如何建立 RF（随机森林）和 PSO（粒子群优化器）的混合模型以找到产品的最佳折扣？

Question

我需要为每种产品（例如 A、B、C）找到最佳折扣，以便我可以最大限度地提高总销售额。我有每个产品的现有随机森林模型，将折扣和季节映射到销售。我如何组合这些模型并将它们提供给优化器以找到每个产品的最佳折扣？

选型理由：

1. RF：它能够在预测变量和响应（sales_uplift_norm）之间提供更好的（wrt 线性模型）关系。
2. PSO：在许多白皮书中建议（可在 researchgate/IEEE 获得），还有这里和这里的python 包的可用性。

输入数据：用于在产品级别构建模型的示例数据。数据一览如下：

我遵循的想法/步骤：

1. 为每个产品建立射频模型

    # pre-processed data
    products_pre_processed_data = {key:pre_process_data(df, key) for key, df in df_basepack_dict.items()}
    # rf models
    products_rf_model = {key:rf_fit(df) for key, df in products_pre_processed_data .items()}

• 将模型传递给优化器
  • 目标函数：最大化sales_uplift_norm（RF模型的响应变量）
  • 约束：
    • 总支出（A + B + C <= 20 的支出），支出 = total_units_sold_of_products * discount_percentage * mrp_of_products
    • 产品下限(A, B, C): [0.0, 0.0, 0.0] # 折扣百分比下限
    • 产品上限(A, B, C): [0.3, 0.4, 0.4] # 折扣百分比上限

sudo/示例代码# 因为我找不到将 product_models 传递到优化器的方法。

from pyswarm import pso
def obj(x):
    model1 = products_rf_model.get('A')
    model2 = products_rf_model.get('B')
    model3 = products_rf_model.get('C')
    return -(model1 + model2 + model3) # -ve sign as to maximize

def con(x):
    x1 = x[0]
    x2 = x[1]
    x3 = x[2]
    return np.sum(units_A*x*mrp_A + units_B*x*mrp_B + units_C* x *spend_C)-20 # spend budget

lb = [0.0, 0.0, 0.0]
ub = [0.3, 0.4, 0.4]

xopt, fopt = pso(obj, lb, ub, f_ieqcons=con)

亲爱的 SO 专家，请求您的指导（几周以来一直在努力寻找任何指导）关于如何使用带有 RF的PSO 优化器（或任何其他优化器，如果我没有遵循正确的优化器）。

添加用于模型的函数：

def pre_process_data(df,product):
    data = df.copy().reset_index()
#     print(data)
    bp = product
    print("----------product: {}----------".format(bp))
    # Pre-processing steps
    print("pre process df.shape {}".format(df.shape))
        #1. Reponse var transformation
    response = data.sales_uplift_norm # already transformed

        #2. predictor numeric var transformation 
    numeric_vars = ['discount_percentage'] # may include mrp, depth
    df_numeric = data[numeric_vars]
    df_norm = df_numeric.apply(lambda x: scale(x), axis = 0) # center and scale

        #3. char fields dummification
    #select category fields
    cat_cols = data.select_dtypes('category').columns
    #select string fields
    str_to_cat_cols = data.drop(['product'], axis = 1).select_dtypes('object').astype('category').columns
    # combine all categorical fields
    all_cat_cols = [*cat_cols,*str_to_cat_cols]
#     print(all_cat_cols)

    #convert cat to dummies
    df_dummies = pd.get_dummies(data[all_cat_cols])

        #4. combine num and char df together
    df_combined = pd.concat([df_dummies.reset_index(drop=True), df_norm.reset_index(drop=True)], axis=1)
    
    df_combined['sales_uplift_norm'] = response
    df_processed = df_combined.copy()
    print("post process df.shape {}".format(df_processed.shape))
#     print("model fields: {}".format(df_processed.columns))
    return(df_processed)


def rf_fit(df, random_state = 12):
    
    train_features = df.drop('sales_uplift_norm', axis = 1)
    train_labels = df['sales_uplift_norm']
    
    # Random Forest Regressor
    rf = RandomForestRegressor(n_estimators = 500,
                               random_state = random_state,
                               bootstrap = True,
                               oob_score=True)
    # RF model
    rf_fit = rf.fit(train_features, train_labels)

    return(rf_fit)

编辑：将数据集更新为简化版本。

Answer 1

您可以在下面找到完整的解决方案！

与您的方法的根本区别如下：

1. 由于随机森林模型将season特征作为输入，因此必须计算每个季节的最佳折扣。
2. 检查pyswarm的文档，该con函数产生的输出必须符合con(x) >= 0.0. 因此，正确的约束是正确的20 - sum(...)，而不是相反。另外，没有给出units和变量；mrp我只是假设值为 1，您可能想要更改这些值。

对原始代码的其他修改包括：

1. 预处理和管道包装器sklearn以简化预处理步骤。
2. 最佳参数存储在输出.xlsx文件中。
3. PSO 的参数maxiter已设置为5加速调试，您可能需要将其值设置为另一个值（默认 = 100）。

因此，代码是：

import pandas as pd 
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import OneHotEncoder, StandardScaler
from sklearn.compose import ColumnTransformer
from sklearn.ensemble import RandomForestRegressor 
from sklearn.base import clone

# ====================== RF TRAINING ======================
# Preprocessing
def build_sample(season, discount_percentage):
    return pd.DataFrame({
        'season': [season],
        'discount_percentage': [discount_percentage]
    })

columns_to_encode = ["season"]
columns_to_scale = ["discount_percentage"]
encoder = OneHotEncoder()
scaler = StandardScaler()
preproc = ColumnTransformer(
    transformers=[
        ("encoder", Pipeline([("OneHotEncoder", encoder)]), columns_to_encode),
        ("scaler", Pipeline([("StandardScaler", scaler)]), columns_to_scale)
    ]
)

# Model
myRFClassifier = RandomForestRegressor(
    n_estimators = 500,
    random_state = 12,
    bootstrap = True,
    oob_score = True)

pipeline_list = [
    ('preproc', preproc),
    ('clf', myRFClassifier)
]

pipe = Pipeline(pipeline_list)

# Dataset
df_tot = pd.read_excel("so_data.xlsx")
df_dict = {
    product: df_tot[df_tot['product'] == product].drop(columns=['product']) for product in pd.unique(df_tot['product'])
}

# Fit
print("Training ...")
pipe_dict = {
    product: clone(pipe) for product in df_dict.keys()
}

for product, df in df_dict.items():
    X = df.drop(columns=["sales_uplift_norm"])
    y = df["sales_uplift_norm"]
    pipe_dict[product].fit(X,y)

# ====================== OPTIMIZATION ====================== 
from pyswarm import pso
# Parameter of PSO
maxiter = 5

n_product = len(pipe_dict.keys())

# Constraints
budget = 20
units  = [1, 1, 1]
mrp    = [1, 1, 1]

lb = [0.0, 0.0, 0.0]
ub = [0.3, 0.4, 0.4]

# Must always remain >= 0
def con(x):
    s = 0
    for i in range(n_product):
        s += units[i] * mrp[i] * x[i]

    return budget - s

print("Optimization ...")

# Save optimal discounts for every product and every season
df_opti = pd.DataFrame(data=None, columns=df_tot.columns)
for season in pd.unique(df_tot['season']):

    # Objective function to minimize
    def obj(x):
        s = 0
        for i, product in enumerate(pipe_dict.keys()):
            s += pipe_dict[product].predict(build_sample(season, x[i]))
        
        return -s

    # PSO
    xopt, fopt = pso(obj, lb, ub, f_ieqcons=con, maxiter=maxiter)
    print("Season: {}\t xopt: {}".format(season, xopt))

    # Store result
    df_opti = pd.concat([
        df_opti,
        pd.DataFrame({
            'product': list(pipe_dict.keys()),
            'season': [season] * n_product,
            'discount_percentage': xopt,
            'sales_uplift_norm': [
                pipe_dict[product].predict(build_sample(season, xopt[i]))[0] for i, product in enumerate(pipe_dict.keys())
            ]
        })
    ])

# Save result
df_opti = df_opti.reset_index().drop(columns=['index'])
df_opti.to_excel("so_result.xlsx")
print("Summary")
print(df_opti)

它给 ：

Training ...
Optimization ...
Stopping search: maximum iterations reached --> 5
Season: summer   xopt: [0.1941521  0.11233673 0.36548761]
Stopping search: maximum iterations reached --> 5
Season: winter   xopt: [0.18670604 0.37829516 0.21857777]
Stopping search: maximum iterations reached --> 5
Season: monsoon  xopt: [0.14898102 0.39847885 0.18889792]
Summary
  product   season  discount_percentage  sales_uplift_norm
0       A   summer             0.194152           0.175973
1       B   summer             0.112337           0.229735
2       C   summer             0.365488           0.374510
3       A   winter             0.186706          -0.028205
4       B   winter             0.378295           0.266675
5       C   winter             0.218578           0.146012
6       A  monsoon             0.148981           0.199073
7       B  monsoon             0.398479           0.307632
8       C  monsoon             0.188898           0.210134