How to model constraints in optimization problems using docplex (python)?

Question

I need to solve an optimization problem that is similar to the knapsack problem. I have detailed the optimization problem in this post: knapsack optimization with dynamic variables I actually need to tu use python instead of OPL, so I have installed the docplex and clpex packages in order to use the cplex optimization framework.

So here is the OPL code that I want to convert to python using docplex

{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);
}

Here is my first code attempt:

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()

I actually don't know how to model correctly the variables xg, xc and z like in the OPL code?

Any ideas on how to model them correctly. Thank you in advance

EDIT: Here is the edit after @HuguesJuille suggestion, I have cleaned the code and it works correctly now.

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")

I hope that this will help a beginner like me having the same problem.

Hugues Juille · Accepted Answer · 2018-09-07 07:05:25Z

2

If I understood correctly your data model (I'm not sure you data is consistent in your example (Categories_groups and Groups_Products don't have the same collections of values for 'groups').), the definition of your decision variables and expressions would look like this:

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}

Here, the 'z' decision variable is defined as a dictionary. It can then be indexed easily.

One can also find documentation about writing docplex models here: https://rawgit.com/IBMDecisionOptimization/docplex-doc/master/docs/mp/creating_model.html

Note that using pandas may be more efficient for defining complex slicing if you need to build models handling large datasets.

answered Sep 7, 2018 at 7:05

Hugues Juille

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1 Comment

sel Over a year ago

Thank you very much for your answer and valuable pieces of advice. I have updated my question to add the new variables and now my code works correctly. I only have this warning "Warning: No object with index: 0" and the same warning until index 8. Do you have an idea why am having this problem? I have googled this but couldn't find any answer. Thank you in advance. Regards.

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