.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_userguide/example_simple.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_userguide_example_simple.py: Usage Example ============= In this page, we provide a simple example of using the Gurobi Machine Learning package. The example is entirely abstract. Its aim is only to illustrate the basic functionalities of the package in the most simple way. For some more realistic applications, please refer to the notebooks in the `examples <../auto_examples/index.html>`__ section. Before proceeding to the example itself, we need to import a number of packages. Here, we will use Scikit-learn to train regression models. We generate random data for the regression using the `make_regression `__ function. For the regression model, we use a `multi-layer perceptron regressor `__ neural network. We import the corresponding objects. .. GENERATED FROM PYTHON SOURCE LINES 22-31 .. code-block:: Python import gurobipy as gp import numpy as np from sklearn.datasets import make_regression from sklearn.metrics import mean_squared_error from sklearn.neural_network import MLPRegressor from gurobi_ml import add_predictor_constr .. GENERATED FROM PYTHON SOURCE LINES 32-37 Certainly, we need gurobipy to build an optimization model and from the gurobi_ml package we need the :func:`add_predictor_constr `. function. We also need numpy. .. GENERATED FROM PYTHON SOURCE LINES 40-43 We start by building artificial data to train our regressions. To do so, we use *make_regression* to obtain data with 10 features. .. GENERATED FROM PYTHON SOURCE LINES 43-47 .. code-block:: Python X, y = make_regression(n_features=10, noise=1.0) .. GENERATED FROM PYTHON SOURCE LINES 48-50 Now, create the *MLPRegressor* object and fit it. .. GENERATED FROM PYTHON SOURCE LINES 50-56 .. code-block:: Python nn = MLPRegressor([20] * 2, max_iter=10000, random_state=1) nn.fit(X, y) .. raw:: html

MLPRegressor(hidden_layer_sizes=[20, 20], max_iter=10000, random_state=1)

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.. GENERATED FROM PYTHON SOURCE LINES 57-85 We now turn to the optimization model. In the spirit of adversarial machine learning examples, we use some training examples. We pick :math:`n` training examples randomly. For each of the examples, we want to find an input that is in a small neighborhood of it that leads to the output that is closer to :math:`0` with the regression. Denoting by :math:`X^E` our set of examples and by :math:`g` the prediction function of our regression model, our optimization problem reads: .. math:: \begin{aligned} &\min \sum_{i=1}^n y_i^2 \\ &\text{s.t.:}\\ &y_i = g(X_i) & & i = 1, \ldots, n,\\ &X^E - \delta \leq X \leq X^E + \delta,\\ \end{aligned} where :math:`X` is a matrix of variables of dimension :math:`n \times 10` (the number of examples we consider and number of features in the regression respectively), :math:`y` is a vector of free (unbounded) variables and :math:`\delta` a small positive constant. First, let’s pick randomly 2 training examples using numpy, and create our gurobipy model. .. GENERATED FROM PYTHON SOURCE LINES 85-94 .. code-block:: Python n = 2 index = np.random.choice(X.shape[0], n, replace=False) X_examples = X[index, :] y_examples = y[index] m = gp.Model() .. GENERATED FROM PYTHON SOURCE LINES 95-107 Our only decision variables in this case, are the five inputs and outputs for the regression. We use ``gurobipy.MVar`` matrix variables that are most convenient in this case. The input variables have the same shape as ``X_examples``. Their lower bound is ``X_examples - delta`` and their upper bound ``X_examples + delta``. The output variables have the shape of ``y_examples`` and are unbounded. By default, in Gurobi variables are non-negative, we therefore need to set an infinite lower bound. .. GENERATED FROM PYTHON SOURCE LINES 107-112 .. code-block:: Python input_vars = m.addMVar(X_examples.shape, lb=X_examples - 0.2, ub=X_examples + 0.2) output_vars = m.addMVar(y_examples.shape, lb=-gp.GRB.INFINITY) .. GENERATED FROM PYTHON SOURCE LINES 113-124 The constraints linking ``input_vars`` and ``output_vars`` can now be added with the function :func:`add_predictor_constr `. Note that because of the shape of the variables this will add the 5 different constraints. The function returns an instance of a :class:`modeling object ` that we can use later on. .. GENERATED FROM PYTHON SOURCE LINES 124-128 .. code-block:: Python pred_constr = add_predictor_constr(m, nn, input_vars, output_vars) .. GENERATED FROM PYTHON SOURCE LINES 129-134 The method :func:`print_stats ` of the modeling object outputs the details of the regression model that was added to the Gurobi. .. GENERATED FROM PYTHON SOURCE LINES 134-138 .. code-block:: Python pred_constr.print_stats() .. rst-class:: sphx-glr-script-out .. code-block:: none Model for mlpregressor: 160 variables 82 constraints 80 general constraints Input has shape (2, 10) Output has shape (2, 1) -------------------------------------------------------------------------------- Layer Output Shape Variables Constraints Linear Quadratic General ================================================================================ dense (2, 20) 80 40 0 40 (relu) dense0 (2, 20) 80 40 0 40 (relu) dense1 (2, 1) 0 2 0 0 -------------------------------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 139-141 To finish the model, we set the objective, and then we can optimize it. .. GENERATED FROM PYTHON SOURCE LINES 141-147 .. code-block:: Python m.setObjective(output_vars @ output_vars, gp.GRB.MINIMIZE) m.optimize() .. rst-class:: sphx-glr-script-out .. code-block:: none Gurobi Optimizer version 11.0.3 build v11.0.3rc0 (linux64 - "Ubuntu 20.04.6 LTS") CPU model: Intel(R) Xeon(R) Platinum 8375C CPU @ 2.90GHz, instruction set [SSE2|AVX|AVX2|AVX512] Thread count: 1 physical cores, 2 logical processors, using up to 2 threads Optimize a model with 82 rows, 182 columns and 1322 nonzeros Model fingerprint: 0x619d154b Model has 2 quadratic objective terms Model has 80 general constraints Variable types: 182 continuous, 0 integer (0 binary) Coefficient statistics: Matrix range [2e-03, 2e+00] Objective range [0e+00, 0e+00] QObjective range [2e+00, 2e+00] Bounds range [3e-02, 2e+00] RHS range [4e-02, 1e+00] Presolve added 1 rows and 0 columns Presolve removed 0 rows and 89 columns Presolve time: 0.01s Presolved: 83 rows, 93 columns, 582 nonzeros Presolved model has 1 quadratic objective terms Variable types: 67 continuous, 26 integer (26 binary) Root relaxation: objective 1.269266e+04, 165 iterations, 0.00 seconds (0.00 work units) Nodes | Current Node | Objective Bounds | Work Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time 0 0 12692.6634 0 14 - 12692.6634 - - 0s H 0 0 12950.549874 12692.6634 1.99% - 0s 0 0 12868.2036 0 13 12950.5499 12868.2036 0.64% - 0s 0 0 12872.4970 0 12 12950.5499 12872.4970 0.60% - 0s 0 0 cutoff 0 12950.5499 12950.5499 0.00% - 0s Cutting planes: Gomory: 1 Cover: 1 Implied bound: 4 MIR: 1 Flow cover: 13 Relax-and-lift: 8 Explored 1 nodes (268 simplex iterations) in 0.02 seconds (0.01 work units) Thread count was 2 (of 2 available processors) Solution count 1: 12950.5 Optimal solution found (tolerance 1.00e-04) Best objective 1.295054987376e+04, best bound 1.295054987376e+04, gap 0.0000% .. GENERATED FROM PYTHON SOURCE LINES 148-159 The method :func:`get_error ` is useful to check that the solution computed by Gurobi is correct with respect to the regression model we use. Let :math:`(\bar X, \bar y)` be the values of the input and output variables in the computed solution. The function returns :math:`g(\bar X) - y` using the original regression object. Normally, all values should be small and below Gurobi’s tolerances in this example. .. GENERATED FROM PYTHON SOURCE LINES 159-163 .. code-block:: Python pred_constr.get_error() .. rst-class:: sphx-glr-script-out .. code-block:: none array([[7.10542736e-15], [2.84217094e-14]]) .. GENERATED FROM PYTHON SOURCE LINES 164-167 We can look at the computed values for the output variables and compare them with the original target values. .. GENERATED FROM PYTHON SOURCE LINES 167-171 .. code-block:: Python print("Computed values") print(pred_constr.output_values.flatten()) .. rst-class:: sphx-glr-script-out .. code-block:: none Computed values [ 16.058843 112.66172125] .. GENERATED FROM PYTHON SOURCE LINES 172-177 .. code-block:: Python print("Original values") print(y_examples) .. rst-class:: sphx-glr-script-out .. code-block:: none Original values [125.06118302 245.59008756] .. GENERATED FROM PYTHON SOURCE LINES 178-181 Finally, we can remove ``pred_constr`` with the method :func:`remove() `. .. GENERATED FROM PYTHON SOURCE LINES 181-183 .. code-block:: Python pred_constr.remove() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.257 seconds) .. _sphx_glr_download_auto_userguide_example_simple.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: example_simple.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: example_simple.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_