通过设计 GA(遗传算法)求解下面所示图的最大割问题。补充:最大割问题 即:即将一个无向图切成 2 个部分(子图),从而使得 2 个子图之间的边数最 多
时间: 2024-02-16 19:02:50 浏览: 22
为了使用遗传算法解决最大割问题,我们需要定义适应度函数、交叉函数和变异函数。下面是一个简单的示例代码:
```python
import numpy as np
import networkx as nx
# 构建图
G = nx.Graph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 0), (0, 2), (1, 3), (2, 4)])
# 定义适应度函数
def fitness_function(individual):
cut = 0
for (u, v) in G.edges():
if individual[u] != individual[v]:
cut += 1
return cut
# 定义交叉函数
def crossover(parent1, parent2):
crossover_point = np.random.randint(1, G.number_of_nodes() - 1)
offspring1 = np.concatenate([parent1[:crossover_point], parent2[crossover_point:]])
offspring2 = np.concatenate([parent2[:crossover_point], parent1[crossover_point:]])
return offspring1, offspring2
# 定义变异函数
def mutate(individual):
mutation_point = np.random.randint(0, G.number_of_nodes())
individual[mutation_point] = 1 - individual[mutation_point]
return individual
# 定义遗传算法参数
population_size = 50
mutation_rate = 0.1
crossover_rate = 0.8
num_generations = 100
# 初始化种群
population = np.random.randint(0, 2, size=(population_size, G.number_of_nodes()))
# 迭代遗传算法
for generation in range(num_generations):
# 计算适应度
fitness = np.array([fitness_function(individual) for individual in population])
# 选择
parents = np.random.choice(population, size=population_size, replace=True, p=fitness/fitness.sum())
# 交叉
offspring = []
for i in range(population_size // 2):
parent1, parent2 = parents[2*i], parents[2*i+1]
if np.random.rand() < crossover_rate:
offspring1, offspring2 = crossover(parent1, parent2)
else:
offspring1, offspring2 = parent1, parent2
offspring.append(offspring1)
offspring.append(offspring2)
# 变异
for i in range(population_size):
if np.random.rand() < mutation_rate:
population[i] = mutate(population[i])
# 更新种群
population = np.array(offspring)
# 选出最优解
best_individual = population[np.argmax([fitness_function(individual) for individual in population])]
print("最优解:", best_individual)
print("最大割:", fitness_function(best_individual))
```
在这个示例代码中,我们使用Python中的networkx库构建了一个小型的图,然后定义了适应度函数、交叉函数和变异函数。接着,我们初始化种群,并在每一代中进行选择、交叉和变异操作。最后,选出最优解并输出最大割。