如何解决如何建立混合模型以找到最优的产品折扣？
我需要找到每种产品的最佳折扣（例如A，B，C），以便我能使总销售额最大化。对于每种产品，我都有现有的随机森林模型，这些模型将折扣和季节映射到销售额。如何结合这些模型并将其馈送到优化器以找到每种产品的最佳折扣？
选择型号的原因：
- RF：能够在预测变量和响应（sales_uplift_norm）之间提供更好的（不包括线性模型）关系。
- PSO：在许多白皮书中都建议使用（可在researchgate / IEEE上获得），以及在python here和here中的软件包的可用性。
输入数据：sample data用于在产品级别构建模型。数据一览如下：
想法/跟随我的步骤：
- 为每种产品构建RF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（支出A + B + C
- 产品（A，B，C）的下界：[0.0，0.0，0.0]＃折扣百分比下界
- 产品（A，B，C）的上限：[0.3，0.4，0.4]＃折扣百分比上限
sudo / sample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)
尊敬的SO专家，请就如何使用 PSO优化器（或其他优化器，如果我没有遵循正确的方法）的问题，寻求您的指导（几周以来一直在努力寻找任何指导） ）与射频。
添加用于模型的功能：
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。
解决方法
您可以在下面找到完整的解决方案！
与您的方法的基本区别如下：
- 由于随机森林模型将
season功能作为输入，因此必须为每个季节计算最佳折扣。 - 检查pyswarm的文档，
con函数产生的输出必须符合con(x) >= 0.0。因此，正确的约束是20 - sum(...)，而不是相反的约束。另外，没有给出units和mrp变量；我只是假设值为1，您可能想更改这些值。
对原始代码的其他修改包括：
-
sklearn的预处理和管道包装程序，以简化预处理步骤。 - 最佳参数存储在输出
.xlsx文件中。 - 已将PSO的
maxiter参数设置为5，以加快调试速度，您可能希望将其值设置为另一个值（默认=100）。 li>
因此，代码为：
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]
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)
它给出了：
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
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