How to apply termination conditions to each objective function in multi-objective model

Hi,

If the time limit is hit for an objective, do you want to stop the optimization altogether, or continue the solve with the next objective?

Regards,

Chris

Dear Chris,

I want to continue to solve.

Regards,

Kiseop

We don't have a good way to do this at the moment. Something you can try is to implement your own soft time limit in a callback. If there is a callback which is frequently called while solving your problem, you can use it to check whether your time limit has been hit, and if so, set mipabsstop to a large value to make the Optimizer accept the current solution. Then reset mipabsstop at the start of the next objective (in the beforeobjective callback).

Unfortunately there is not a convenient callback in which to check time limits. I would suggest trying the cutround callback, added in Xpress 9.6, which is called at every opportunity for cut separation during the solve, which means once every round of cuts added at the root node, and at least once per node solve in the branch and bound tree. This might provide enough resolution to implement your time limits.

Below is an example showing roughly how to do this. In a future release we plan to add proper support for this use case.

Regards,

Chris

import xpress as xp
 
 
time_limits = [
  10, 20, 30, 40, 50   # etc.
]
 
 
def cutround(cb_prob, data, ifxpress):
  """Called at every opportunity for cut separation during the solve,
  which means once every round of cuts added at the root node, and at
  least once per node solve in the branch and bound tree."""
  # Check the time limit for this objective
  global time_limits
  current_obj_index = cb_prob.attributes.solvedobjs
  time_limit = time_limits[current_obj_index]
  # The time attribute is reset to zero at the start of every objective
  solve_time = cb_prob.attributes.time
  if (
    (solve_time > time_limit) and
    # Only move on to the next objective if we found a solution (optional)
    (cb_prob.attributes.mipsols > 0)
  ):
    # Accept the current solution
    print(f'Objective {current_obj_index + 1} hit time limit after {solve_time} seconds')
    cb_prob.controls.mipabsstop = xp.infinity
 
 
def beforeobjective(cb_prob, data):
  """Called before every objective is solved"""
  # Reset stopping conditions
  cb_prob.controls.mipabsstop = 0
 
 
model = xp.problem()
 
# Define problem here...
 
model.addcbcutround(cutround)
model.addcbbeforeobjective(beforeobjective)
 
model.optimize()

Dear Chris,

I tried implementing it based on the code you provided, and it seems to be working fine for now.

Thank you for your help.

In future releases, it would be nice to have a feature that allows you to set different termination conditions for each objective in a multi-objective model.

In Gurobi, this feature can be easily applied as follows.

self.model.setObjectiveN(stock_out_min_urgent,   0, 15, 1.0, 0.0, 0.0, ‘StockOutMinUrgent’)

self.model.setObjectiveN(stock_out_min_OEM,     1, 14, 1.0, 0.0, 0.0, ‘StockOutMinOEM’)

env0 = self.model.getMultiobjEnv(0)

env1 = self.model.getMultiobjEnv(1)

env0.setParam(‘TimeLimit’, 30)

env0.setParam(‘MIPGap’, 0.05)

env1.setParam(‘TimeLimit’, 30)

Thank you.

Best regards,

Kiseop