something problems in Python code

Answered

汉涛 田

• March 03, 2024 09:10

How can I express this problem in the language of gurobi 11 (python code), my own code always gives errors： variable x when x>=0，objective=2*x whenx<0，objective=-3*|x| -10

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  Gurobot (AI-generated response)

  Gurobi Staff

  • March 03, 2024 19:41

  To model an optimization problem in Gurobi where the objective function changes based on the value of a variable, you can use a piecewise-linear objective function or introduce auxiliary variables and constraints to handle the different cases. For the problem you've described, you need to handle two cases based on the value of x:

  1. When x >= 0, the objective is 2 * x.
  2. When x < 0, the objective is -3 * abs(x) - 10.

  Here's how you can express this in Gurobi using Python:

  from gurobi import *
  
  # Create a new model
  m = Model("piecewise-linear")
  
  # Create variable
  x = m.addVar(lb=-GRB.INFINITY, name="x")
  
  # Auxiliary variables
  x_pos = m.addVar(name="x_pos")  # For positive part of x
  x_neg = m.addVar(name="x_neg")  # For negative part of x
  
  # Objective function
  m.setObjective(2 * x_pos - 3 * x_neg - 10, GRB.MAXIMIZE)
  
  # Add constraints
  m.addConstr(x == x_pos - x_neg, "x_split")  # Split x into positive and negative parts
  m.addConstr(x_pos >= 0, "x_pos_nonneg")
  m.addConstr(x_neg >= 0, "x_neg_nonneg")
  
  # Optimize model
  m.optimize()
  
  # Print result
  if m.status == GRB.OPTIMAL:
      print('Optimal value:', m.objVal)
      print('x:', x.X)
  else:
      print('No optimal solution found.')

  In this code:

  • x is your variable that can take any real value.
  • x_pos and x_neg are auxiliary variables representing the positive and negative parts of x, respectively.
  • The constraint x == x_pos - x_neg splits x into its positive and negative components.
  • The objective function is set to maximize 2 * x_pos - 3 * x_neg - 10.
  • Finally, the model is solved, and the optimal value of the objective function along with the value of x is printed.

  Please replace GRB.MAXIMIZE with GRB.MINIMIZE if you intend to minimize the objective function instead.

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