Add example for discovering boolean expressions

examples/example_parity.py

@@ -0,0 +1,126 @@
+"""
+Evolving boolean expressions
+============================
+
+Example demonstrating the use of Cartesian genetic programming for
+generating boolean expressions from a truth table.
+"""
+
+# The docopt str is added explicitly to ensure compatibility with
+# sphinx-gallery.
+docopt_str = """
+   Usage:
+     example_parity.py [--max-generations=<N>]
+
+   Options:
+     -h --help
+     --max-generations=<N>  Maximum number of generations [default: 300]
+"""
+
+from docopt import docopt
+
+import cgp
+
+args = docopt(docopt_str)
+
+# %%
+# We first define a truth table (here 3bit parity generator).
+
+truth_table = {
+    (0, 0, 0): 0,
+    (0, 0, 1): 1,
+    (0, 1, 0): 1,
+    (0, 1, 1): 0,
+    (1, 0, 0): 1,
+    (1, 0, 1): 0,
+    (1, 1, 0): 0,
+    (1, 1, 1): 1,
+}
+
+
+# %%
+# Then we define the objective function for the evolution. It check whether the
+# output of our expression matches the expected value for all input
+# combinations.
+
+
+def objective(individual):
+
+    if not individual.fitness_is_None():
+        return individual
+
+    f = individual.to_func()
+    fitness = 0
+    for message, parity_bit in truth_table.items():
+        y = f(*message)
+        fitness += float(y == bool(parity_bit))
+
+    individual.fitness = fitness
+
+    return individual
+
+
+class AND2(cgp.OperatorNode):
+    """A node that ands its two inputs."""
+
+    _arity = 2
+    _def_output = "bool(x_0) and bool(x_1)"
+    _def_numpy_output = "np.logical_and(x_0.astype(bool), x_1.astype(bool))"
+    _def_sympy_output = "x_0 & x_1"
+    _def_torch_output = "torch.logical_and(x_0.bool(), x_1.bool())"
+
+
+class OR2(cgp.OperatorNode):
+    """A node that ors its two inputs."""
+
+    _arity = 2
+    _def_output = "bool(x_0) or bool(x_1)"
+    _def_numpy_output = "np.logical_or(x_0.astype(bool), x_1.astype(bool))"
+    _def_sympy_output = "x_0 | x_1"
+    _def_torch_output = "torch.logical_or(x_0.bool(), x_1.bool())"
+
+
+class NOT(cgp.OperatorNode):
+    """A node that nots its input."""
+
+    _arity = 1
+    _def_output = "not bool(x_0)"
+    _def_numpy_output = "np.logical_not(x_0.astype(bool))"
+    _def_sympy_output = "Not(x_0)"
+    _def_torch_output = "torch.logical_not(x_0.bool())"
+
+
+class XOR2(cgp.OperatorNode):
+    """A node that xors its two inputs."""
+
+    _arity = 2
+    _def_output = "bool(x_0) != bool(x_1)"
+    _def_numpy_output = "np.logical_xor(x_0.astype(bool), x_1.astype(bool))"
+    _def_sympy_output = "Xor(x_0, x_1)"
+    _def_torch_output = "torch.logical_xor(x_0.bool(), x_1.bool())"
+
+
+genome_params = {
+    "n_inputs": 3,
+    "primitives": (AND2, OR2, NOT, XOR2),
+}
+
+# create population that will be evolved
+pop = cgp.Population(genome_params=genome_params)
+
+
+# %%
+# Next, we perform the evolution mostly relying on the libraries default
+# hyperparameters.
+pop = cgp.evolve(
+    objective,
+    pop,
+    termination_fitness=8.0,  # eight rows in truth table, so max fitness is 8
+    print_progress=True,
+)
+
+
+# %%
+# After finishing the evolution, we log the final evolved expression.
+f = pop.champion.to_sympy(simplify=True)
+print(f'Final expression: {f}')