如何使用docplex (python)对优化问题中的约束进行建模？

Question

我需要解决一个类似背包问题的优化问题。本文详细介绍了优化问题：knapsack optimization with dynamic variables实际上需要使用python而不是OPL，因此我已经安装了docplex和clpex包，以便使用cplex优化框架。

下面是我想使用docplex转换为python的OPL代码

{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);
}

下面是我的第一次代码尝试：

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()

实际上，我不知道如何正确建模像OPL代码中的变量xg、xc和z？

任何关于如何正确建模的想法。提前谢谢你

编辑：这里是@HuguesJuille建议之后的编辑，我已经清理了代码，它现在工作正常。

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_<hostname>.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")

我希望这能帮助像我这样的初学者有同样的问题。

Answer 1

如果我正确理解了您的数据模型(我不确定您的示例中的数据是否一致(Categories_groups和Groups_Products没有相同的“组”值集合))，那么您的决策变量和表达式的定义将如下所示：

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}

在这里，“z”决策变量被定义为字典。然后，可以很容易地将其编入索引。

您还可以在这里找到关于编写docplex模型的文档：model.html

请注意，如果需要构建处理大型数据集的模型，那么使用熊猫可以更有效地定义复杂的切片。