遗传算法解8皇后问题python
时间: 2023-11-05 20:03:39 浏览: 38
以下是一个遗传算法的实现,用于解决8皇后问题:
```python
import random
# 定义棋盘大小和种群大小
BOARD_SIZE = 8
POPULATION_SIZE = 100
# 定义遗传算法的参数
MUTATION_RATE = 0.25
CROSSOVER_RATE = 0.75
GENERATIONS = 1000
# 生成随机种群
def generate_population(size):
population = []
for i in range(size):
chromosome = [random.randint(0, BOARD_SIZE-1) for _ in range(BOARD_SIZE)]
population.append(chromosome)
return population
# 计算染色体的适应度
def fitness(chromosome):
conflicts = 0
for i in range(BOARD_SIZE):
for j in range(i+1, BOARD_SIZE):
if chromosome[i] == chromosome[j]:
conflicts += 1
elif abs(i-j) == abs(chromosome[i]-chromosome[j]):
conflicts += 1
return 1.0 / (conflicts + 1)
# 选择种群中适应度较高的染色体
def selection(population):
fitness_scores = [fitness(chromosome) for chromosome in population]
total_fitness = sum(fitness_scores)
probabilities = [fitness_score / total_fitness for fitness_score in fitness_scores]
cumulative_probabilities = [sum(probabilities[:i+1]) for i in range(len(probabilities))]
selected_population = []
for i in range(len(population)):
r = random.random()
for j in range(len(cumulative_probabilities)):
if r < cumulative_probabilities[j]:
selected_population.append(population[j])
break
return selected_population
# 对染色体进行交叉
def crossover(parent1, parent2):
crossover_point = random.randint(1, BOARD_SIZE-2)
child1 = parent1[:crossover_point] + parent2[crossover_point:]
child2 = parent2[:crossover_point] + parent1[crossover_point:]
return child1, child2
# 对染色体进行变异
def mutation(chromosome):
if random.random() < MUTATION_RATE:
index1, index2 = random.sample(range(BOARD_SIZE), 2)
chromosome[index1], chromosome[index2] = chromosome[index2], chromosome[index1]
return chromosome
# 进行遗传算法
def genetic_algorithm():
population = generate_population(POPULATION_SIZE)
for generation in range(GENERATIONS):
population = selection(population)
next_generation = []
while len(next_generation) < POPULATION_SIZE:
parent1, parent2 = random.sample(population, 2)
if random.random() < CROSSOVER_RATE:
child1, child2 = crossover(parent1, parent2)
next_generation.append(mutation(child1))
next_generation.append(mutation(child2))
else:
next_generation.append(mutation(parent1))
next_generation.append(mutation(parent2))
population = next_generation
best_chromosome = max(population, key=fitness)
if fitness(best_chromosome) == 1:
return best_chromosome
return None
# 测试
solution = genetic_algorithm()
if solution:
print(solution)
else:
print("No solution found")
```
该遗传算法的实现比较简单,首先生成一个随机种群,然后进行多次迭代,每次迭代都通过选择、交叉和变异操作不断更新种群,直到找到符合条件的染色体或者达到最大迭代次数为止。在每次迭代中,选择操作使用了轮盘赌算法,交叉操作使用了单点交叉,变异操作使用了交换两个基因的方式。适应度函数使用了皇后之间的冲突数量的倒数,这样是为了让适应度越高的染色体的值越大,方便进行选择操作。
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