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### Is it possible to solve bi-objective model directly in GAMS?

Posted: **Mon Sep 02, 2019 5:01 pm**

by **richard**

Hi all,

Is there any command that can solve multi objective model directly? I mean, without using weighted sum or epsilon constraint methods, can we solve multi objective model in gams?

Many thanks!

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Tue Sep 03, 2019 2:50 pm**

by **dirkse**

Richard,

Your post raises an interesting question. What exactly is a bi-objective model? The name seems self-explanatory and self-contradictory at the same time (e.g. "We need to both minimize costs and maximize production.")

To be complete a definition would include some characterization of what it means to solve such a model.

-Steve

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Tue Sep 03, 2019 6:42 pm**

by **richard**

Dear Steve,

Thanks very much for your answer.

I have a bi-objective model for nursing home location and allocation problem. I heard cplex have a feature that can solve multi-objective model directly, and GAMS supported this feature too.

Is this true?

I searched a lot, but I didn't find anything.

Many thanks!

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Wed Sep 04, 2019 4:03 pm**

by **dirkse**

Richard,

Your last post gave lots of specifics related to the algebra of your model, but my question was more basic: what does it mean to say that a point is a solution?

For example, a point xbar solves a uni-objective model min z = f(x) if xbar is feasible and f(xbar) <= f(x) for all feasible x.

-Steve

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Wed Sep 04, 2019 4:21 pm**

by **richard**

Dear Steve,

If you want the truth, I'm just looking for a good solution And nothing special in my mind.

Thanks so much!

Richard

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Thu Sep 05, 2019 4:14 pm**

by **dirkse**

Richard,

If we exclude the EMP model type from the discussion (that's a whole other story), then GAMS does not have a multi-objective model type.

The model you describe seems to be a good representative example. You have two objectives - distance traveled and construction costs - and you'd like a solution that does a good job of balancing the two. This is quite reasonable in practice, but mathematically it is not very complete. With GAMS, it's easy to build the basic model and then write some GAMS code to:

1. Optimize a weighted sum of the two objectives. By varying the weights you can generate different solutions to get a feel for the possibilities.

2. Constrain one objective and optimize the other.

3. Construct a sort of "efficient frontier" - a set of non-dominated solutions that show the best you can do as you shift the emphasis from minimizing construction cost to minimizing distance traveled.

-Steve

### Re: Is it possible to solve bi-objective model directly in GAMS?

Posted: **Fri Sep 06, 2019 9:38 am**

by **richard**

Steve Thanks very much for your answer!