Nested quicksum

Answered

DR

February 17, 2023 12:49

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Dear community,

 

I am struggling with the quicksum function while trying to fomulate the following formula in python:

 

How do I write this by using quicksum()? I tried it that way:

import gurobipy as gp
gp.quicksum( gp.quicksum( gp.quicksum( a[j,k] * b[i,j] for k in set_K ) + gp.quicksum( c[i,j,k] * d[i,j] for k in set_K ) for j in set_J ) for i in set_I )

 

Is that correct? Thanks for your help!

Related to

• Python

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  Riley Clement

  • Gurobi Staff

  February 18, 2023 01:21 Edited

  Hi DR,

  gurobipy.quicksum takes exactly one argument, and that argument should be an iterable such as a list, tuple or generator expression.  You can use a generator expression like so:

  gp.quicksum(a[j,k]*b[i,j] + c[i,j,k]*d[i,j] for i in set_I for j in set_J for k in set_K)

  or alternatively using itertools

  import itertools
  gp.quicksum(a[j,k]*b[i,j] + c[i,j,k]*d[i,j] for i,j,k in itertools.product(set_I, set_J, set_K))

  It may help your understanding to write these generator expressions as list comprehensions so you can understand what is being given as an argument to gp.quicksum.

  - Riley

   

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  DR

  February 20, 2023 10:58

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  Thanks, Riley! Is it also possible to write such expressions with the groupby function from the gurobipy_pandas package?

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  Riley Clement

  • Gurobi Staff

  February 20, 2023 22:49

  Hi DR,

  You should be able to use gurobipy-pandas here.  Note that with the exception of b and d, the variables have different indices and would be associated with different dataframes.  As an example consider the following code

  import pandas as pd
  import gurobipy as gp
  from gurobipy import GRB
  import gurobipy_pandas as gppd
  import itertools
  
  a_df = pd.DataFrame(
      index = pd.MultiIndex.from_tuples(itertools.product(range(3), range(4)), names=["j", "k"])
  )
  b_df = pd.DataFrame(
      index = pd.MultiIndex.from_tuples(itertools.product(range(2), range(3)), names=["i", "j"])
  )
  model = gp.Model()
  model.ModelSense = GRB.MAXIMIZE
  a = gppd.add_vars(model, a_df, vtype=GRB.BINARY, name="a")
  b = gppd.add_vars(model, b_df, vtype=GRB.BINARY, name="b")
  model.update()

   

  The following sum (in the style of your original model):

  gp.quicksum(a[j,k]*b[i,j] for i,j,k in itertools.product(range(2), range(3), range(4)))

  is equivalent to

  (a*b).sum()

  using gurobipy-pandas.

  The groupby is only needed if creating multiple constraints of the same form at the same time, which is not the case for your quicksum expression. 

  - Riley

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