.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/examples_bbo/plot_constrained_black_box_optimization.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_examples_bbo_plot_constrained_black_box_optimization.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_examples_bbo_plot_constrained_black_box_optimization.py:


Constrained Black-Box Optimization with Rejection Sampling
==========================================================

**Author(s)**: Romain Egele.

In this tutorial, we illustrate how to solve constrained `black-box optimization (Wikipedia) <https://en.wikipedia.org/wiki/Derivative-free_optimization>`_ (also known as derivative-free optimization) using DeepHyper.

Black-box optimization refers to a class of methods where an objective function :math:`f(x) = y \in \mathbb{R}` can only be queried through input–output evaluations :math:`\{ (x_1, y_1), \ldots, (x_n, y_n) \}`. No closed-form expression, derivatives, or structural information about :math:`f` are required.

In *constrained* optimization, we further introduce one or more rules that restrict the set of admissible solutions. These constraints carve out the feasible region of the search space and can substantially influence both the behavior and performance of the optimizer.

In the following example, we define a simple two-dimensional problem, impose a linear constraint, and solve it using DeepHyper’s Centralized Bayesian Optimization (CBO) engine.

There exists multiple ways of handling constraints in DeepHyper:

#. Rejection sampling (shown in this tutorial) where we sample from the unconstrained search space 
   then reject unfeasible solutions. While this approach is simple it can become computationnaly 
   intractable.
#. Learning to avoid failures (see :ref:`Learn to Avoid Failures with Bayesian Optimization <sphx_glr_examples_examples_bbo_plot_notify_failures_hpo.py>`).
#. Define the constraint as an other objective in a multi-objective optimization setup (tutorial coming soon).
#. Custom chained sampler (tutorial coming soon).

.. GENERATED FROM PYTHON SOURCE LINES 24-32

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd

    from deephyper.analysis.hpo import plot_search_trajectory_single_objective_hpo, parameters_at_max
    from deephyper.hpo import HpProblem, CBO








.. GENERATED FROM PYTHON SOURCE LINES 33-36

Optimization Problem
--------------------
We define a 2D search space over variables ``x`` and ``y``.

.. GENERATED FROM PYTHON SOURCE LINES 36-54

.. code-block:: Python


    pb = HpProblem()
    pb.add((-10.0, 10.0), "x")
    pb.add((-10.0, 10.0), "y")


    def f(job):
        """Objective function: maximize x^2 + y^2."""
        return job.parameters["x"] ** 2 + job.parameters["y"] ** 2


    def constraint_fn_test(s: pd.DataFrame):
        """Feasibility condition: |x| + |y| <= 10."""
        return np.abs(s["x"]) + np.abs(s["y"]) <= 10


    pb.set_constraint_fn(constraint_fn_test)








.. GENERATED FROM PYTHON SOURCE LINES 55-57

We now set up a constrained Bayesian optimization search using a genetic algorithm
to optimize the acquisition function periodically.

.. GENERATED FROM PYTHON SOURCE LINES 57-71

.. code-block:: Python


    search = CBO(
        pb,
        acq_optimizer="ga",
        acq_optimizer_kwargs={"acq_optimizer_freq": 2},
        acq_func_kwargs={
            # Exploration/Exploitation mechanism
            "kappa": 200.0,
            "scheduler": {"type": "periodic-exp-decay", "period": 20, "kappa_final": 1.96},
        },
        verbose=1,
    )
    results = search.search(f, max_evals=300)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Results file already exists, it will be renamed to /Users/rp5/Documents/DeepHyper/deephyper/examples/examples_bbo/results_20251202-183859.csv

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.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: Python

    results






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>p:x</th>
          <th>p:y</th>
          <th>objective</th>
          <th>job_id</th>
          <th>job_status</th>
          <th>m:timestamp_submit</th>
          <th>m:timestamp_gather</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-0.305958</td>
          <td>0.912106</td>
          <td>0.925547</td>
          <td>0</td>
          <td>DONE</td>
          <td>0.035106</td>
          <td>0.035407</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-6.820836</td>
          <td>1.816490</td>
          <td>49.823445</td>
          <td>1</td>
          <td>DONE</td>
          <td>0.101091</td>
          <td>0.101396</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-4.840870</td>
          <td>3.503860</td>
          <td>35.711064</td>
          <td>2</td>
          <td>DONE</td>
          <td>0.123162</td>
          <td>0.123370</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.088796</td>
          <td>-2.283004</td>
          <td>5.219990</td>
          <td>3</td>
          <td>DONE</td>
          <td>0.145206</td>
          <td>0.145405</td>
        </tr>
        <tr>
          <th>4</th>
          <td>2.684667</td>
          <td>-5.163577</td>
          <td>33.869963</td>
          <td>4</td>
          <td>DONE</td>
          <td>0.208886</td>
          <td>0.209121</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>295</th>
          <td>-1.039183</td>
          <td>-8.137491</td>
          <td>67.298654</td>
          <td>295</td>
          <td>DONE</td>
          <td>32.092250</td>
          <td>32.092437</td>
        </tr>
        <tr>
          <th>296</th>
          <td>1.625939</td>
          <td>2.803522</td>
          <td>10.503414</td>
          <td>296</td>
          <td>DONE</td>
          <td>32.177547</td>
          <td>32.177734</td>
        </tr>
        <tr>
          <th>297</th>
          <td>8.500303</td>
          <td>1.130088</td>
          <td>73.532245</td>
          <td>297</td>
          <td>DONE</td>
          <td>32.387930</td>
          <td>32.388125</td>
        </tr>
        <tr>
          <th>298</th>
          <td>-6.364424</td>
          <td>-1.098310</td>
          <td>41.712184</td>
          <td>298</td>
          <td>DONE</td>
          <td>32.424693</td>
          <td>32.424850</td>
        </tr>
        <tr>
          <th>299</th>
          <td>-3.280660</td>
          <td>6.682292</td>
          <td>55.415752</td>
          <td>299</td>
          <td>DONE</td>
          <td>32.602325</td>
          <td>32.602513</td>
        </tr>
      </tbody>
    </table>
    <p>300 rows × 7 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 75-79

Extracting the Best Parameters
------------------------------
To recover the parameters corresponding to the best observed objective value,
we can use :func:`deephyper.analysis.hpo.parameters_at_max`.

.. GENERATED FROM PYTHON SOURCE LINES 79-85

.. code-block:: Python


    parameters, objective = parameters_at_max(results)
    print("\nOptimum values")
    print(f"x: {parameters['x']:.3f}, y: {parameters['y']:.2f}")
    print("objective:", objective)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Optimum values
    x: -9.970, y: 0.02
    objective: 99.40231418419825




.. GENERATED FROM PYTHON SOURCE LINES 86-92

Visualizing the Search Trajectory
---------------------------------
We plot the evolution of the best objective value to verify that optimization
progresses correctly toward the maximum :math:`100`.

We clearly see the periodic exploration/exploitation effect of the scheduler.

.. GENERATED FROM PYTHON SOURCE LINES 92-100

.. code-block:: Python


    WIDTH_PLOTS = 8
    HEIGHT_PLOTS = WIDTH_PLOTS / 1.618

    fig, ax = plt.subplots(figsize=(WIDTH_PLOTS, HEIGHT_PLOTS))
    plot_search_trajectory_single_objective_hpo(results, mode="max", ax=ax)
    _ = plt.title("Search Trajectory")




.. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_001.png
   :alt: Search Trajectory
   :srcset: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 101-105

Visualizing the Feasible Region and Evaluations
-----------------------------------------------
We now plot all evaluated points in the (x, y) plane, color-coded by
objective value, along with the constraint boundary ``x + y = 10``.

.. GENERATED FROM PYTHON SOURCE LINES 105-121

.. code-block:: Python



    fig, ax = plt.subplots(figsize=(WIDTH_PLOTS, HEIGHT_PLOTS))
    item = ax.scatter(results["p:x"], results["p:y"], c=results["objective"], label="Evaluations")
    ax.plot([0, 10], [10, 0], "r:")
    ax.plot([0, 10], [-10, 0], "r:")
    ax.plot([-10, 0], [0, -10], "r:")
    ax.plot([0, -10], [10, 0], "r:", label="Constraint")
    ax.set_xlabel(r"$x$")
    ax.set_ylabel(r"$y$")
    ax.set_xlim(-10, 10)
    ax.set_ylim(-10, 10)
    ax.legend()
    ax.grid()
    ax.grid(which="minor", linestyle=":")
    cb = plt.colorbar(item)
    cb.set_label(r"Objective")


.. image-sg:: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_002.png
   :alt: plot constrained black box optimization
   :srcset: /examples/examples_bbo/images/sphx_glr_plot_constrained_black_box_optimization_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 33.894 seconds)


.. _sphx_glr_download_examples_examples_bbo_plot_constrained_black_box_optimization.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_constrained_black_box_optimization.ipynb <plot_constrained_black_box_optimization.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_constrained_black_box_optimization.py <plot_constrained_black_box_optimization.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_constrained_black_box_optimization.zip <plot_constrained_black_box_optimization.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_