Implement genetic algorithm for optimizing continuous functions

genetic_algorithm/genetic_algorithm_optimization.py

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+import random
+from collections.abc import Callable, Sequence
+from concurrent.futures import ThreadPoolExecutor
+
+import numpy as np
+
+# Parameters
+N_POPULATION = 100  # Population size
+N_GENERATIONS = 500  # Maximum number of generations
+N_SELECTED = 50  # Number of parents selected for the next generation
+MUTATION_PROBABILITY = 0.1  # Mutation probability
+CROSSOVER_RATE = 0.8  # Probability of crossover
+SEARCH_SPACE = (-10, 10)  # Search space for the variables
+
+# Random number generator
+rng = np.random.default_rng()
+
+
+class GeneticAlgorithm:
+    def __init__(
+        self,
+        function: Callable[[float, float], float],
+        bounds: Sequence[tuple[int | float, int | float]],
+        population_size: int,
+        generations: int,
+        mutation_prob: float,
+        crossover_rate: float,
+        maximize: bool = True,
+    ) -> None:
+        self.function = function  # Target function to optimize
+        self.bounds = bounds  # Search space bounds (for each variable)
+        self.population_size = population_size
+        self.generations = generations
+        self.mutation_prob = mutation_prob
+        self.crossover_rate = crossover_rate
+        self.maximize = maximize
+        self.dim = len(bounds)  # Dimensionality of the function (number of variables)
+
+        # Initialize population
+        self.population = self.initialize_population()
+
+    def initialize_population(self) -> list[np.ndarray]:
+        """
+        Initialize the population with random individuals within the search space.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     function=lambda x, y: x**2 + y**2,
+        ...     bounds=[(-10, 10), (-10, 10)],
+        ...     population_size=5,
+        ...     generations=10,
+        ...     mutation_prob=0.1,
+        ...     crossover_rate=0.8,
+        ...     maximize=False
+        ... )
+        >>> len(ga.initialize_population())
+        5  # The population size should be equal to 5.
+        >>> all(len(ind) == 2 for ind in ga.initialize_population())
+        # Each individual should have 2 variables
+        True
+        """
+        return [
+            np.array([rng.uniform(b[0], b[1]) for b in self.bounds])
+            for _ in range(self.population_size)
+        ]
+
+    def fitness(self, individual: np.ndarray) -> float:
+        """
+        Calculate the fitness value (function value) for an individual.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     function=lambda x, y: x**2 + y**2,
+        ...     bounds=[(-10, 10), (-10, 10)],
+        ...     population_size=10,
+        ...     generations=10,
+        ...     mutation_prob=0.1,
+        ...     crossover_rate=0.8,
+        ...     maximize=False
+        ... )
+        >>> individual = np.array([1.0, 2.0])
+        >>> ga.fitness(individual)
+        -5.0  # The fitness should be -1^2 + 2^2 = 5 for minimizing
+        >>> ga.maximize = True
+        >>> ga.fitness(individual)
+        5.0  # The fitness should be 1^2 + 2^2 = 5 when maximizing
+        """
+        value = float(self.function(*individual))  # Ensure fitness is a float
+        return value if self.maximize else -value  # If minimizing, invert the fitness
+
+    def select_parents(
+        self, population_score: list[tuple[np.ndarray, float]]
+    ) -> list[np.ndarray]:
+        """
+        Select top N_SELECTED parents based on fitness.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     function=lambda x, y: x**2 + y**2,
+        ...     bounds=[(-10, 10), (-10, 10)],
+        ...     population_size=10,
+        ...     generations=10,
+        ...     mutation_prob=0.1,
+        ...     crossover_rate=0.8,
+        ...     maximize=False
+        ... )
+        >>> population_score = [
+        ...     (np.array([1.0, 2.0]), 5.0),
+        ...     (np.array([-1.0, -2.0]), 5.0),
+        ...     (np.array([0.0, 0.0]), 0.0),
+        ... ]
+        >>> selected_parents = ga.select_parents(population_score)
+        >>> len(selected_parents)
+        2  # Should select the two parents with the best fitness scores.
+        >>> np.array_equal(selected_parents[0], np.array([1.0, 2.0]))
+        # Parent 1 should be [1.0, 2.0]
+        True
+        >>> np.array_equal(selected_parents[1], np.array([-1.0, -2.0]))
+        # Parent 2 should be [-1.0, -2.0]
+        True
+        """
+
+        if not population_score:
+            raise ValueError("Population score is empty, cannot select parents.")
+
+        population_score.sort(key=lambda score_tuple: score_tuple[1], reverse=True)
+        selected_count = min(N_SELECTED, len(population_score))
+        return [ind for ind, _ in population_score[:selected_count]]
+
+    def crossover(
+        self, parent1: np.ndarray, parent2: np.ndarray
+    ) -> tuple[np.ndarray, np.ndarray]:
+        """
+        Perform uniform crossover between two parents to generate offspring.
+
+        Args:
+            parent1 (np.ndarray): The first parent.
+            parent2 (np.ndarray): The second parent.
+        Returns:
+            tuple[np.ndarray, np.ndarray]: The two offspring generated by crossover.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     lambda x, y: -(x**2 + y**2),
+        ...     [(-10, 10), (-10, 10)],
+        ...     10, 100, 0.1, 0.8, True
+        ... )
+        >>> parent1, parent2 = np.array([1, 2]), np.array([3, 4])
+        >>> len(ga.crossover(parent1, parent2)) == 2
+        True
+        """
+        if random.random() < self.crossover_rate:
+            cross_point = random.randint(1, self.dim - 1)
+            child1 = np.concatenate((parent1[:cross_point], parent2[cross_point:]))
+            child2 = np.concatenate((parent2[:cross_point], parent1[cross_point:]))
+            return child1, child2
+        return parent1, parent2
+
+    def mutate(self, individual: np.ndarray) -> np.ndarray:
+        """
+        Apply mutation to an individual.
+
+        Args:
+            individual (np.ndarray): The individual to mutate.
+
+        Returns:
+            np.ndarray: The mutated individual.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     lambda x, y: -(x**2 + y**2),
+        ...     [(-10, 10), (-10, 10)],
+        ...     10, 100, 0.1, 0.8, True
+        ... )
+        >>> ind = np.array([1.0, 2.0])
+        >>> mutated = ga.mutate(ind)
+        >>> len(mutated) == 2  # Ensure it still has the correct number of dimensions
+        True
+        """
+        for i in range(self.dim):
+            if random.random() < self.mutation_prob:
+                individual[i] = rng.uniform(self.bounds[i][0], self.bounds[i][1])
+        return individual
+
+    def evaluate_population(self) -> list[tuple[np.ndarray, float]]:
+        """
+        Evaluate the fitness of the entire population in parallel.
+
+        Returns:
+            list[tuple[np.ndarray, float]]:
+                The population with their respective fitness values.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     lambda x, y: -(x**2 + y**2),
+        ...     [(-10, 10), (-10, 10)],
+        ...     10, 100, 0.1, 0.8, True
+        ... )
+        >>> eval_population = ga.evaluate_population()
+        >>> len(eval_population) == ga.population_size  # Ensure population size
+        True
+        >>> all(
+        ...     isinstance(ind, tuple) and isinstance(ind[1], float)
+        ...     for ind in eval_population
+        ... )
+        True
+        """
+        with ThreadPoolExecutor() as executor:
+            return list(
+                executor.map(
+                    lambda individual: (individual, self.fitness(individual)),
+                    self.population,
+                )
+            )
+
+    def evolve(self, verbose: bool = True) -> np.ndarray:
+        """
+        Evolve the population over the generations to find the best solution.
+
+        Args:
+            verbose (bool): If True, prints the progress of the generations.
+
+        Returns:
+            np.ndarray: The best individual found during the evolution process.
+
+        Example:
+        >>> ga = GeneticAlgorithm(
+        ...     function=lambda x, y: x**2 + y**2,
+        ...     bounds=[(-10, 10), (-10, 10)],
+        ...     population_size=10,
+        ...     generations=10,
+        ...     mutation_prob=0.1,
+        ...     crossover_rate=0.8,
+        ...     maximize=False
+        ... )
+        >>> best_solution = ga.evolve(verbose=False)
+        >>> len(best_solution)
+        2  # The best solution should be a 2-element array (var_x, var_y)
+        >>> isinstance(best_solution[0], float)  # First element should be a float
+        True
+        >>> isinstance(best_solution[1], float)  # Second element should be a float
+        True
+        """
+        best_individual = None
+        for generation in range(self.generations):
+            # Evaluate population fitness (multithreaded)
+            population_score = self.evaluate_population()
+
+            # Ensure population_score isn't empty
+            if not population_score:
+                raise ValueError("Population score is empty. No individuals evaluated.")
+
+            # Check the best individual
+            best_individual = max(
+                population_score, key=lambda score_tuple: score_tuple[1]
+            )[0]
+            best_fitness = self.fitness(best_individual)
+
+            # Select parents for next generation
+            parents = self.select_parents(population_score)
+            next_generation = []
+
+            # Generate offspring using crossover and mutation
+            for i in range(0, len(parents), 2):
+                parent1, parent2 = (
+                    parents[i],
+                    parents[(i + 1) % len(parents)],
+                )  # Wrap around for odd cases
+                child1, child2 = self.crossover(parent1, parent2)
+                next_generation.append(self.mutate(child1))
+                next_generation.append(self.mutate(child2))
+
+            # Ensure population size remains the same
+            self.population = next_generation[: self.population_size]
+
+            if verbose and generation % 10 == 0:
+                print(f"Generation {generation}: Best Fitness = {best_fitness}")
+
+        return best_individual
+
+
+# Example target function for optimization
+def target_function(var_x: float, var_y: float) -> float:
+    """
+    Example target function (parabola) for optimization.
+    Args:
+        var_x (float): The x-coordinate.
+        var_y (float): The y-coordinate.
+    Returns:
+        float: The value of the function at (var_x, var_y).
+
+    Example:
+    >>> target_function(0, 0)
+    0
+    >>> target_function(1, 1)
+    2
+    """
+    return var_x**2 + var_y**2  # Simple parabolic surface (minimization)
+
+
+# Set bounds for the variables (var_x, var_y)
+bounds = [(-10, 10), (-10, 10)]  # Both var_x and var_y range from -10 to 10
+
+# Instantiate and run the genetic algorithm
+ga = GeneticAlgorithm(
+    function=target_function,
+    bounds=bounds,
+    population_size=N_POPULATION,
+    generations=N_GENERATIONS,
+    mutation_prob=MUTATION_PROBABILITY,
+    crossover_rate=CROSSOVER_RATE,
+    maximize=False,  # Minimize the function
+)
+
+best_solution = ga.evolve()
+print(f"Best solution found: {best_solution}")
+print(f"Best fitness (minimum value of function): {target_function(*best_solution)}")