Conditions for mpvars in constraints, directly or indirectly

[p_sopa]

Hello,

I have the following problem

declarations
PathCost: array(100) of real
PathLoad: array(100) of mpvar
.......
......
end-declarations

.......constraints etc.......

objective is TotalCost = sum(l in 1..100) PathCost(l) * PathLoad(l)

In reality the PathCost for each path depends on its load. The higher
the load the smaller the cost per unit load.
How can I make the PathCost change according to the PathLoad which is
an mpvar? Seems like a conversion to a non linear problem.

Changing to
TotalCost = sum(l in 1..100) (PathCost(l) / (50-PathLoad(l) ) ) *
PathLoad(l)
gives problem infeasible

Maybe
TotalCost = sum(l in 1..100) ( PathCost(l) / AdjustArray(PathLoad
(l)) ) * PathLoad(l)
I could not find a way to do it

Maybe adding some code like that
if ( PathLoad(l) >=20 ) PathCost(l) = PathCost(l)*0.2
I could not find a way to do that either

Any other way?

Thanks..

[Christian Bermúdez]

I hope this can give you a hint to solve your problem. It´s still a non-linear problem, I think (I'm "brainstorming" :p)... I added a binary variable:

 

new declarations

x: array(100) of mpvar

 

new lines of code

forall(i in 1..100) x(i) is_binary

 

new restrictions

PathLoad(l) - x(l)  * 10000000 <= 20

"new" objective 
TotalCost = sum(l in 1..100) PathCost(l) * PathLoad(l) * (1 - x(l)) * 0.2

 

Did you check the reference problems in the Mosel documentation? Maybe they have solved that already.

 

2008/12/9 p_sopa <peter...@yahoo.com>

[Christian Bermúdez]

Add this to my original idea and see if it works. You owe me a beer if it does:

 

new declarations

PathLoad_A: array(100) of mpvar

 

new restrictions

PathLoad_A(l) >= PathLoad(l) - (1 - x(l))  * 10000000

PathLoad_A(l) >= 0

 

"new" objective
TotalCost = sum(l in 1..100) PathCost(l) * PathLoad_A(l) * 0.2

The idea here is to add more "copy" variables to help with your cost adjustments, and sum those in the objective function. Use the original load variable for the main restrictions of your problem.

 

2008/12/9 Christian Bermúdez <as.coraz...@gmail.com>

[p_sopa]

Hi, OK I have got the beer.. So I adjust the pathload instead of the
pathcost? But how do I set X(l) the binary variable. I need to say
that for certain conditions X(l) is 1 otherwise is 0.

Peter

[Calidosaúrico]

Yes; but when you say in the model

"forall(i in 1..100) x(i) is_binary"

you are implying that (X(I) can only take values of 0 or 1). And the
conditions for the X(I) values are expressed in the "PathLoad(l)" and
"PathLoad_A(l)" restrictions. The rest is done by the optimizer.

I hope this can still help you (though I guess you have already
figured that out). Sorry for the long delay of my reply.