model.setObjectiveN()

Answered

John Chu

March 06, 2023 17:25 Edited

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I am implementing a hierarchial multi-objective functions.

Let's say there are three objective functions. f_1, f_2, and f_3 such that f = [f_1, f_2, f_3] in Python. Further note that the weight for each objective is defined as follows.

coef = [1,4,1]

Then, is the following hierarchical multi-objective function going to minimize

1*f_1 + 4*f_2 + 1*f_3 with the first priority for f_1, second priority for f_2, and third priority for f_3?

In addition, I set relative tolerance = 0.05. May I ask if it means that I only allow 5 percent for the next objective?

For example, at i = 0, I am setting the objective function for f_1, and am I only allowing 5 percent from f_2? and f_2 only allows 5 percent for f_3? If my following code does not implement the features described above, would you mind giving me any suggestion?

# Coding

for i in range(3):
    objn = f[i]
    model.setObjectiveN(expr=objn, index=i, priority=SetObjPriority[i], weight=obj_coef[i+1], 
                        abstol=0.00, reltol = 0.05, name = obj_names[i])

model.optimize()

Related to

• Python
• Multiple Objectives

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:47

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  Jaromił Najman

  • Gurobi Staff

  March 07, 2023 09:06

  Then, is the following hierarchical multi-objective function going to minimize

  1*f_1 + 4*f_2 + 1*f_3 with the first priority for f_1, second priority for f_2, and third priority for f_3?

  As long as all priorities are different, Gurobi will not blend objectives, cf. Working With Multiple Objectives.

  For example, at i = 0, I am setting the objective function for f_1, and am I only allowing 5 percent from f_2? and f_2 only allows 5 percent for f_3?

  The reltol setting allows for an overall degradation of a given objective of at most reltol % over all subsequent optimizations, not only the the next optimization. So after solving f_1, f_2 could degrade f_1 by 1% and then f_3 could degrade f_1 by another 1%.

  Best regards, 
  Jaromił

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  John Chu

  March 17, 2023 03:11

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  Thank you very much!

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