## Minimise value of variables in MINLP solution

Problems with syntax of GAMS
cargarsan5
User
Posts: 2
Joined: 2 weeks ago

### Minimise value of variables in MINLP solution

Hello everybody,

I have a MINLP problem (BONMIN solver). This problem have some variables (P_size(j), P(j,t)...)

This is the objective function

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``````eqOpt1.. total_cost =e=  sum(j,w_C(j)*SBASE*P_size(j));
``````
and this equation as constraint (and others of electrical problem)

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``````eq10(j,t).. P_size(j) =g= P(j,t);
``````
So in my solution P_size(j) is calculate good, but P(j,t) not choose the minimum value (that is I want), GAMS provide a solution close to the maximum value P_size(j)~P(j,t). How can i do it? I am always interested in having the smallest value of P

Thank you so much

abhosekar
Moderator
Posts: 176
Joined: 8 months ago

### Re: Minimise value of variables in MINLP solution

You are minimizing your objective function which contains P_size and that is what you tell the solver to minimize.
To satisfy the constraint, P_size ~ P is enough (it can very well give you the maximum P that satisfies the constraint. It has no incentive to do better). You are not telling the solver anywhere to minimize P.

I don't know anything about your problem but you have to think about the structure of your problem.
Assuming P is a positive variable, is your problem feasible if P is 0? If yes, why is it not the minimum you are interested in? (this might give you hints to add additional constraints). The constraint you show (P_size =g= P) will be feasible for all values of P less than the value reported in the solution. So which constraint is violated if you really minimize P?

How does minimizing P affect your cost (i.e., the objective?) If it doesn't you might be talking about multiobjective optimization where minimizing P is your second objective. In this case, you have to think if your objectives are conflicting (i.e., does minimizing P increase the cost?). If yes, you have to look up literature on multiobjective optimization. If not, you can simply minimize cost, fix variables at the solution and do another solve where you minimize P.

Hope this helps.

- Atharv