Originally posted by: Abdelkader

Hi everybody,

 

Does someone know if Min Max Optimization possible with OPL CPLEX, example:

Minimize Max_{j}{f_1,..,f_j,..,f_n}

 

If yes how to implement ? Please provide me with a short code as a model. 

 

Many thanks in advance and to Alex especially.

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi

range r=1..5;
dvar int x[i in r] in r;

minimize max(i in r) x[i];
subject to
{

}

could help ?

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

I'll test it anklet you know. Many Thanks to you Alex.
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

A question: does it solve the min-max problem by returning the minimum of the maximum of a set of objectives, i.e., f*= minmax{f_i} ?
Thanks in advance,

Abdelkader
#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi

yes the optimization is done for the min of the max/

range r=1..5;
dvar int x[i in r] in r;

minimize max(i in r) x[i];
subject to
{
 forall(i in r:i!=1) x[i]==2;
}

gives

either 1 or 2 for x[1]

whereas if you write

range r=1..5;
dvar int x[i in r] in r;

//minimize max(i in r) x[i];
subject to
{
 forall(i in r:i!=1) x[i]==2;
}

int m=max(i in r) x[i];

execute
{
writeln(m);
}
 

no optimization is done but m is computed.

 

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

Great dear Alex. I'll test it and will feed you back.

Best,

Abdelkader 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

Dear Alex,

It seems working. However, i would like to know how to minimize the maximum of objectives as follows:

minimize max(i in r) x[i][j], that should give something like min (j in s) x[i*][j] where i* is the index of the maximum objective among all the objectives indexed by i. Then we minimize with regards to this maximal objective x[i*][j], where j=1,..,s.

But I face some struggles to implement it. Could you help please ?

Best,

Abdelkader

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

for your different objectives, you may use dexpr:

range r=1..5;
dvar int x[i in r] in r;

dexpr int obj[j in r]=sum(i in r:i!=j) x[i];

minimize max(j in r) obj[j];
subject to
{
 
}

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

Nice Alex,

A question: where does variables x[i] are taking their values?

What is the form of each objective function ? Is it f_j(x)=sum_{i}x[i]  for all i, for all x?

Cheers

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi,

x are decision variables and I wrote

dexpr int obj[j in r]=sum(i in r:i!=j) x[i];

as an example for objectives.

obj 1 is x2+x3+x4+x5 (sum for all i in r such as i different from 1)

regards

 

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: Abdelkader

Wonderful! That's what I've understood.

I'll let you know.

Best

#DecisionOptimization
#OPLusingCPLEXOptimizer