Ilp - count number of times variables received a value-CodePudding

In an ILP, is it possible to have a variable whose value will be the number of variables with value N?

N is a bounded integer, with lower bound 1.

Thank you

CodePudding user response：

This achieves the goal. It is written in pyomo but should be fairly easy to translate to other frameworks.

Code:

# magic number counter

import pyomo.environ as pyo

M = 100
magic_number=7

m = pyo.ConcreteModel()

m.I = pyo.Set(initialize=[1,2,3,4])

m.x    = pyo.Var(m.I, domain=pyo.NonNegativeIntegers, bounds=(1, M))
m.magic = pyo.Var(m.I, domain=pyo.Binary)

# obj:  max sum of x, plus some sugar for magic numbers's

m.obj = pyo.Objective(expr=sum(m.x[i]   0.1*m.magic[i] for i in m.I), sense=pyo.maximize)

# constraints

m.sum_limit = pyo.Constraint(expr=pyo.sum_product(m.x) <= 19)

@m.Constraint(m.I)
def linking_1(m, i):
    return m.x[i] <= magic_number   (1 - m.magic[i]) * M

@m.Constraint(m.I)
def linking_2(m, i):
    return m.x[i] >= magic_number * m.magic[i]

solver = pyo.SolverFactory('glpk')
soln = solver.solve(m)
print(soln)
m.display()

print(f"\nmagic numbers {magic_number}'s produced: {pyo.value(pyo.sum_product(m.magic))}")

Output:

Problem: 
- Name: unknown
  Lower bound: 19.2
  Upper bound: 19.2
  Number of objectives: 1
  Number of constraints: 10
  Number of variables: 9
  Number of nonzeros: 21
  Sense: maximize
Solver: 
- Status: ok
  Termination condition: optimal
  Statistics: 
    Branch and bound: 
      Number of bounded subproblems: 5
      Number of created subproblems: 5
  Error rc: 0
  Time: 0.005478858947753906
Solution: 
- number of solutions: 0
  number of solutions displayed: 0

Model unknown

  Variables:
    x : Size=4, Index=I
        Key : Lower : Value : Upper : Fixed : Stale : Domain
          1 :     1 :   7.0 :   100 : False : False : NonNegativeIntegers
          2 :     1 :   4.0 :   100 : False : False : NonNegativeIntegers
          3 :     1 :   7.0 :   100 : False : False : NonNegativeIntegers
          4 :     1 :   1.0 :   100 : False : False : NonNegativeIntegers
    magic : Size=4, Index=I
        Key : Lower : Value : Upper : Fixed : Stale : Domain
          1 :     0 :   1.0 :     1 : False : False : Binary
          2 :     0 :   0.0 :     1 : False : False : Binary
          3 :     0 :   1.0 :     1 : False : False : Binary
          4 :     0 :   0.0 :     1 : False : False : Binary

  Objectives:
    obj : Size=1, Index=None, Active=True
        Key  : Active : Value
        None :   True : 19.200000000000003

  Constraints:
    sum_limit : Size=1
        Key  : Lower : Body : Upper
        None :  None : 19.0 :  19.0
    linking_1 : Size=4
        Key : Lower : Body   : Upper
          1 :  None :    0.0 :   0.0
          2 :  None : -103.0 :   0.0
          3 :  None :    0.0 :   0.0
          4 :  None : -106.0 :   0.0
    linking_2 : Size=4
        Key : Lower : Body : Upper
          1 :  None :  0.0 :   0.0
          2 :  None : -4.0 :   0.0
          3 :  None :  0.0 :   0.0
          4 :  None : -1.0 :   0.0

magic numbers 7's produced: 2.0