multiobjective optimization

GAMS
1

Hi everyone!

I am converting a single objective problem to multiobjective problem. I have two conflicting objectives. I am writing them seperately and trying to solve them as model 1 and model 2. Gams gives me two different solution obviously for two different objectives but my aim is finding a compromise solution for these two conflicting objectives. How can i make this happen?

Thanks a lot.
Best.

2

There are two classical ways: weighted combined objective and hierarchical objective. You can do this directly in GAMS or use a solver that supports MOO, e.g. https://www.gams.com/latest/docs/S_CPLEX.html#CPLEX_MULTIPLE_OBJECTIVES. If you get ambitious and want to spec out the Parteo frontier there are some advanced examples in the GAMS model library, e.g. https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_epscm.html and obviously the famous Markowitz model trading off risk and return in a portfolio: https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_meanvar.html.

-Michael

3

you can also use this code
https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_ParetoOptimalFront.html

4

Thank you for your help.

I tried the pareto optimal front and again it gave me two different solutions for my objective functions. Does it must be like that?

5

That’s the meaning of the pareto optimal front solutions
you will have more than one solution

6

Yes but these two solutions are not suitable for each other. I want a comprimise solution to ensure both objectives in a suitable point. Sorry I am new on this subject so I need more detail.