nsga2算法的python
时间: 2023-07-25 13:06:17 浏览: 45
NSGA-II(Non-dominated Sorting Genetic Algorithm II)是一个常见的多目标优化算法。下面是使用Python实现NSGA-II算法的示例代码:
```python
import random
import numpy as np
class Individual:
def __init__(self, size, bounds):
self.size = size
self.bounds = bounds
self.position = np.random.uniform(bounds[0], bounds[1], size)
self.fitness = None
self.rank = None
self.distance = None
def evaluate(self, objective_function):
self.fitness = objective_function(self.position)
class NSGA2:
def __init__(self, objective_function, bounds, population_size, max_generations, crossover_probability=0.9, mutation_probability=0.1):
self.objective_function = objective_function
self.bounds = bounds
self.population_size = population_size
self.max_generations = max_generations
self.crossover_probability = crossover_probability
self.mutation_probability = mutation_probability
self.population = [Individual(len(bounds), bounds) for _ in range(population_size)]
self.fronts = []
self.crowding_distances = None
def run(self):
for individual in self.population:
individual.evaluate(self.objective_function)
for generation in range(self.max_generations):
parents = self.selection()
offspring = self.reproduction(parents)
self.environmental_selection(offspring)
return self.fronts[0]
def selection(self):
tournament_size = 2
parents = []
for _ in range(self.population_size):
tournament = random.sample(self.population, tournament_size)
winner = min(tournament, key=lambda individual: individual.rank)
parents.append(winner)
return parents
def reproduction(self, parents):
offspring = []
for i in range(0, self.population_size, 2):
parent1, parent2 = parents[i], parents[i+1]
if random.random() < self.crossover_probability:
child1, child2 = self.crossover(parent1, parent2)
offspring.append(child1)
offspring.append(child2)
else:
offspring.append(parent1)
offspring.append(parent2)
for individual in offspring:
self.mutation(individual)
for individual in offspring:
individual.evaluate(self.objective_function)
return offspring
def crossover(self, parent1, parent2):
alpha = random.uniform(0, 1)
child1, child2 = Individual(parent1.size, parent1.bounds), Individual(parent2.size, parent2.bounds)
child1.position = alpha * parent1.position + (1 - alpha) * parent2.position
child2.position = alpha * parent2.position + (1 - alpha) * parent1.position
return child1, child2
def mutation(self, individual):
for i in range(individual.size):
if random.random() < self.mutation_probability:
individual.position[i] = random.uniform(self.bounds[0][i], self.bounds[1][i])
def environmental_selection(self, offspring):
for individual in offspring:
individual.rank = None
individual.distance = None
self.population += offspring
fronts = self.fast_non_dominated_sort(self.population)
self.fronts = []
rank = 1
for front in fronts:
self.calculate_crowding_distance(front)
self.fronts.append(front)
for individual in front:
individual.rank = rank
rank += 1
if len(self.fronts) == 2:
break
self.population = []
for front in self.fronts:
self.population += front[:-1]
def fast_non_dominated_sort(self, population):
fronts = [[]]
for individual in population:
individual.domination_set = set()
individual.dominated_count = 0
for other_individual in population:
if individual == other_individual:
continue
if all(individual.fitness <= other_individual.fitness) and any(individual.fitness < other_individual.fitness):
individual.domination_set.add(other_individual)
elif all(individual.fitness >= other_individual.fitness) and any(individual.fitness > other_individual.fitness):
individual.dominated_count += 1
if individual.dominated_count == 0:
fronts[0].append(individual)
current_front = 0
while len(fronts[current_front]) > 0:
next_front = []
for individual in fronts[current_front]:
for other_individual in individual.domination_set:
other_individual.dominated_count -= 1
if other_individual.dominated_count == 0:
next_front.append(other_individual)
current_front += 1
if len(next_front) > 0:
fronts.append(next_front)
return fronts
def calculate_crowding_distance(self, front):
n = len(front)
for individual in front:
individual.distance = 0
for i in range(len(self.objective_function)):
sorted_front = sorted(front, key=lambda individual: individual.fitness[i])
min_fitness = sorted_front[0].fitness[i]
max_fitness = sorted_front[-1].fitness[i]
if max_fitness == min_fitness:
continue
for j in range(1, n-1):
individual = sorted_front[j]
prev_individual = sorted_front[j-1]
next_individual = sorted_front[j+1]
individual.distance += (next_individual.fitness[i] - prev_individual.fitness[i]) / (max_fitness - min_fitness)
```
这段代码实现了一个基本的NSGA-II算法,包括个体类、NSGA-II类、选择、繁殖、环境选择等方法。它可以通过以下步骤使用:
1. 定义目标函数,返回一个向量。
2. 定义变量范围和种群大小等参数。
3. 创建一个NSGA-II对象并运行。
4. 应用算法的结果将是帕累托前沿(Pareto Front)上的一组解。
请注意,这只是一个简单的示例,可以根据需要进行修改和改进。