具有模拟退火的神经网络模型的优化变量

Question

我在数据上实现了一个 MLP 神经网络模型，为了优化 4 个变量，定义了一个基于 MLP 模型的函数，并对该函数进行了模拟退火运行。我不知道为什么会出现此错误（附在下面）。

神经网络代码：

# mlp for regression
from numpy import sqrt
from pandas import read_csv
from sklearn.model_selection import train_test_split
from tensorflow.keras import Sequential
from tensorflow.keras.layers import Dense
import tensorflow
from tensorflow import keras
from matplotlib import pyplot
from keras.layers import Dropout
from tensorflow.keras import regularizers

# determine the number of input features
n_features = X_train.shape[1]
# define model
model = Sequential()
model.add(Dense(150, activation='tanh', kernel_initializer='zero',kernel_regularizer=regularizers.l2(0.001), input_shape=(n_features,))) #relu/softmax/tanh
model.add(Dense(100, activation='tanh', kernel_initializer='zero',kernel_regularizer=regularizers.l2(0.001)))
model.add(Dense(50, activation='tanh', kernel_initializer='zero',kernel_regularizer=regularizers.l2(0.001)))
model.add(Dropout(0.0))
model.add(Dense(1))
# compile the model
opt= keras.optimizers.Adam(learning_rate=0.001)
#opt = tensorflow.keras.optimizers.RMSprop(learning_rate=0.001,rho=0.9,momentum=0.0,epsilon=1e-07,centered=False,name="RMSprop")
model.compile(optimizer=opt, loss='mse')
# fit the model
history=model.fit(X_train, y_train, validation_data = (X_test,y_test), epochs=100, batch_size=10, verbose=0,validation_split=0.3)
# evaluate the model
error = model.evaluate(X_test, y_test, verbose=0)
print('MSE: %.3f, RMSE: %.3f' % (error, sqrt(error)))
# plot learning curves
pyplot.title('Learning Curves')
pyplot.xlabel('Epoch')
pyplot.ylabel('Cross Entropy')
pyplot.plot(history.history['loss'], label='train')
pyplot.plot(history.history['val_loss'], label='val')
pyplot.legend()
pyplot.show()

功能代码：

def objective_function(X):
  wob   = X[0]
  torque= X[1]
  RPM   = X[2]
  pump  = X[3]
  input=[wob,torque,RPM, 0.00017,0.027,pump,0,0.5,0.386,0.026,0.0119,0.33,0.83,0.48]
  input = pd.DataFrame(input)
  obj= model.predict(input)
  return obj

用于优化的模拟退火：

import time
import random
import math
import numpy as np

## custom section
initial_temperature = 100
cooling = 0.8 # cooling coef.
number_variables = 4
upper_bounds = [1,1,1,1]
lower_bounds = [0,0,0,0]
computing_time = 1 # seconds


## simulated Annealing algorithm

## 1. Genertate an initial solution randomly
initial_solution = np.zeros((number_variables))
for v in range(number_variables):
    initial_solution[v] = random.uniform(lower_bounds[v], upper_bounds[v])
current_solution = initial_solution
best_solution = initial_solution
n=1 # no of solutions accepted
best_fitness = objective_function(best_solution)
current_temperature = initial_temperature # current temperature
start = time.time()
no_attemps = 100 # number of attemps in each level of temperature
record_best_fitness = []

for i in range(9999999):
    for j in range(no_attemps):
        for k in range(number_variables):
            ## 2. generate a candidate solution y randomly based on solution x
            current_solution[k] = best_solution[k] + 0.1*(random.uniform(lower_bounds[k], upper_bounds[k]))
            current_solution[k] = max(min(current_solution[k], upper_bounds[k]), lower_bounds[k]) # repaire the solution respecting the bounds

  ## 3. check if y is better than x
        current_fitness = objective_function(current_solution)
        E = abs(current_fitness - best_solution)
        if i==0 and j==0:
            EA = E
        if current_fitness < best_fitness:
            p = math.exp(-E/(EA*current_temperature))
            # make a decision to accept the worse solution or not
            ## 4. make a decision whether r < p
            if random.random()<p:
                accept = True # this worse solution is not accepted
            else:
                accept = False # this worse solution is not accepted
        else:
            accept = True # accept better solution
        ## 5. make a decision whether step comdition of inner loop is met
        if accept == True:
            best_solution = current_solution # update the best solution
            best_fitness = objective_function(best_solution)
            n = n + 1 #count the solutions accepted
            EA = (EA*(n-1)+E)/n # accept EA
    print('interation : {}, best_solution:{}, best_fitness:{}'. format(i, best_solution, best_fitness))
    record_best_fitness.append(best_fitness)
    ## 6. decrease the temperature
    current_temperature = current_temperature * cooling
    ## 7. stop condition of outer loop is met
    end = time.time()
    if end-start >= computing_time:
        break

错误图片：

Answer 1

它是针对你的输入形状，在 MLP 神经网络中你的输入形状是 [none,14]，但是在你的函数的输入 id [14,1] 中，所以你需要转置它。

def objective_function(X):
  wob   = X[0]
  torque= X[1]
  RPM   = X[2]
  pump  = X[3]
  input=[wob,torque,RPM, 0.00017,0.027,pump,0,0.5,0.386,0.026,0.0119,0.33,0.83,0.48]
  input = pd.DataFrame(input)
  input=input.T
  model1.predict(input)
  return obj

具有模拟退火的神经网络模型的优化变量

Optimization variables of a neural network model with simulated annealing

python

function

optimization

mlp

simulated-annealing