人工智能导论(第五版)王万良课后习题(第五、六章)
农夫、狐狸、鸡、小米都在一条河的左岸,现在要把它们全部送到右岸去。农夫有一条船,过河时,除农夫外,船上至多能载狐狸、鸡和小米中的一样。(提示:8.用四元组(农夫,狐狸,鸡,米)表示状态,其中每个元素都可为0或1,0表示在左岸,1表示在右岸:b.把每次过河的一种安排作为一个算符,每次过河都必须有农夫,因为只有他可以划船。6.2 用遗传算法求解下列函数的最大值,f(x)=0.4+sinc(4x)+1.
5.2 用状态空间搜索法求解农夫、狐狸、鸡、小米问题。农夫、狐狸、鸡、小米都在一条河的左岸,现在要把它们全部送到右岸去。农夫有一条船,过河时,除农夫外,船上至多能载狐狸、鸡和小米中的一样。狐狸要吃鸡,鸡要吃小米,除非农夫在那里。试规划出一个确保全部安全的过河计划。(提示:8.用四元组(农夫,狐狸,鸡,米)表示状态,其中每个元素都可为0或1,0表示在左岸,1表示在右岸:b.把每次过河的一种安排作为一个算符,每次过河都必须有农夫,因为只有他可以划船。)
6.2 用遗传算法求解下列函数的最大值,f(x)=0.4+sinc(4x)+1.1sinc(4x+2)+0.8sinc(x-2)+0.7sinc(6x-4),x∈[-2,2]
以下是一个简单的使用遗传算法求解函数最大值的代码(Python):
import numpy as np
# 定义目标函数def fitness_function(x):
return 0.4+sinc(4x)+1.1sinc(4x+2)+0.8sinc(x-2)+0.7sinc(6x-4)
# 初始化种群def initialize_population(population_size, chromosome_length):
return np.random.randint(0, 30, (population_size, chromosome_length))
# 计算适应度def calculate_fitness(population):
return np.array([fitness_function(chromosome) for chromosome in population])
# 选择操作def selection(population, fitness):
return population[np.argmax(fitness)]
# 交叉操作def crossover(parent1, parent2):
crossover_point = np.random.randint(1, len(parent1))
child1 = np.concatenate((parent1[:crossover_point], parent2[crossover_point:]))
child2 = np.concatenate((parent2[:crossover_point], parent1[crossover_point:]))
return child1, child2
# 变异操作def mutation(chromosome):
mutation_point = np.random.randint(len(chromosome))
chromosome[mutation_point] = np.random.randint(0, 10)
return chromosome
# 遗传算法主程序def genetic_algorithm(population_size, chromosome_length, generations):
population = initialize_population(population_size, chromosome_length)
for _ in range(generations):
fitness = calculate_fitness(population)
parent1 = selection(population, fitness)
parent2 = selection(population, fitness)
child1, child2 = crossover(parent1, parent2)
child1 = mutation(child1)
child2 = mutation(child2)
population = np.vstack((population, child1, child2))
best_chromosome = selection(population, calculate_fitness(population))
return best_ch
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