以下是NSGA-II算法的Python实现代码示例： ```python import random import numpy as np class Individual: def __init__(self, decision_variables): self.decision_variables = decision_variables self.objectives = [] self.rank = None self.crowding_distance = 0 def fast_non_dominated_sort(population): fronts = [[]] for individual in population: individual.domination_count = 0 individual.dominated_solutions = [] for other_individual in population: if individual dominates other_individual: individual.dominated_solutions.append(other_individual) elif other_individual dominates individual: individual.domination_count += 1 if individual.domination_count == 0: individual.rank = 0 fronts[0].append(individual) i = 0 while fronts[i]: next_front = [] for individual in fronts[i]: for dominated_solution in individual.dominated_solutions: dominated_solution.domination_count -= 1 if dominated_solution.domination_count == 0: dominated_solution.rank = i + 1 next_front.append(dominated_solution) i += 1 fronts.append(next_front) return fronts[:-1] def crowding_distance_assignment(front): for individual in front: individual.crowding_distance = 0 number_of_objectives = len(front[0].objectives) for objective_index in range(number_of_objectives): front.sort(key=lambda x: x.objectives[objective_index]) front[0].crowding_distance = float('inf') front[-1].crowding_distance = float('inf') for i in range(1, len(front)-1): front[i].crowding_distance += (front[i+1].objectives[objective_index] - front[i-1].objectives[objective_index]) def tournament_selection(parent_population, offspring_population): combined_population = parent_population + offspring_population fronts = fast_non_dominated_sort(combined_population) selected_population = [] for front in fronts: if len(selected_population) + len(front) <= len(parent_population): selected_population.extend(front) else: front_copy = list(front) crowding_distance_assignment(front_copy) front_copy.sort(reverse=True, key=lambda x: x.crowding_distance) selected_population.extend(front_copy[:len(parent_population) - len(selected_population)]) break return selected_population # Example usage population_size = 100 number_of_generations = 100 decision_variable_bounds = [(0, 1), (0, 1)] offspring_population = [] for _ in range(population_size): decision_variables = [random.uniform(lb, ub) for lb, ub in decision_variable_bounds] individual = Individual(decision_variables) # Evaluate objectives here... offspring_population.append(individual) parent_population = offspring_population.copy() for generation in range(number_of_generations): new_offspring_population = [] # Generate offspring using crossover and mutation operators. parent_population = tournament_selection(parent_population, new_offspring_population) ``` ### 关于代码说明 上述代码实现了NSGA-II的主要逻辑，包括快速非支配排序和拥挤度距离计算功能[^5]。此外，还提供了锦标赛选择方法来生成下一代种群。