Pareto multi-objective optimization problem

[Matts Davids]

Hello sir,

Has anyone have worked on optimization formulations that consider Pareto multi-objective optimization problems? Would you mind the AMPL codes for such types of problems?

Sincerely yours,

Davids

[AMPL Google Group]

You can define any number of different objective functions in an AMPL model. A solver option for getting good solutions for multiple objectives is listed under "multiobj" in the AMPL-Gurobi Parameter Reference and in the CPLEX Options for AMPL. There is also a more detailed explanation of this option at https://groups.google.com/d/msg/ampl/cDKRsJFHJcQ/AhZsBmnqDQAJ; it gives examples from Gurobi but they also work for CPLEX. (I don't know of a similar option for other solvers.)

Also I am not aware of any solver that will compute Pareto optimal solutions in general. You would have to write a program to do that; I don't know of any great examples, but here are two:

• I have some old examples of computing an efficient frontier using the MATLAB and Java APIs, which I could post if you think they would be helpful.
• Also there is an example of an AMPL script that trades off two objectives -- see https://groups.google.com/g/ampl/c/eq3UADMUEaU/m/e0fxviv8GAAJ -- but it is specific to one application.

--
Robert Fourer
am...@googlegroups.com

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