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GA.py
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import numpy as np
import random
# 默认找最大值，如需更改为寻找最小值，将evaluation加负号
varNum = 2 # 变量数目
rank = 32 # 编码位数
low = np.array([-5, -5]) # 变量下界
high = np.array([5, 5]) # 变量上界
epochs = 100 # 迭代次数
population = 20 # 群体数目
crossoverRate = 0.8 # 交叉率
mutateRate = 0.1 # 变异率
def evaluation(codes):
x = decode(codes)
# f = -x[0] ** 2 + 10 * np.cos(2 * np.pi * x[0]) + 30
# f = x[0] ** 2
f = (20 + np.e - 20 * np.exp(-0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))) -
np.exp(0.5 * (np.cos(2 * np.pi * x[0]) + np.cos(2 * np.pi * x[1]))))
return f
def encode(nums):
precision = (high - low) / (np.power(2, rank) - 1)
for i in range(len(nums)):
nums[i] = (nums[i] - low[i]) / precision[i]
code = np.vectorize(np.binary_repr)(nums.astype(int), width=rank)
return code
def decode(codes):
precision = (high - low) / (np.power(2, rank) - 1)
nums = codes.copy().astype(float)
for i in range(len(codes)):
for j in range(len(codes[0])):
nums[i][j] = int(codes[i][j], 2) * precision[i] + low[i]
return nums
def softmax(x):
exp_x = np.exp(x - np.max(x)) # 避免指数溢出，减去最大值
return exp_x / exp_x.sum(axis=0, keepdims=True)
def selection(codes, quantity):
vals = evaluation(codes)
index = np.argsort(vals)[::-1]
vals = softmax(vals)
selects = [[] for _ in range(len(codes))]
for i in range(len(codes)):
selects[i].append(codes[i][index[0]])
for k in range(len(codes)):
for i in range(quantity - 1):
aRate = random.random()
cumulative = 0
for j in range(len(vals)):
cumulative += vals[j]
if aRate < cumulative:
selects[k].append(codes[k][j])
break
return np.array(selects)
def crossover(codes):
re_codes = codes.copy()
for k in range(len(codes)):
for i in range(len(codes[0])):
if random.random() < crossoverRate:
select_idx = random.randint(0, len(codes) - 1)
while select_idx == i:
select_idx = random.randint(0, len(codes[0]) - 1)
select_code = codes[k][select_idx]
crossPos = random.randint(1, len(select_code) - 2)
re_codes[k][i] = codes[k][i][:crossPos] + select_code[crossPos:]
return re_codes
def mutation(codes):
re_codes = codes.copy()
for k in range(len(codes)):
for i in range(len(codes[0])):
code = list(str(re_codes[k][i]))
for j in range(len(code)):
if random.random() < mutateRate:
if code[j] == '1':
code[j] = '0'
else:
code[j] = '1'
re_codes[k][i] = ''.join(code)
return re_codes
def geneticAlgorithms():
nums = np.zeros((varNum, population))
for i in range(varNum):
nums[i, :] = np.random.uniform(low[i], high[i], population)
codes = encode(nums)
for epoch in range(epochs):
origCode = codes.copy()
codes = crossover(codes)
codes = mutation(codes)
codes = np.hstack((origCode, codes))
codes = np.unique(codes, axis=1)
codes = selection(codes, population)
vals = evaluation(codes)
index = np.argsort(vals)[::-1]
ans = [[] for _ in range(len(codes))]
for i in range(len(codes)):
ans[i].append(codes[i][index[:3]])
ans = np.reshape(np.array(ans), (varNum, -1))
return evaluation(ans), decode(ans), ans
if __name__ == '__main__':
results = geneticAlgorithms()
for result in results:
print(result)
print('------------------------------------------------')