遗传算法解决0-1背包问题

Posted 2020-10-31 最后的绝地武士

  1 import numpy
  2 import matplotlib.pyplot as plt
  3 
  4 
  5 data = numpy.array([[77, 92],
  6                     [22, 22],
  7                     [29, 87],
  8                     [50, 46],
  9                     [99, 90]])
 10 
 11 
 12 class GA(object):
 13     """
 14     遗传算法解决0-1背包问题
 15     """
 16 
 17     def __init__(self, length, number, iter_number):
 18         """
 19         参数初始化
 20         :param length: 5
 21         :param number: 300
 22         :param iter_number: 300
 23         """
 24         self.length = length  # 确定染色体编码长度
 25         self.number = number  # 确定初始化种群数量
 26         self.iteration = iter_number  # 设置迭代次数
 27         self.bag_capacity = 100  # 背包容量
 28 
 29         self.retain_rate = 0.2  # 每一代精英选择出前20%
 30         self.random_selection_rate = 0.5  # 对于不是前20%的，有0.5的概率可以进行繁殖
 31         self.mutation_rate = 0.01  # 变异概率0.01
 32 
 33     def initial_population(self):
 34         """
 35         种群初始化，
 36 
 37         :return: 返回种群集合
 38         """
 39         init_population = numpy.random.randint(low=0, high=2, size=[self.length, self.number], dtype=numpy.int16)
 40         return init_population
 41 
 42     def weight_price(self, chromosome):
 43         """
 44         计算累计重量和累计价格
 45         :param chromosome:
 46         :return:返回每一个个体的累计重量和价格
 47         """
 48         w_accumulation = 0
 49         p_accumulation = 0
 50         for i in range(len(chromosome)):
 51 
 52             w = chromosome[i]*data[i][0]
 53             p = chromosome[i]*data[i][1]
 54             w_accumulation = w + w_accumulation
 55             p_accumulation = p + p_accumulation
 56 
 57         return w_accumulation, p_accumulation
 58 
 59     def fitness_function(self, chromosome):
 60         """
 61         计算适应度函数，一般来说，背包的价值越高越好，但是
 62         当重量超过100时，适应度函数=0
 63         :param chromosome:
 64         :return:
 65         """
 66 
 67         weight, price = self.weight_price(chromosome)
 68         if weight > self.bag_capacity:
 69             fitness = 0
 70         else:
 71             fitness = price
 72 
 73         return fitness
 74 
 75     def fitness_average(self, init_population):
 76         """
 77         求出这个种群的平均适应度，才能知道种群已经进化好了
 78         :return:返回的是一个种群的平均适应度
 79         """
 80         f_accumulation = 0
 81         for z in range(init_population.shape[1]):
 82             f_tem = self.fitness_function(init_population[:, z])
 83             f_accumulation = f_accumulation + f_tem
 84         f_accumulation = f_accumulation/init_population.shape[1]
 85         return f_accumulation
 86 
 87     def selection(self, init_population):
 88         """
 89         选择
 90         :param init_population:
 91         :return: 返回选择后的父代，数量是不定的
 92         """
 93         sort_population = numpy.array([[], [], [], [], [], []])  # 生成一个排序后的种群列表，暂时为空
 94         for i in range(init_population.shape[1]):
 95 
 96             x1 = init_population[:, i]
 97             # print(\'打印x1\', x1)
 98             x2 = self.fitness_function(x1)
 99             x = numpy.r_[x1, x2]
100             # print(\'打印x\', x)
101             sort_population = numpy.c_[sort_population, x]
102 
103         sort_population = sort_population.T[numpy.lexsort(sort_population)].T  # 联合排序，从小到大排列
104 
105         # print(\'排序后长度\', sort_population.shape[1])
106         print(sort_population)
107 
108         # 选出适应性强的个体，精英选择
109         retain_length = sort_population.shape[1]*self.retain_rate
110 
111         parents = numpy.array([[], [], [], [], [], []])  # 生成一个父代列表，暂时为空
112         for j in range(int(retain_length)):
113             y1 = sort_population[:, -(j+1)]
114             parents = numpy.c_[parents, y1]
115 
116         # print(parents.shape[1])
117 
118         rest = sort_population.shape[1] - retain_length  # 精英选择后剩下的个体数
119         for q in range(int(rest)):
120 
121             if numpy.random.random() < self.random_selection_rate:
122                 y2 = sort_population[:, q]
123                 parents = numpy.c_[parents, y2]
124 
125         parents = numpy.delete(parents, -1, axis=0)  # 删除最后一行，删除了f值
126         # print(\'打印选择后的个体数\')
127         # print(parents.shape[0])
128 
129         parents = numpy.array(parents, dtype=numpy.int16)
130 
131         return parents
132 
133     def crossover(self, parents):
134         """
135         交叉生成子代，和初始化的种群数量一致
136         :param parents:
137         :return:返回子代
138         """
139         children = numpy.array([[], [], [], [], []])  # 子列表初始化
140 
141         while children.shape[1] < self.number:
142             father = numpy.random.randint(0, parents.shape[1] - 1)
143             mother = numpy.random.randint(0, parents.shape[1] - 1)
144             if father != mother:
145                 # 随机选取交叉点
146                 cross_point = numpy.random.randint(0, self.length)
147                 # 生成掩码，方便位操作
148                 mark = 0
149                 for i in range(cross_point):
150                     mark |= (1 << i)
151 
152                 father = parents[:, father]
153                 # print(father)
154                 mother = parents[:, mother]
155 
156                 # 子代将获得父亲在交叉点前的基因和母亲在交叉点后（包括交叉点）的基因
157                 child = ((father & mark) | (mother & ~mark)) & ((1 << self.length) - 1)
158 
159                 children = numpy.c_[children, child]
160 
161                 # 经过繁殖后，子代的数量与原始种群数量相等，在这里可以更新种群。
162                 # print(\'子代数量\', children.shape[1])
163         # print(children.dtype)
164         children = numpy.array(children, dtype=numpy.int16)
165         return children
166 
167     def mutation(self, children):
168         """
169         变异
170 
171         :return:
172         """
173         for i in range(children.shape[1]):
174 
175             if numpy.random.random() < self.mutation_rate:
176                 j = numpy.random.randint(0, self.length - 1)  # s随机产生变异位置
177                 children[:, i] ^= 1 << j  # 产生变异
178         children = numpy.array(children, dtype=numpy.int16)
179         return children
180 
181     def plot_figure(self, iter_plot, f_plot, f_set_plot):
182         """
183         画出迭代次数和平均适应度曲线图
184         画出迭代次数和每一步迭代最大值图
185         :return:
186         """
187         plt.figure()
188 
189         ax1 = plt.subplot(121)
190         ax2 = plt.subplot(122)
191 
192         plt.sca(ax1)
193         plt.plot(iter_plot, f_plot)
194         plt.ylim(0, 140)  # 设置y轴范围
195 
196         plt.sca(ax2)
197         plt.plot(iter_plot, f_set_plot)
198         plt.ylim(0, 140)  # 设置y轴范围
199         plt.show()
200 
201     def main(self):
202         """
203         main函数,用来进化
204         对当前种群依次进行选择、交叉并生成新一代种群，然后对新一代种群进行变异
205         :return:
206         """
207         init_population = self.initial_population()
208         # print(init_population)
209 
210         iter_plot = []
211         f_plot = []
212         iteration = 0
213 
214         f_set_plot = []
215 
216         while iteration < self.iteration:  # 设置迭代次数300
217 
218             parents = self.selection(init_population)  # 选择后的父代
219             children = self.crossover(parents)
220             mutation_children = self.mutation(children)
221 
222             init_population = mutation_children
223 
224             f_set = []  # 求出每一步迭代的最大值
225             for init in range(init_population.shape[1]):
226                 f_set_tem = self.fitness_function(init_population[:, init])
227                 f_set.append(f_set_tem)
228 
229             f_set = max(f_set)
230 
231             f_set_plot.append(f_set)
232 
233             iter_plot.append(iteration)
234             iteration = iteration+1
235             print("第%s进化得如何******************************************" % iteration)
236             f_average = self.fitness_average(init_population)
237             f_plot.append(f_average)
238             print(f_set)
239             # f_accumulation = f_accumulation + f
240             # f_print = f_accumulation/(iteration + 1)
241             # print(f_print)
242         self.plot_figure(iter_plot, f_plot, f_set_plot)
243 
244 
245 if __name__ == \'__main__\':
246     g1 = GA(5, 300, 100)
247     g1.main()