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"""
Multi-objective optimization using Pagmo
========================================
"""
# %%
# In this example we are going to explore optimization using the :class:`~openturns.Pagmo` solver.
# %%
import openturns as ot
import openturns.viewer as otv
# %%
# List available algorithms
for algo in ot.Pagmo.GetAlgorithmNames():
print(algo)
# %%
# Create the problem, from ZDT test suite
f = ot.SymbolicFunction(
["x1", "x2"], ["x1", "var g := 1.0 + 9.0 * (x1 + x2); g * (1.0 - sqrt(x1 / g))"]
)
zdt1 = ot.OptimizationProblem(f)
zdt1.setBounds(ot.Interval([0.0] * 2, [1.0] * 2))
# %%
# We create the first generation of points by sampling into the bounding box
pop0 = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * 2).getSample(100)
# %%
# We create the algorithm that should evolve over 10 generations
algo = ot.Pagmo(zdt1, "nsga2", pop0)
algo.setMaximumIterationNumber(10)
# %%
# Benefit from parallel evaluations if the function allows it
algo.setBlockSize(8)
# %%
# We run the algo
algo.run()
pop1 = algo.getResult().getFinalPoints()
# %%
# We list the available Pareto fronts
fronts = algo.getResult().getParetoFrontsIndices()
len(fronts)
# %%
# We show the Pareto front
graph = ot.Graph("Pareto front", "y1", "y2", True, "upper right")
front = algo.getResult().getFinalValues().select(fronts[0]).sortAccordingToAComponent(0)
data = ot.Sample(2 * front.getSize() - 1, 2)
for i in range(front.getSize()):
data[2 * i] = front[i]
if i != front.getSize() - 1:
data[2 * i + 1, 0] = front[i + 1, 0]
data[2 * i + 1, 1] = front[i, 1]
curve = ot.Curve(data)
curve.setLegend(f"front {0}")
graph.add(curve)
graph.setGrid(True)
_ = otv.View(graph)
# %%
# We show the Pareto front from successive generations
fronts = []
for gen in range(5):
algo = ot.Pagmo(zdt1, "nsga2", pop0)
algo.setMaximumIterationNumber(gen)
algo.run()
front0 = algo.getResult().getParetoFrontsIndices()[0]
fronts.append(algo.getResult().getFinalValues().select(front0))
graph = ot.Graph("Successive fronts", "y1", "y2", True, "upper right")
for k in range(len(fronts)):
front = fronts[k].sortAccordingToAComponent(0)
print(front)
data = ot.Sample(2 * front.getSize() - 1, 2)
for i in range(front.getSize()):
data[2 * i] = front[i]
if i != front.getSize() - 1:
data[2 * i + 1, 0] = front[i + 1, 0]
data[2 * i + 1, 1] = front[i, 1]
curve = ot.Curve(data)
curve.setLegend(f"generation {k}")
graph.add(curve)
graph.setGrid(True)
_ = otv.View(graph)
otv.View.ShowAll()
# %%
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