.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/example_multi_genome.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_example_multi_genome.py: Example for evolutionary regression with multiple genomes ========================================================= Example demonstrating the use of Cartesian genetic programming with multiple genomes per individual for a simple regression task with a piecewise target function. .. GENERATED FROM PYTHON SOURCE LINES 9-30 .. code-block:: default # The docopt str is added explicitly to ensure compatibility with # sphinx-gallery. docopt_str = """ Usage: example_multi_genome.py [--max-generations=] Options: -h --help --max-generations= Maximum number of generations [default: 300] """ import matplotlib.pyplot as plt import numpy as np import scipy.constants from docopt import docopt import cgp args = docopt(docopt_str) .. GENERATED FROM PYTHON SOURCE LINES 31-34 We first define a target function. The function applies different transformations to the input depending whether the input is less or greater than or equal to zero. We thus need to fit two different functions. .. GENERATED FROM PYTHON SOURCE LINES 34-40 .. code-block:: default def f_target(x): return np.select([x < 0, x >= 0], [-x, x ** 2 + 1.0]) .. GENERATED FROM PYTHON SOURCE LINES 41-46 Then we define the objective function for the evolution. It uses the mean-squared error between the output of the expression represented by a given individual and the target function evaluated on a set of random points. We here either evaluate the function represented by the first (``f[0]``) or the second genome (``f[1]``), depending whether the input is less or greater than zero. .. GENERATED FROM PYTHON SOURCE LINES 46-66 .. code-block:: default def objective(individual): if not individual.fitness_is_None(): return individual n_function_evaluations = 1000 np.random.seed(1234) # Note that f is now a list of functions because individual is an instance # of `InvidividualMultiGenome` f = individual.to_numpy() x = np.random.uniform(-4, 4, n_function_evaluations) y = np.piecewise(x, [x < 0, x >= 0], f) loss = np.sum((f_target(x) - y) ** 2) individual.fitness = -loss / n_function_evaluations return individual .. GENERATED FROM PYTHON SOURCE LINES 67-72 Next, we set up the evolutionary search. First, we define the parameters for the population, the genomes of individuals, and the evolutionary algorithm. Note that we define ``genome_params`` as a list of parameter dictionaries which causes the population to create instances of ``InvidividualMultiGenome``. .. GENERATED FROM PYTHON SOURCE LINES 72-89 .. code-block:: default population_params = {"n_parents": 1, "seed": 8188211} single_genome_params = { "n_inputs": 1, "n_outputs": 1, "n_columns": 12, "n_rows": 1, "levels_back": 5, "primitives": (cgp.Add, cgp.Sub, cgp.Mul, cgp.ConstantFloat), } genome_params = [single_genome_params, single_genome_params] ea_params = {"n_offsprings": 4, "mutation_rate": 0.03, "n_processes": 1} evolve_params = {"max_generations": int(args["--max-generations"]), "termination_fitness": 0.0} .. GENERATED FROM PYTHON SOURCE LINES 90-91 We create a population that will be evolved .. GENERATED FROM PYTHON SOURCE LINES 91-93 .. code-block:: default pop = cgp.Population(**population_params, genome_params=genome_params) .. GENERATED FROM PYTHON SOURCE LINES 94-95 and an instance of the (mu + lambda) evolutionary algorithm .. GENERATED FROM PYTHON SOURCE LINES 95-97 .. code-block:: default ea = cgp.ea.MuPlusLambda(**ea_params) .. GENERATED FROM PYTHON SOURCE LINES 98-99 We define a callback for recording of fitness over generations .. GENERATED FROM PYTHON SOURCE LINES 99-107 .. code-block:: default history = {} history["fitness_champion"] = [] def recording_callback(pop): history["fitness_champion"].append(pop.champion.fitness) .. GENERATED FROM PYTHON SOURCE LINES 108-109 and finally perform the evolution .. GENERATED FROM PYTHON SOURCE LINES 109-112 .. code-block:: default cgp.evolve(pop, objective, ea, **evolve_params, print_progress=True, callback=recording_callback) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [2/300] max fitness: -30.901735782503778 [3/300] max fitness: -30.901735782503778 [4/300] max fitness: -20.460618313162673 [5/300] max fitness: -20.460618313162673 [6/300] max fitness: -17.767232897765027 [7/300] max fitness: -17.767232897765027 [8/300] max fitness: -17.767232897765027 [9/300] max fitness: -17.767232897765027 [10/300] max fitness: -17.767232897765027 [11/300] max fitness: -17.767232897765027 [12/300] max fitness: -17.767232897765027 [13/300] max fitness: -17.767232897765027 [14/300] max fitness: -17.767232897765027 [15/300] max fitness: -17.767232897765027 [16/300] max fitness: -17.767232897765027 [17/300] max fitness: -17.767232897765027 [18/300] max fitness: -17.767232897765027 [19/300] max fitness: -17.767232897765027 [20/300] max fitness: -17.767232897765027 [21/300] max fitness: -17.767232897765027 [22/300] max fitness: -17.767232897765027 [23/300] max fitness: -17.767232897765027 [24/300] max fitness: -17.767232897765027 [25/300] max fitness: -17.767232897765027 [26/300] max fitness: -17.767232897765027 [27/300] max fitness: -17.767232897765027 [28/300] max fitness: -17.767232897765027 [29/300] max fitness: -17.767232897765027 [30/300] max fitness: -17.767232897765027 [31/300] max fitness: -17.767232897765027 [32/300] max fitness: -17.767232897765027 [33/300] max fitness: -17.767232897765027 [34/300] max fitness: -17.767232897765027 [35/300] max fitness: -17.767232897765027 [36/300] max fitness: -17.767232897765027 [37/300] max fitness: -17.767232897765027 [38/300] max fitness: -17.767232897765027 [39/300] max fitness: -17.767232897765027 [40/300] max fitness: -17.767232897765027 [41/300] max fitness: -17.767232897765027 [42/300] max fitness: -17.767232897765027 [43/300] max fitness: -17.767232897765027 [44/300] max fitness: -17.767232897765027 [45/300] max fitness: -8.357349504202604 [46/300] max fitness: -2.101173731642708 [47/300] max fitness: -2.101173731642708 [48/300] max fitness: -1.584095706383146 [49/300] max fitness: -1.584095706383146 [50/300] max fitness: -1.584095706383146 [51/300] max fitness: -1.584095706383146 [52/300] max fitness: -1.2705362372221112 [53/300] max fitness: -1.2705362372221112 [54/300] max fitness: -1.2705362372221112 [55/300] max fitness: -1.2705362372221112 [56/300] max fitness: -1.2705362372221112 [57/300] max fitness: -1.2705362372221112 [58/300] max fitness: -1.2705362372221112 [59/300] max fitness: -1.2705362372221112 [60/300] max fitness: -1.2705362372221112 [61/300] max fitness: -1.2705362372221112 [62/300] max fitness: -1.2705362372221112 [63/300] max fitness: -1.2705362372221112 [64/300] max fitness: -1.2705362372221112 [65/300] max fitness: -1.2705362372221112 [66/300] max fitness: -1.2705362372221112 [67/300] max fitness: -1.2705362372221112 [68/300] max fitness: -1.2705362372221112 [69/300] max fitness: -1.2705362372221112 [70/300] max fitness: -1.2705362372221112 [71/300] max fitness: -1.2705362372221112 [72/300] max fitness: -1.2705362372221112 [73/300] max fitness: -1.2705362372221112 [74/300] max fitness: -1.2705362372221112 [75/300] max fitness: -1.2705362372221112 [76/300] max fitness: -1.2705362372221112 [77/300] max fitness: -1.2705362372221112 [78/300] max fitness: -1.2705362372221112 [79/300] max fitness: -1.2705362372221112 [80/300] max fitness: -1.2705362372221112 [81/300] max fitness: -1.2705362372221112 [82/300] max fitness: -1.2705362372221112 [83/300] max fitness: -1.2705362372221112 [84/300] max fitness: -1.2705362372221112 [85/300] max fitness: -1.2705362372221112 [86/300] max fitness: -1.2705362372221112 [87/300] max fitness: -1.2705362372221112 [88/300] max fitness: -1.2705362372221112 [89/300] max fitness: -1.2705362372221112 [90/300] max fitness: -1.2705362372221112 [91/300] max fitness: -1.2705362372221112 [92/300] max fitness: -1.2705362372221112 [93/300] max fitness: -1.2705362372221112 [94/300] max fitness: -1.2705362372221112 [95/300] max fitness: -1.2705362372221112 [96/300] max fitness: -1.2705362372221112 [97/300] max fitness: -1.2705362372221112 [98/300] max fitness: -1.2705362372221112 [99/300] max fitness: -1.2705362372221112 [100/300] max fitness: -1.2705362372221112 [101/300] max fitness: -1.2705362372221112 [102/300] max fitness: -1.2705362372221112 [103/300] max fitness: -1.2705362372221112 [104/300] max fitness: -1.2705362372221112 [105/300] max fitness: -1.2705362372221112 [106/300] max fitness: 0.0 .. GENERATED FROM PYTHON SOURCE LINES 113-114 After finishing the evolution, we print the evolved expression and plot the result. .. GENERATED FROM PYTHON SOURCE LINES 114-144 .. code-block:: default expr = pop.champion.to_sympy() print(expr) print(f"--> x<=0: {expr[0]}, \n x> 0: {expr[1]}") width = 9.0 fig, axes = plt.subplots(1, 2, figsize=(width, width / scipy.constants.golden)) ax_fitness, ax_function = axes[0], axes[1] ax_fitness.set_xlabel("Generation") ax_fitness.set_ylabel("Fitness") ax_fitness.plot(history["fitness_champion"], label="Champion") ax_fitness.set_yscale("symlog") ax_fitness.set_ylim(-1.0e2, 0.1) ax_fitness.axhline(0.0, color="0.7") f = pop.champion.to_numpy() x = np.linspace(-5.0, 5.0, 20)[:, np.newaxis] y = np.piecewise(x, [x < 0, x >= 0], f) y_target = f_target(x) ax_function.plot(x, y_target, lw=2, alpha=0.5, label="Target") ax_function.plot(x, y, "x", label="Champion") ax_function.legend() ax_function.set_ylabel(r"$f(x)$") ax_function.set_xlabel(r"$x$") fig.savefig("example_multi_genome.pdf", dpi=300) .. image:: /auto_examples/images/sphx_glr_example_multi_genome_001.png :alt: example multi genome :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [-x_0, x_0**2 + 1.0] --> x<=0: -x_0, x> 0: x_0**2 + 1.0 .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.919 seconds) .. _sphx_glr_download_auto_examples_example_multi_genome.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: example_multi_genome.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: example_multi_genome.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_