目錄

1. 模擬退火算法實現步驟?

2. python實現

3. 實驗結果

4. 參考文獻

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模擬退火算法的基本原理在這里就不一一贅述了， 關于原理，可以參考百度百科、博客1、博客2

在本節按照基本實現步驟實現模擬退火算法， 對于模擬退火算法的高級封裝(類封裝)， 可以參考模擬退火算法之特征選擇的python實現(二)

1. 模擬退火算法實現步驟?

2. python實現

            
              import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.neural_network import MLPRegressor
from sklearn.metrics import mean_squared_error
import scipy.io as sio
from sklearn.model_selection import train_test_split


def get_data_subset(x_data, columns):
    return x_data[:, columns]


def get_initial_solution(feature_size, selected_feature):
    sol = np.arange(feature_size-1)
    np.random.shuffle(sol)
    return sol[:selected_feature]


def get_neighbor(current_solution, feature_size, temperature):
    all_features = range(feature_size-1)
    selected = current_solution
    not_selected = np.setdiff1d(all_features, selected)

    # swap one selected feature with one non-selected feature
    num_swaps = int(min(np.ceil(np.abs(np.random.normal(0, 0.1*len(selected)*temperature))), np.ceil(0.1*len(selected))))
    feature_out = np.random.randint(0, len(selected), num_swaps)  # 產生num_swaps個樣本索引（從range(len(selected))中）
    selected = np.delete(selected, feature_out)

    feature_in = np.random.randint(0, len(not_selected), num_swaps)  # 產生num_swaps個樣本索引（從range(len(not_selected))中）
    selected = np.append(selected, not_selected[feature_in])

    return selected


def get_cost(solution, x_train, x_test, y_train, y_test):
    x_scale, y_scale = StandardScaler(), StandardScaler()
    x_train_scaled = x_scale.fit_transform(x_train)
    x_test_scaled = x_scale.transform(x_test)
    y_train_scaled = y_scale.fit_transform(y_train.reshape(-1, 1))
    y_test_scaled = y_scale.transform(y_test.reshape(-1, 1))
    limited_train_data = get_data_subset(x_train_scaled, solution)
    limited_test_data = get_data_subset(x_test_scaled, solution)
    model = MLPRegressor(hidden_layer_sizes=43)
    model.fit(limited_train_data, y_train_scaled.ravel())
    y_test_pred = model.predict(limited_test_data)
    y_test_pred = y_scale.inverse_transform(y_test_pred)
    return round(mean_squared_error(y_test, y_test_pred), 4)


def get_probability(temperature, delta_cost):
    return np.exp(delta_cost/temperature)


def simulated_annealing(initT, minT, alpha, iterations, features, x_train, x_test, y_train, y_test):
    temperature = initT  # 當前溫度
    solution = get_initial_solution(feature_size=features_size, selected_feature=sel_feature)
    cost = get_cost(solution, x_train, x_test, y_train, y_test)
    temp_history = [temperature]
    best_cost_history = []
    best_solution_history = []
    best_cost = cost
    best_solution = solution
    while temperature > minT:
        for k in range(iterations):
            next_solution = get_neighbor(solution, features, temperature)
            next_cost = get_cost(next_solution, x_train, x_test, y_train, y_test)

            probability = 0
            if next_cost > cost:  # 計算向差方向移動的概率 (即移動后的解比當前解要差)
                probability = get_probability(temperature, cost-next_cost)
            if next_cost < cost or np.random.random() < probability:  # 朝著最優解移動或以一定概率向差方向移動
                cost = next_cost
                solution = next_solution
            if next_cost < best_cost:  # 最優值和最優解
                best_cost = cost
                best_solution = solution
        print("當前溫度：", round(temperature, 2))
        print("當前溫度下最好的得分：", best_cost)
        print("當前溫度下波長數量：", len(solution))
        temperature *= alpha
        temp_history.append(temperature)
        best_cost_history.append(best_cost)
        best_solution_history.append(best_solution)
    return temp_history, best_cost_history, best_solution_history


# 1.數據獲取
mat = sio.loadmat('NDFNDF_smote.mat')
data = mat['NDFNDF_smote']
x, y = data[:, :50], data[:, 50]
print('原始數據大小：', x.shape, y.shape)

# 2.樣本集劃分和預處理
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=1)

features_size = x.shape[1]
sel_feature = 5
temp_his, best_cost_his, best_solution_his = simulated_annealing(initT=100,
                                                                 minT=1,
                                                                 alpha=0.95,
                                                                 iterations=50,
                                                                                 
features=features_size,
                                                                 x_train=x_train,
                                                                 x_test=x_test,
                                                                 y_train=y_train,
                                                                 y_test=y_test)
            
          

3. 實驗結果

4. 參考文獻

謝云.? 模擬退火算法的原理及實現 . 1999. PhD Thesis.

陳華根, 吳健生, 王家林, & 陳冰. (2004).? 模擬退火算法機理研究 ?(Doctoral dissertation).