我尝试优化“Totpod”之和，约束条件是每个“Cat”只能被选择一次，但如果我改变我的代码，要么什么都得不到，要么得到所有的组件。
这是我的代码：
导入库：
```python
import numpy as np
import pandas as pd
import scipy.optimize as sc
from pulp import LpProblem, LpVariable, LpMaximize, lpSum, LpMinimize, value
prob = LpProblem("Maximize_TotPod", LpMaximize)

data={'a':['Amu',508], 'b':['Coif',508], 'c':['Amu', 253]}
df= pd.DataFrame.from_dict(data, orient='index', columns=['Cat', 'Totpod'])

cat_vars = LpVariable.dicts("Cat", df['Cat'], cat="Binary")

totpod_sum = df['Totpod'].sum()

prob += lpSum(cat_vars[cat] * df.loc[df['Cat'] == cat, 'Totpod'].sum() for cat in df['Cat'])

for cat in df['Cat']:
    prob += cat_vars[cat] <= 1

prob.solve()

selected_cats = [cat for cat in df['Cat'] if cat_vars[cat].value() == 1]
total_sum = totpod_sum + value(prob.objective)
print("Selected index:", selected_cats)
print("Max Totpod:", total_sum)

<details>
<summary>英文:</summary>
I tried to optimize the sum of &#39;Totpod&#39; under the constraint that each &#39;Cat&#39; could only be taken once but if I change my code I either got nothing or all the components.
Here is my code:
    

Cat	Fo	Pod	Pa2	Pa3	Pa4	Pa5	Pa6	Coif Amu An1 An2 Bot Ceint Arm	Totpod

    import numpy as np
    import pandas as pd
    import scipy.optimize as sc
    from pulp import LpProblem, LpVariable, LpMaximize, lpSum, LpMinimize, value
    prob = LpProblem("Maximize_TotPod", LpMaximize)
    
    data={'a':['Amu',508], 'b':['Coif',508], 'c':['Amu', 253]}
    df= pd.DataFrame.from_dict(data, orient='index', columns=['Cat', 'Totpod'])
    # Creating binary decision variables for each 'Cat' value
    cat_vars = LpVariable.dicts("Cat", df['Cat'], cat="Binary")
    # Calculating the total sum of 'Totpod' values
    totpod_sum = df['Totpod'].sum()
    # Objective function: maximize the sum of 'Totpod'
    prob += lpSum(cat_vars[cat] * df.loc[df['Cat'] == cat, 'Totpod'].sum() for cat in df['Cat'])
    # Constraint: select each 'Cat' only once
    for cat in df['Cat']:
        prob += cat_vars[cat] <= 1
    # Solving the problem
    prob.solve()
    selected_cats = [cat for cat in df['Cat'] if cat_vars[cat].value() == 1]
    total_sum = totpod_sum + value(prob.objective)
    # Printing the selected index and the max of Totpod
    print("Selected index:", selected_cats)
    print("Max Totpod':", total_sum)
It returns me ['Amu', 'Coif', 'Amu'] and 3299.0 while I want ['a', 'b'] and (508+508) 1016
Do you know how I can modify to make it works, I don't mind using another optimizer 
</details>
# 答案1
**得分**: 1
以下是您要翻译的部分：
IIUC，您可以将`selected_cats`简单生成为唯一`Cat`值的列表，以及通过按`Cat`分组，取最大`Totpod`值并对它们求和来获得最优（我假设您指的是最大）`Totpod`总和：
```python
selected_cats = df['Cat'].unique().tolist()
total_sum = df.groupby('Cat')['Totpod'].max().sum()
print("Selected index:", selected_cats)
print("Max Totpod:", total_sum)

Selected index: ['Amu', 'Coif']
Max Totpod: 1016