Add example to show how to initialize individuals of the initial gene…

…ration

examples/example_initialize_individuals.py

@@ -0,0 +1,133 @@
+"""
+Minimal example for fixed initial conditions
+============================================
+
+Example demonstrating the use of Cartesian genetic programming for a simple
+regression task (see `example_minimal.py`). However, here we initialize the
+initial parent population to a specific expression.
+"""
+
+# The docopt str is added explicitly to ensure compatibility with
+# sphinx-gallery.
+docopt_str = """
+   Usage:
+     example_initialize_individuals.py
+
+   Options:
+     -h --help
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.constants
+from docopt import docopt
+
+import cgp
+
+args = docopt(docopt_str)
+
+# %%
+# We first define a target function.
+
+
+def f_target(x):
+    return x ** 2 + 1.0
+
+
+# %%
+# 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.
+
+
+def objective(individual):
+
+    if not individual.fitness_is_None():
+        return individual
+
+    n_function_evaluations = 1000
+
+    np.random.seed(1234)
+
+    f = individual.to_func()
+    loss = 0
+    for x in np.random.uniform(-4, 4, n_function_evaluations):
+        # the callable returned from `to_func` accepts and returns
+        # lists; accordingly we need to pack the argument and unpack
+        # the return value
+        y = f(x)
+        loss += (f_target(x) - y) ** 2
+
+    individual.fitness = -loss / n_function_evaluations
+
+    return individual
+
+
+# %%
+# We want to initialize all individuals to the same expression (for
+# illustration, functionally not necessarily the best idea). We can provide a
+# function to the `Population` constructor which is called for each individual
+# of the initial parent population. Unfortunately, we can not provide the
+# expression directly, but rather need to manually set (parts of) the
+# individuals genome to the correct values. See Jordan, Schmidt et al. (2020)
+# https://doi.org/10.7554/eLife.66273 figure 2 for details about the encoding.
+def individual_init(ind):
+    # f(x) = x * x
+    ind.genome.set_expression_for_output([2, 0, 0])
+    assert ind.to_sympy(simplify=False) == "x_0*x_0"
+    return ind
+
+
+pop = cgp.Population(individual_init=individual_init)
+
+# %%
+# Next, we set up the evolutionary search. We define a callback for recording
+# of fitness over generations
+history = {}
+history["fitness_champion"] = []
+
+
+def recording_callback(pop):
+    history["fitness_champion"].append(pop.champion.fitness)
+
+
+# %%
+# and finally perform the evolution relying on the libraries default
+# hyperparameters except that we terminate the evolution as soon as one
+# individual has reached fitness zero.
+pop = cgp.evolve(
+    objective, pop, termination_fitness=0.0, print_progress=True, callback=recording_callback
+)
+
+
+# %%
+# After finishing the evolution, we plot the result and log the final
+# evolved expression.
+
+
+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_func()
+x = np.linspace(-5.0, 5.0, 20)
+y = [f(x_i) for x_i in x]
+y_target = [f_target(x_i) for x_i in 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_initialize_individuals.pdf", dpi=300)