how to write this objective function in python

Answered

Bing SONG

• November 25, 2023 18:54

Decision variables is p_{ij} and y{ij}.p_{ij} is a continuous non-negative variable and y{ij} is a variable that can only take 0 or 1.

Related to

• General Constraints
• Python

0

• 

  Simranjit Kaur

  Gurobi Staff

  • November 27, 2023 00:25

  Hi,

  You can model your objective function with the help of adding general constraints that model the exponential function (for example, with the method addGenConstrExp if using the Python API), and using the trick in the article How do I divide by a variable in Gurobi?. Specifically, you can do something like below, where aux, exp, z, and q are helper variables:

  m.addConstrs( aux[i] == gp.quicksum( (a[i] + p[i,j] - b[i]*w[i,j]) * y[i,j] for j in range(N) ) for i in range(M))
  
  for i in range(M):
    m.addGenConstrExp(exp[i], aux[i])
    m.addConstr( z[i] * (1+exp[i]) == 1)
    m.addConstr( q[i] == exp[i] * z[i])
  
  obj = gp.quicksum( p[i,j] * q[i] for i in range(M) for j in range(N))
  m.setObjective(obj)

  Best regards,
  Simran

  0

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