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1. How to Use Feasopt via docplex Python API #

Feasopt is IBM CPLEX's tool for finding feasible solutions when your model is infeasible, by relaxing constraints (with configurable weights to prioritize which constraints stay intact). Here's a step-by-step guide with practical code:

First, ensure you have docplex installed (and access to CPLEX, since Feasopt is a CPLEX-exclusive feature). Then:

• Import required modules:

  from docplex.mp.model import Model
  

• Build your model (even if it's known to be infeasible):
  Let's use a simple conflicting MIP example to demonstrate:

  mdl = Model(name="infeasible_mip_demo")
  x = mdl.integer_var(name="x")
  y = mdl.integer_var(name="y")
  
  # Add conflicting constraints
  mdl.add_constraint(x + y >= 10, "hard_limit_upper")
  mdl.add_constraint(x + y <= 5, "hard_limit_lower")
  mdl.add_constraint(x >= 0, "non_neg_x")
  mdl.add_constraint(y >= 0, "non_neg_y")
  

• Configure Feasopt and solve:
  You can either use the direct feasopt() method, or fine-tune relaxation weights to prioritize keeping certain constraints intact. Here are both approaches:

  # Option 1: Quick Feasopt run (defaults to minimal relaxation)
  feas_solution = mdl.feasopt()
  
  # Option 2: Customize relaxation weights and solver settings
  # Assign higher weights to constraints you don't want to relax
  mdl.add_feasopt_weight("hard_limit_upper", 10.0)  # Prioritize keeping this constraint tight
  mdl.add_feasopt_weight("hard_limit_lower", 1.0)   # Allow relaxing this more easily
  
  # Set Feasopt mode to minimize relaxation impact
  mdl.parameters.feasopt.mode = 1
  mdl.parameters.feasopt.tolerance = 1e-6
  
  # Solve with custom settings
  custom_solution = mdl.solve()
  

• Inspect the results:
  Once solved, you can check which constraints were relaxed and the feasible values:

  if custom_solution:
      print("Feasible solution found!")
      print(f"x = {custom_solution[x]}, y = {custom_solution[y]}")
      # Check relaxed constraints
      for constraint in mdl.iter_constraints():
          slack_val = custom_solution.get_slack(constraint)
          if abs(slack_val) > 1e-6:
              print(f"Constraint {constraint.name} relaxed by {slack_val:.2f}")
  

2. Can Feasopt Fix an Infeasible Mixed Integer Programming (MIP) Model? #

Absolutely! Feasopt works natively with MIP models. When your MIP returns an infeasible status, Feasopt will:

• Pinpoint conflicting constraints or variable bounds
• Allow controlled relaxation of these elements (softening inequalities or adjusting bounds)
• Minimize the weighted sum of relaxations, so the resulting solution deviates as little as possible from your original model's intent

Crucially, Feasopt respects integer variable requirements—you don't need to modify your integer variable definitions. The solution will still return integer values for your variables, unless you explicitly choose to relax variable bounds (which you can control with weights).

Using the example above, Feasopt would relax either hard_limit_upper or hard_limit_lower (based on your weight settings) to make the model feasible, and output integer values for x and y that satisfy the relaxed constraints.

内容的提问来源于stack exchange，提问作者DasPlaies