Re: [Help-glpk] Can GLPK use multiple object?

[Manish Jain]

The min(x,y) constraint is also a linear constraint, and can be coded using binary variables.

obj: min x 

s.t. x + y >= 8

      z1 = ....

      z2 < ....

      -1*(1-s1)M <= y - z1 <= 0

      -1*(1-s2)M <= y - z2 <= 0

      s1 + s2 = 1

      s1, s2 \in {0,1}

This formulation will lock y to the minimum of z1 and z2. M is a huge +ve constant in this.

Disadvantages of the above formulation:

1. s1,s2 are binary and hence this formulation could potentially be slower.

2. sometimes, the constant M can affect the tolerance / robustness of the solution. You can read more literature to learn how and why.

I would also suggest that you read about disjunctive programming which teaches how to encode if-else type of constraints in linear forms.

Hopefully it helps.

Manish Jain
University of Southern California

On Tue, Jul 20, 2010 at 2:36 PM, xiaomi <address@hidden> wrote:

No. Not their sum. For example this problem:

Object: minimize X
Constraint:  X+Y>=8, Y=min(Z1,Z2) Z1=...., Z2<.....

Do I describe Y as "Y<=Z1, Y<=Z2" ?  That is not correct unless I maxmize Y in my object at the same time as minimizing X. So I asked whether multiple objects are functional.





Mansour Moufid :

2010/7/20 xiaomi <address@hidden>:
 

I am running a project that need to minimize more than one variable in
LP solver. Can GLPK do that? If yes, how to do so?
   

Minimize their sum?

 

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