我需要解決類似于背包問題的優化問題。我在這篇文章中詳細介紹了優化問題：knapsack optimization with dynamic variables我實際上需要使用python而不是OPL，所以我安裝了docplex和clpex包以便使用cplex優化框架。

所以這里是我想用docplex轉換為python的OPL代碼

{string} categories=...;

{string} groups[categories]=...;

{string} allGroups=union (c in categories) groups[c];

{string} products[allGroups]=...;

{string} allProducts=union (g in allGroups) products[g];

float prices[allProducts]=...;

int Uc[categories]=...;

float Ug[allGroups]=...;

float budget=...;

dvar boolean z[allProducts]; // product out or in ?

dexpr int xg[g in allGroups]=(1<=sum(p in products[g]) z[p]);

dexpr int xc[c in categories]=(1<=sum(g in groups[c]) xg[g]);

maximize

sum(c in categories) Uc[c]*xc[c]+

sum(c in categories) sum(g in groups[c]) Uc[c]*Ug[g]*xg[g];

subject to

{

ctBudget:

sum(p in allProducts) z[p]*prices[p]<=budget;

}

{string} solution={p | p in allProducts : z[p]==1};

execute

{

writeln("solution = ",solution);

}

這是我的第一次代碼嘗試：

from collections import namedtuple

from docplex.mp.model import Model

# --------------------------------------------------------------------

# Initialize the problem data

# --------------------------------------------------------------------

Categories_groups = {"Carbs": ["Meat","Milk"],"Protein":["Pasta","Bread"], "Fat": ["Oil","Butter"]}

Groups_Products = {"1":["Product11","Product12"], "2": ["Product21","Product22","Product23"], "3":["Product31","Product32"],"4":["Product41","Product42"], "5":["Product51"],"6":["Product61","Product62"]}

Products_Prices ={"Product11":1,"Product12":4,"Product21":1,"Product22":3,"Product23":2,"Product31":4,"Product32":2,"Product41":1,"Product42":3,"Product51":1,"Product61":2,"Product62":1}

Uc=[1,1,0];

Ug=[0.8,0.2,0.1,1,0.01,0.6];

budget=3;

def build_diet_model(**kwargs):

allcategories = Categories_groups.keys()

allgroups = Groups_Products.keys()

prices=Products_Prices.values()

# Model

mdl = Model(name='summary', **kwargs)

for g, products in Groups_Products.items():

xg = mdl.sum(z[p] for p in products)# this line is not correct as I dont know how to add the condition like in the OPL code, and I was unable to model the variable z and add it as decision variable to the model.

mdl.add_constraint(mdl.sum(Products_Prices[p] * z[p] for p in Products_Prices.keys() <= budget)

mdl.maximize(mdl.sum(Uc[c] * xc[c] for c in Categories_groups.keys()) +

model.sum(xg[g] * Uc[c] * Ug[g] for c, groups in Categories_groups.items() for g in groups))

mdl.solve()

if __name__ == '__main__':

build_diet_model()

我實際上不知道如何在OPL代碼中正確建模變量xg，xc和z？

有關如何正確建模的任何想法。先感謝您

編輯：這是@HuguesJuille建議后的編輯，我已經清理了代碼，現在它正常工作。

from docplex.mp.model import Model

from docplex.util.environment import get_environment

# ----------------------------------------------------------------------------

# Initialize the problem data

# ----------------------------------------------------------------------------

Categories_groups = {"Carbs": ["Meat","Milk"],"Protein":["Pasta","Bread"], "Fat": ["Oil","Butter"]}

Groups_Products = {"Meat":["Product11","Product12"], "Milk": ["Product21","Product22","Product23"], "Pasta": ["Product31","Product32"],

"Bread":["Product41","Product42"], "Oil":["Product51"],"Butter":["Product61","Product62"]}

Products_Prices ={"Product11":1,"Product12":4, "Product21":1,"Product22":3,"Product23":2,"Product31":4,"Product32":2,

"Product41":1,"Product42":3, "Product51": 1,"Product61":2,"Product62":1}

Uc={"Carbs": 1,"Protein":1, "Fat": 0 }

Ug = {"Meat": 0.8, "Milk": 0.2, "Pasta": 0.1, "Bread": 1, "Oil": 0.01, "Butter": 0.6}

budget=3;

def build_userbasket_model(**kwargs):

allcategories = Categories_groups.keys()

allgroups = Groups_Products.keys()

allproducts = Products_Prices.keys()

# Model

mdl = Model(name='userbasket', **kwargs)

z = mdl.binary_var_dict(allproducts, name='z([%s])')

xg = {g: 1 <= mdl.sum(z[p] for p in Groups_Products[g]) for g in allgroups}

xc = {c: 1 <= mdl.sum(xg[g] for g in Categories_groups[c]) for c in allcategories}

mdl.add_constraint(mdl.sum(Products_Prices[p] * z[p] for p in allproducts) <= budget)

mdl.maximize(mdl.sum(Uc[c] * xc[c] for c in allcategories) + mdl.sum(

xg[g] * Uc[c] * Ug[g] for c in allcategories for g in Categories_groups[c]))

mdl.solve()

return mdl

if __name__ == '__main__':

"""DOcplexcloud credentials can be specified with url and api_key in the code block below.

Alternatively, Context.make_default_context() searches the PYTHONPATH for

the following files:

* cplex_config.py

* cplex_config_.py

* docloud_config.py (must only contain context.solver.docloud configuration)

These files contain the credentials and other properties. For example,

something similar to::

context.solver.docloud.url = "https://docloud.service.com/job_manager/rest/v1"

context.solver.docloud.key = "example api_key"

"""

url = None

key = None

mdl = build_userbasket_model()

# will use IBM Decision Optimization on cloud.

if not mdl.solve(url=url, key=key):

print("*** Problem has no solution")

else:

mdl.float_precision = 3

print("* model solved as function:")

mdl.print_solution()

# Save the CPLEX solution as "solution.json" program output

with get_environment().get_output_stream("solution.json") as fp:

mdl.solution.export(fp, "json")

我希望這會幫助像我這樣的初學者遇到同樣的問題。

總結

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