print(
"Final criteria: C2=%f, PhiP=%f, MinDist=%f"
% (result.getC2(), result.getPhiP(), result.getMinDist())
)
# Linear profile
linearProfile = ot.LinearProfile(T0, iMax)
# 2) Simulated Annealing LHS with linear temperature profile, PhiP optimization
optimalLHSAlgorithm = ot.SimulatedAnnealingLHS(lhs, spaceFillingPhiP, linearProfile)
print("lhs=", optimalLHSAlgorithm)
design = optimalLHSAlgorithm.generate()
print("Generating design using linear temperature profile & PhiP criterion =", design)
result = optimalLHSAlgorithm.getResult()
print(
"Final criteria: C2=%f, PhiP=%f, MinDist=%f"
% (result.getC2(), result.getPhiP(), result.getMinDist())
)
# 3) Simulated Annealing LHS with geometric temperature profile, PhiP
# optimization & initial design
initialDesign = ot.Sample(design)
optimalLHSAlgorithm = ot.SimulatedAnnealingLHS(
initialDesign, distribution, spaceFillingPhiP, geomProfile
)
print("lhs=", optimalLHSAlgorithm)
print("initial design=", initialDesign)
print(
"PhiP=%f, C2=%f"
% (ot.SpaceFillingPhiP().evaluate(design), ot.SpaceFillingC2().evaluate(design))
)
design = optimalLHSAlgorithm.generate()
print("Generating design using linear temperature profile & PhiP criterion =", design)
result = optimalLHSAlgorithm.getResult()
print(
"Final criteria: C2=%f, PhiP=%f, MinDist=%f"
% (result.getC2(), result.getPhiP(), result.getMinDist())
)
# 4) Simulated Annealing LHS with linear temperature profile, PhiP
# optimization and nStart > 1
nStart = 10
design = optimalLHSAlgorithm.generateWithRestart(nStart)
print("Generating design using linear temperature profile & PhiP criterion =", design)
results = optimalLHSAlgorithm.getResult()
print(
"Final criteria: C2=%f, PhiP=%f, MinDist=%f"
% (results.getC2(), results.getPhiP(), results.getMinDist())
)
for i in range(nStart):
design = results.getOptimalDesign(i)
print(" Intermediate design for restart iteration number ", i, design)
print(
" Final criteria: C2=%f, PhiP=%f, MinDist=%f"
% (results.getC2(i), results.getPhiP(i), results.getMinDist(i))
)
# 5) Fix https://github.com/openturns/openturns/issues/1826
optimalLHSAlgorithm = ot.SimulatedAnnealingLHS(
initialDesign, distribution, spaceFillingMinDist, geomProfile
)
design = optimalLHSAlgorithm.generate()
result = optimalLHSAlgorithm.getResult()
# optim ok
# Final MinDist is >= initial one
optimal_design = [
[0.58, 0.3, 0.18],
[0.9, 0.38, 0.3],
[0.38, 0.74, 0.66],
[0.06, 0.5, 0.26],
[0.34, 0.98, 0.5],
[0.26, 0.7, 0.14],
[0.74, 0.34, 0.62],
[0.82, 0.66, 0.58],
[0.78, 0.06, 0.1],
[0.54, 0.94, 0.06],
[0.46, 0.22, 0.54],
[0.1, 0.78, 0.46],
[0.94, 0.02, 0.82],
[0.5, 0.26, 0.86],
[0.42, 0.58, 0.42],
[0.22, 0.18, 0.34],
[0.18, 0.54, 0.94],
[0.14, 0.14, 0.74],
[0.7, 0.46, 0.98],
[0.66, 0.86, 0.78],
[0.98, 0.1, 0.38],
[0.62, 0.62, 0.02],
[0.3, 0.42, 0.7],
[0.02, 0.9, 0.9],
[0.86, 0.82, 0.22],
]
assert result.getMinDist() >= ot.SpaceFillingMinDist().evaluate(initialDesign)
assert result.getC2() <= ot.SpaceFillingMinDist().evaluate(initialDesign)
assert result.getPhiP() <= ot.SpaceFillingPhiP().evaluate(initialDesign)
ott.assert_almost_equal(result.getC2(), 0.05473015652160929)
ott.assert_almost_equal(result.getPhiP(), 3.517772966753692)
ott.assert_almost_equal(result.getMinDist(), 0.29120439557122074)
ott.assert_almost_equal(result.getOptimalDesign(), optimal_design)
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