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How to create a multi-objective model with objective priority

I'm trying to solve a multi-objective problem in which I have to minimize two different objectives but with one taking priority over the other one.

To solve the problem, and hence the question, I tried to use weighted sum of both objective functions. The problem here is that that approach finds the minimum value between the two problems which I don't want. I want to solve one objective and then, maintaning that specific value, I want to solve the other problem.

Solution

  • Version 12.9 of CPLEX has the ability to do exactly that: solve one objective, fix its value, and move to the next objective. Here's an example LP:

    Maximize multi-objectives
first: abstol=2
   x1
second: priority=-1
   x2
Subject to
   x1 + x2 = 10
General
   x1 x2
End

    This feature is described in the release notes, as well as in these slides.