Creating multidimensional decision variables (Python)

[Hendrik B]

Hi,

I am implementing a version of the bin packing problem in ortools and I have a problem with initializing a two dimensional decision variable. When running my code, there is no error for this variable, but I believe it has something to do with it:

from __future__ import print_function
import sys
from ortools.linear_solver import pywraplp

def main(sol='hand'):

  solver = pywraplp.Solver('LinearExample',
                           pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

  #
  # data
  #
  nb_items = 12
  nb_resources = 7
  items = list(range(nb_items))
  resources = list(range(nb_resources))

  capacity = [150, 150, 150, 150, 150, 150, 150]
  value = [96, 76, 56, 11, 86, 10, 66, 86, 83, 12, 9, 81]

  
  ### variables ###
  # Assign variable:
  assign={}
  for r in resources:
      assign = [solver.IntVar(0, 1, 'Assign[%r][%d]' % (r, j)) for j in items]
  
  # objective: minimize number of techs:
  z = solver.Sum((value[i] * assign[r][i]) for i in items for r in resources)
 
  ### constraints ###
  # Assign:
  for j in value:
      solver.Add(solver.Sum(assign[r][j] == 1 for r in resources))

 
  # Bin capacity:
  for r in resources:
      solver.Add(solver.Sum(value[j] * assign[r][j] for j in value) <= capacity[r])
  
  ## Objective:
  objective = solver.Maximize(z)

  #
  # solution and search
  #
  solver.Solve()

  print()
  print('z: ', int(solver.Objective().Value()))

  print()
  print('walltime  :', solver.WallTime(), 'ms')
  if sol == 'CBC':
    print('iterations:', solver.Iterations())

if __name__ == '__main__':

  sol = 'GLPK'
  if len(sys.argv) > 1:
    sol = sys.argv[1]
    if sol != 'GLPK' and sol != 'CBC':
      print('Solver must be either GLPK or CBC')
      sys.exit(1)

  main(sol)

Running the code gives me the following error message:

    z = solver.Sum((value[i] * assign[r][i]) for i in items for r in ressources)

TypeError: 'Variable' object does not support indexing

I assume that the variable 'assign' is not created correctly. Does anybody has a suggestion on how to fix this issue? Thank you in advance.

[Laurent Perron]

 assign = [solver.IntVar(0, 1, 'Assign[%r][%d]' % (r, j)) for j in items]

'assign' is a single dimension array.

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[Hendrik B]

Thank you Laurent, I was trying a couple of different things and must have missed that part. This is the implementation that works (including two constraints that had a wrong index):

  assign={}
  for r in resources:

      assign[r] = [solver.IntVar(0, 1, 'Assign[%r][%d]' % (r, j)) for j in items]

 
  # objective: minimize number of techs:
  z = solver.Sum((value[i] * assign[r][i]) for i in items for r in resources)

  ### constraints ###
  # Assign:

  for j in items:
      solver.Add(solver.Sum(assign[r][j] for r in resources)  == 1)

  for r in resources:
      solver.Add(solver.Sum(value[j] * assign[r][j] for j in items) <= capacity[r])

[Hendrik B]

How would I convert this into a 3D variable? If I understand correctly, for the 2D version, I created an empty list and appended a list inside the resources for-loop:

 

  assign = {}
  for r in resources:
      assign[r] = [solver.BoolVar('Assign[%r][%d]' % (r, j)) for j in items]

 Now, for the 3D version, what kind of list do I create initially and do I have to append an empty list in-between the for-loops? I tried the following two version, which do not work:

Version 1:

  #3D Variable assign (attempt 1):
  assign = {}
  for r in resources:
      for i in items:
          assign[r][i] = [solver.IntVar(0, 1, 'Assign[%r][%i][%d]' % (r, i, j)) for j in items]

Version 2:

  #3D Variable assign (attempt 1):
  assign = defaultdict(list)
  for r in resources:
      for i in items:
          assign[r][i].append(solver.IntVar(0, 1, 'Assign[%r][%i][%d]' % (r, i, j)) for j in items)

 

[Laurent Perron]

assign[(i, j)] = ...

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

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