Originally posted by: guvenc

Hi all,

I have a mathematical model. You can see a small section from it below. This section leads to some interesting behavioral difference when I write a constraint in two different ways. 

Could you please enlighten me about the behavioural difference of seemingly same constraints?

 

tuple rjt { string r; string j; float t; }

tuple rpjt { string r; string p; string j; float t; }

{rjt} RJT = ...;
{rpjt} RPJT = ...;

float Y[RPJT] = ...;

dvar float+ X[RJT];

minimize X;

//Alternative 1

subject to

{

forall (rjt in RJT)

X[rjt] == sum(rpjt in RPJT) Y[<rjt.r,rpjt.p,rjt.j,rjt.t>];

}

//Alternative 2

subject to

{

forall (rjt in RJT)

X[rjt] == sum(rpjt in RPJT: rpjt.r == rjt.r && rpjt.j == rjt.j && rpjt.t == rjt.t) Y[rpjt];

}

Alternative 1 leads to an "CPLEX cannot extract expression" error.

Alternative 2 works and lead to an optimal solution.

What am I missing? Are those alternatives not the same thing?

 

Thank you in advance.

Guvenc

 

 

 

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Hi,

for alternative 1 I would write

forall (<r,j,t> in RJT)

X[<r,j,t>] == sum(<r,p,j,t> in RPJT) Y[<r,p,j,t>];

because with your way you do a full Euclidian product and you could get errors

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: guvenc

Hi Alex,

I tested your suggestion for Alternative 1 and gives the same result as Alternative 2.

What do you mean by a full Euclidian Product? (the length of RJT and RPJT is not equal.)

I am confused how the following expressions affect the calculations.

forall (rjt in RJT)

forall (<r,j,t> in RJT)

 

Another question:

forall (<r,j,t> in RJT) // How does the equality of r,j,t here

X[<r,j,t>]

== sum(<r,p,j,t> in RPJT) Y[<r,p,j,t>]; // and r,j,t here is ensured? 

Should not it be written like 

forall (<r1,j1,t1> in RJT)
X[<r1,j1,t1>] == sum(<r2,p,j2,t2> in RPJT: r1 ==r2 && j1==j2 && t1==t2) Y[<r1,p,j1,t1>];

 

Are those all the same as Alternative 2? Is Alternative 2 a good way to deal with tuples as well?

 

Thank you for your first anser. It is very usefull. 

Regards

Guvenc

 

 

#CPLEXOptimizers
#DecisionOptimization

Hi

see explicit vs implicit slicing at https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/ilog.odms.ide.help/OPL_Studio/opllangref/topics/opl_langref_formalParams_filtering.html

Alternative 1 and 2 should behave the same. Some prefer alternative 1, others prefer alternative 2

In

forall (rjt in RJT)

X[rjt] == sum(rpjt in RPJT) Y[<rjt.r,rpjt.p,rjt.j,rjt.t>];

you could have some rjt in RJT with some p with <rjt.r,rpjt.p,rjt.j,rjt.t> not in the set.

If you changed that into

forall (rjt in RJT)

X[rjt] == sum(rpjt in RPJT:<rjt.r,rpjt.p,rjt.j,rjt.t> in RPJT) Y[<rjt.r,rpjt.p,rjt.j,rjt.t>];

you would not get that error.

regards

 

https://medium.com/@alexfleischer_84755/optimization-simply-do-more-with-less-zoo-buses-and-kids-66940178db6

 

 

 

 

 

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: guvenc

Thank you. Great help Alex

Regards.

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: guvenc

Hi Alex,

 

The following:

      forall (rjt in RJT)

          X[rjt] == sum(rpjt in RPJT:<rjt.r,rpjt.p,rjt.j,rjt.t> in RPJT) Y[<rjt.r,rpjt.p,rjt.j,rjt.t>];

does not give an objective value that I expect. It gives like a 10 times larger objective function value weirdly. 

I also tried 

      forall (rjt in RJT)
          X[rjt] == sum(rpjt in RPJT: <rjt.r,rpjt.p,rjt.j,rjt.t> in RPJT) Y[rpjt]; 

too, just to see what happens, and this one gives approx 4 times large objective function value as well. Both wrong ofcourse.

If you are still keen to help me out, I wonder your input about wrong equations.

 

Nonetheless, I think I will stick to one of the following

    forall (rjt in RJT)
        X[rjt] == sum(rpjt in RPJT: rpjt.r == rjt.r && rpjt.j == rjt.j && rpjt.t == rjt.t) Y[rpjt]; //Alternative 2

    forall (<r,j,t> in RJT)
        X[<r,j,t>] == sum(<r,p,j,t> in RPJT) Y[<r,p,j,t>];// Your reply behaving correctly

    forall (<r1,j1,t1> in RJT)
        X[<r1,j1,t1>] == sum(<r2,p,j2,t2> in RPJT: r1 ==r2 && j1==j2 && t1==t2) Y[<r1,p,j1,t1>];// Thank you once again for direction "Implicit and Explicit   

              Slicing https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/ilog.odms.ide.help/OPL_Studio/opllangref/topics/opl_langref_formalParams_filtering.html"

Regards,

Guvenc

#CPLEXOptimizers
#DecisionOptimization

Hi,

forall (rjt in RJT)

X[rjt] == sum(rpjt in RPJT:<rjt.r,rpjt.p,rjt.j,rjt.t> in RPJT) Y[<rjt.r,rpjt.p,rjt.j,rjt.t>];

 

I provided you was not a fix but a way to show you what your previous formula led to an error. You count too many elements that way. That s why you need slicing. What I gave you is not slicing but a protection against errors.

forall (<r,j,t> in RJT)

X[<r,j,t>] == sum(<r,p,j,t> in RPJT) Y[<r,p,j,t>];

 

is what you should write

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: guvenc

Hi

Yes one of following works fine.

    forall (rjt in RJT)
        X[rjt] == sum(rpjt in RPJT: rpjt.r == rjt.r && rpjt.j == rjt.j && rpjt.t == rjt.t) Y[rpjt];

    forall (<r,j,t> in RJT)
        X[<r,j,t>] == sum(<r,p,j,t> in RPJT) Y[<r,p,j,t>];

    forall (<r1,j1,t1> in RJT)
        X[<r1,j1,t1>] == sum(<r2,p,j2,t2> in RPJT: r1 ==r2 && j1==j2 && t1==t2) Y[<r1,p,j1,t1>];

 

Thank you Alex,

Regards

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#DecisionOptimization