Multiobjective difference index and priority

Answered

Florian Speicher

• June 27, 2024 11:25

Hallo,

I try to set up a multiobjective function using:

setObjectiveN ( expr, index, priority=0, weight=1, abstol=1e-6, reltol=0, name="" )

I wonder what the difference between index and priority is.

Is index a unique identifier for the "part" of the multiobjective and priority the ordering of how the objectives are try to be optimized.

Is it possible have

setObjectiveN ( x, 0, 0, weight=1, abstol=1e-6, reltol=0, name="" )

setObjectiveN ( y, 0, 1, weight=1, abstol=1e-6, reltol=0, name="" )

to get min x+y or will it be min y?

Cheers,

Florian

Related to

• Multiple Objectives

0

• 

  Matthias Miltenberger

  Gurobi Staff

  • June 27, 2024 11:55
  • Edited

  Hi Florian,

  Here's the relevant part from our documentation:

  Objectives are numbered 0 through NumObj-1. The order of the objectives is arbitrary, but you must provide a unique index for each one (specified using the index argument to setObjectiveN).

  Using the same priority will blend the objectives using the given weights.

  I hope that answers your question.

  Cheers,
  Matthias

  0
• 

  Ronald van der Velden

  Gurobi Staff

  • June 27, 2024 12:00

  In addition to the above - to answer your last question explicitly: No, that approach won't work since both parts of the objective use the same index 0. If they would use a different index (0, 1) for each expression but the same priority 0 and weight 1 then you would be optimizing x+y. If you would use different index (0, 1) and different priority (0, 1) then Gurobi would first optimize y (highest priority), then add a bound on that objective y and optimize for objective x.

  Kind regards,
  Ronald

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• 

  Florian Speicher

  • June 27, 2024 12:04

  

  

  

  Thanks for your answers. Can I also do the following.

  setObjectiveN ( x, 0, 0, weight=1, abstol=1e-6, reltol=0, name="" )

  setObjectiveN ( y, 1, 1, weight=1, abstol=1e-6, reltol=0, name="" )

  Which means first min x than min y. Can I also say only optimize objective with prio 0 for 10 seconds. Then take this as best value (add as constraint) and go to objective with prio 1....

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• 

  Matthias Miltenberger

  Gurobi Staff

  • June 27, 2024 13:21

  Please see here for objective-wise termination criteria: How do I set termination criteria in multi-objective environments? – Gurobi Help Center

  Cheers,
  Matthias

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