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+In [1]:
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+import obsidian
+print(f'obsidian version: ' + obsidian.__version__)
+
+import pandas as pd
+import plotly.express as px
+import plotly.io as pio
+pio.renderers.default = "plotly_mimetype+notebook"
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+obsidian version: 0.8.0 ++
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+Introduction¶
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+In this tutorial, we will see how to use obsidian for multi-output optimization. To demonstrate the versatility of the approach, we will seek to maximize one response while minimizing the other.
+$$\underset{X}{argmax} HV\left(+f\left(y_1\right) -f\left(y_2\right)\right)$$
+Furthermore, we will apply a linear constraint on the input variables; requiring that the $X_1 + X_2 \leq 6 $.
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+Set up parameter space and initialize a design¶
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+In [2]:
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+from obsidian import Campaign, Target, ParamSpace, BayesianOptimizer
+from obsidian.parameters import Param_Continuous
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+In [3]:
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+params = [
+ Param_Continuous('X1', 0, 10),
+ Param_Continuous('X2', 0, 10),
+ ]
+
+X_space = ParamSpace(params)
+target = [
+ Target('Response 1', aim='max'),
+ Target('Response 2', aim='min')
+]
+campaign = Campaign(X_space, target, seed=0)
+X0 = campaign.designer.initialize(4, 'LHS')
+
+X0
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+Out[3]:
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+| + | X1 | +X2 | +
|---|---|---|
| 0 | +6.25 | +8.75 | +
| 1 | +1.25 | +6.25 | +
| 2 | +3.75 | +1.25 | +
| 3 | +8.75 | +3.75 | +
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+Collect results (e.g. from a simulation)¶
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+In [4]:
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+from obsidian.experiment import Simulator
+from obsidian.experiment.benchmark import branin_currin
+
+simulator = Simulator(X_space, branin_currin, name='Response', eps=0.05)
+y0 = simulator.simulate(X0)
+Z0 = pd.concat([X0, y0], axis=1)
+
+campaign.add_data(Z0)
+campaign.data
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+Out[4]:
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+| + | X1 | +X2 | +Response 1 | +Response 2 | +Iteration | +
|---|---|---|---|---|---|
| Observation ID | ++ | + | + | + | + |
| 0 | +6.25 | +8.75 | +-154.239634 | +-5.248404 | +0 | +
| 1 | +1.25 | +6.25 | +-8.751383 | +-6.534766 | +0 | +
| 2 | +3.75 | +1.25 | +-29.269633 | +-13.059490 | +0 | +
| 3 | +8.75 | +3.75 | +-26.305781 | +-7.544486 | +0 | +
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+Fit an optimizer and visualize results¶
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+In [5]:
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+campaign.fit()
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+GP model has been fit to data with a train-score of: 1 for response: Response 1 +GP model has been fit to data with a train-score of: 1 for response: Response 2 ++
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+In [6]:
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+from obsidian.plotting import surface_plot, optim_progress
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+In [7]:
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+surface_plot(campaign.optimizer)
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+Optimize new experiment suggestions¶
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+In [8]:
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+from obsidian.constraints import InConstraint_Generic
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+Note: It is a good idea to balance a set of acquisition functions with those that prefer design-space exploration. This helps to ensure that the optimizer is not severely misled by deficiencies in the dataset, particularly for small data. It also helps to ascertain a global optimum.
+A simple choice is Space Filling (SF) although Negative Integrated Posterior Variance (NIPV) is available for single-output optimizations; and there are various other acquisiiton functions whose hyperparameters can be tuned to manage the "explore-exploit" balance.
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+In [9]:
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+X_suggest, eval_suggest = campaign.optimizer.suggest(acquisition = [{'NEHVI':{'ref_point':[-350, -20]}}, 'SF'],
+ # X1 + X2 <= 6, written as -X1 - X2 >= -6
+ ineq_constraints = [InConstraint_Generic(X_space, indices=[0,1], coeff=[-1,-1], rhs=-6)])
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+In [10]:
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+pd.concat([X_suggest, eval_suggest], axis=1)
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+Out[10]:
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+| + | X1 | +X2 | +Response 1 (pred) | +Response 1 lb | +Response 1 ub | +Response 2 (pred) | +Response 2 lb | +Response 2 ub | +f(Response 1) | +f(Response 2) | +aq Value | +aq Value (joint) | +aq Method | +Expected Hypervolume (joint) | +Expected Pareto | +
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | +1.855368e+00 | +3.467079e-15 | +-38.805388 | +-101.625151 | +24.014386 | +-11.443693 | +-8.463541 | +-14.423845 | +0.236315 | +0.973132 | +4.233924 | +4.233924 | +NEHVI | +3.389429 | +False | +
| 1 | +5.782685e-15 | +2.974608e+00 | +-29.479032 | +-100.736606 | +41.778553 | +-9.269232 | +-5.810519 | +-12.727946 | +0.375486 | +0.340895 | +0.350581 | +0.350581 | +SF | +3.406860 | +False | +
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+Collect data at new suggestions¶
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+In [11]:
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+y_iter1 = pd.DataFrame(simulator.simulate(X_suggest))
+Z_iter1 = pd.concat([X_suggest, y_iter1, eval_suggest], axis=1)
+campaign.add_data(Z_iter1)
+campaign.data.tail()
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+Out[11]:
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+| + | X1 | +X2 | +Response 1 | +Response 2 | +Iteration | +Response 1 (pred) | +Response 1 lb | +Response 1 ub | +Response 2 (pred) | +Response 2 lb | +... | +f(Response 2) | +aq Value | +aq Value (joint) | +aq Method | +Expected Hypervolume (joint) | +Expected Pareto | +Response 1 (max) (iter) | +Response 2 (max) (iter) | +Hypervolume (iter) | +Pareto Front | +
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Observation ID | ++ | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + |
| 1 | +1.250000e+00 | +6.250000e+00 | +-8.751383 | +-6.534766 | +0 | +NaN | +NaN | +NaN | +NaN | +NaN | +... | +NaN | +NaN | +NaN | +NaN | +NaN | +NaN | +-8.751383 | +-5.248404 | +949.270665 | +True | +
| 2 | +3.750000e+00 | +1.250000e+00 | +-29.269633 | +-13.059490 | +0 | +NaN | +NaN | +NaN | +NaN | +NaN | +... | +NaN | +NaN | +NaN | +NaN | +NaN | +NaN | +-8.751383 | +-5.248404 | +949.270665 | +False | +
| 3 | +8.750000e+00 | +3.750000e+00 | +-26.305781 | +-7.544486 | +0 | +NaN | +NaN | +NaN | +NaN | +NaN | +... | +NaN | +NaN | +NaN | +NaN | +NaN | +NaN | +-8.751383 | +-5.248404 | +949.270665 | +False | +
| 4 | +1.855368e+00 | +3.467079e-15 | +-116.993962 | +-14.357309 | +1 | +-38.805388 | +-101.625151 | +24.014386 | +-11.443693 | +-8.463541 | +... | +0.973132 | +4.233924 | +4.233924 | +NEHVI | +3.389429 | +False | +-8.751383 | +-2.714921 | +1355.934274 | +False | +
| 5 | +5.782685e-15 | +2.974608e+00 | +-178.155376 | +-2.714921 | +1 | +-29.479032 | +-100.736606 | +41.778553 | +-9.269232 | +-5.810519 | +... | +0.340895 | +0.350581 | +0.350581 | +SF | +3.406860 | +False | +-8.751383 | +-2.714921 | +1355.934274 | +True | +
5 rows × 22 columns
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+Repeat as desired¶
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+In [12]:
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+for iter in range(5):
+ campaign.fit()
+ X_suggest, eval_suggest = campaign.optimizer.suggest(acquisition = [{'NEHVI':{'ref_point':[-350, -20]}}, 'SF'],
+ ineq_constraints = [InConstraint_Generic(X_space, indices=[0,1], coeff=[-1,-1], rhs=-6)])
+ y_iter = pd.DataFrame(simulator.simulate(X_suggest))
+ Z_iter = pd.concat([X_suggest, y_iter, eval_suggest], axis=1)
+ campaign.add_data(Z_iter)
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+GP model has been fit to data with a train-score of: 0.998 for response: Response 1 +GP model has been fit to data with a train-score of: 0.999 for response: Response 2 +GP model has been fit to data with a train-score of: 1 for response: Response 1 +GP model has been fit to data with a train-score of: 1 for response: Response 2 +GP model has been fit to data with a train-score of: 1 for response: Response 1 +GP model has been fit to data with a train-score of: 1 for response: Response 2 +GP model has been fit to data with a train-score of: 0.999 for response: Response 1 +GP model has been fit to data with a train-score of: 1 for response: Response 2 +GP model has been fit to data with a train-score of: 1 for response: Response 1 +GP model has been fit to data with a train-score of: 1 for response: Response 2 ++
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+In [13]:
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+optim_progress(campaign)
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+In [14]:
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+surface_plot(campaign.optimizer, response_id = 0)
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+In [15]:
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+surface_plot(campaign.optimizer, response_id = 1)
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