简单遗传算法-python实现
ObjFunction.py1 import math
2
3
4 def GrieFunc(vardim, x, bound):
5 """
6 Griewangk function
7 """
8 s1 = 0.
9 s2 = 1.
10 for i in range(1, vardim + 1):
11 s1 = s1 + x ** 2
12 s2 = s2 * math.cos(x / math.sqrt(i))
13 y = (1. / 4000.) * s1 - s2 + 1
14 y = 1. / (1. + y)
15 return y
16
17
18 def RastFunc(vardim, x, bound):
19 """
20 Rastrigin function
21 """
22 s = 10 * 25
23 for i in range(1, vardim + 1):
24 s = s + x ** 2 - 10 * math.cos(2 * math.pi * x)
25 return s
GAIndividual.py
1 import numpy as np
2 import ObjFunction
3
4
5 class GAIndividual:
6
7 '''
8 individual of genetic algorithm
9 '''
10
11 def __init__(self,vardim, bound):
12 '''
13 vardim: dimension of variables
14 bound: boundaries of variables
15 '''
16 self.vardim = vardim
17 self.bound = bound
18 self.fitness = 0.
19
20 def generate(self):
21 '''
22 generate a random chromsome for genetic algorithm
23 '''
24 len = self.vardim
25 rnd = np.random.random(size=len)
26 self.chrom = np.zeros(len)
27 for i in xrange(0, len):
28 self.chrom = self.bound + \
29 (self.bound - self.bound) * rnd
30
31 def calculateFitness(self):
32 '''
33 calculate the fitness of the chromsome
34 '''
35 self.fitness = ObjFunction.GrieFunc(
36 self.vardim, self.chrom, self.bound)
GeneticAlgorithm.py
1 import numpy as np
2 from GAIndividual import GAIndividual
3 import random
4 import copy
5 import matplotlib.pyplot as plt
6
7
8 class GeneticAlgorithm:
9
10 '''
11 The class for genetic algorithm
12 '''
13
14 def __init__(self, sizepop, vardim, bound, MAXGEN, params):
15 '''
16 sizepop: population sizepop
17 vardim: dimension of variables
18 bound: boundaries of variables
19 MAXGEN: termination condition
20 param: algorithm required parameters, it is a list which is consisting of crossover rate, mutation rate, alpha
21 '''
22 self.sizepop = sizepop
23 self.MAXGEN = MAXGEN
24 self.vardim = vardim
25 self.bound = bound
26 self.population = []
27 self.fitness = np.zeros((self.sizepop, 1))
28 self.trace = np.zeros((self.MAXGEN, 2))
29 self.params = params
30
31 def initialize(self):
32 '''
33 initialize the population
34 '''
35 for i in xrange(0, self.sizepop):
36 ind = GAIndividual(self.vardim, self.bound)
37 ind.generate()
38 self.population.append(ind)
39
40 def evaluate(self):
41 '''
42 evaluation of the population fitnesses
43 '''
44 for i in xrange(0, self.sizepop):
45 self.population.calculateFitness()
46 self.fitness = self.population.fitness
47
48 def solve(self):
49 '''
50 evolution process of genetic algorithm
51 '''
52 self.t = 0
53 self.initialize()
54 self.evaluate()
55 best = np.max(self.fitness)
56 bestIndex = np.argmax(self.fitness)
57 self.best = copy.deepcopy(self.population)
58 self.avefitness = np.mean(self.fitness)
59 self.trace = (1 - self.best.fitness) / self.best.fitness
60 self.trace = (1 - self.avefitness) / self.avefitness
61 print("Generation %d: optimal function value is: %f; average function value is %f" % (
62 self.t, self.trace, self.trace))
63 while (self.t < self.MAXGEN - 1):
64 self.t += 1
65 self.selectionOperation()
66 self.crossoverOperation()
67 self.mutationOperation()
68 self.evaluate()
69 best = np.max(self.fitness)
70 bestIndex = np.argmax(self.fitness)
71 if best > self.best.fitness:
72 self.best = copy.deepcopy(self.population)
73 self.avefitness = np.mean(self.fitness)
74 self.trace = (1 - self.best.fitness) / self.best.fitness
75 self.trace = (1 - self.avefitness) / self.avefitness
76 print("Generation %d: optimal function value is: %f; average function value is %f" % (
77 self.t, self.trace, self.trace))
78
79 print("Optimal function value is: %f; " %
80 self.trace)
81 print "Optimal solution is:"
82 print self.best.chrom
83 self.printResult()
84
85 def selectionOperation(self):
86 '''
87 selection operation for Genetic Algorithm
88 '''
89 newpop = []
90 totalFitness = np.sum(self.fitness)
91 accuFitness = np.zeros((self.sizepop, 1))
92
93 sum1 = 0.
94 for i in xrange(0, self.sizepop):
95 accuFitness = sum1 + self.fitness / totalFitness
96 sum1 = accuFitness
97
98 for i in xrange(0, self.sizepop):
99 r = random.random()
100 idx = 0
101 for j in xrange(0, self.sizepop - 1):
102 if j == 0 and r < accuFitness:
103 idx = 0
104 break
105 elif r >= accuFitness and r < accuFitness:
106 idx = j + 1
107 break
108 newpop.append(self.population)
109 self.population = newpop
110
111 def crossoverOperation(self):
112 '''
113 crossover operation for genetic algorithm
114 '''
115 newpop = []
116 for i in xrange(0, self.sizepop, 2):
117 idx1 = random.randint(0, self.sizepop - 1)
118 idx2 = random.randint(0, self.sizepop - 1)
119 while idx2 == idx1:
120 idx2 = random.randint(0, self.sizepop - 1)
121 newpop.append(copy.deepcopy(self.population))
122 newpop.append(copy.deepcopy(self.population))
123 r = random.random()
124 if r < self.params:
125 crossPos = random.randint(1, self.vardim - 1)
126 for j in xrange(crossPos, self.vardim):
127 newpop.chrom = newpop.chrom[
128 j] * self.params + (1 - self.params) * newpop.chrom
129 newpop.chrom = newpop.chrom * self.params + \
130 (1 - self.params) * newpop.chrom
131 self.population = newpop
132
133 def mutationOperation(self):
134 '''
135 mutation operation for genetic algorithm
136 '''
137 newpop = []
138 for i in xrange(0, self.sizepop):
139 newpop.append(copy.deepcopy(self.population))
140 r = random.random()
141 if r < self.params:
142 mutatePos = random.randint(0, self.vardim - 1)
143 theta = random.random()
144 if theta > 0.5:
145 newpop.chrom = newpop.chrom[
146 mutatePos] - (newpop.chrom - self.bound) * (1 - random.random() ** (1 - self.t / self.MAXGEN))
147 else:
148 newpop.chrom = newpop.chrom[
149 mutatePos] + (self.bound - newpop.chrom) * (1 - random.random() ** (1 - self.t / self.MAXGEN))
150 self.population = newpop
151
152 def printResult(self):
153 '''
154 plot the result of the genetic algorithm
155 '''
156 x = np.arange(0, self.MAXGEN)
157 y1 = self.trace[:, 0]
158 y2 = self.trace[:, 1]
159 plt.plot(x, y1, 'r', label='optimal value')
160 plt.plot(x, y2, 'g', label='average value')
161 plt.xlabel("Iteration")
162 plt.ylabel("function value")
163 plt.title("Genetic algorithm for function optimization")
164 plt.legend()
165 plt.show()
运行程序：
1 if __name__ == "__main__":
2
3 bound = np.tile([[-600], ], 25)
4 ga = GA(60, 25, bound, 1000, )
5 ga.solve()
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