Hi,
The first idea that comes to my mind is that you need some form of indirection.
In the case of a combinatorial problem using CP, this can be implemented using the "element" function.

Here is a simple OPL example to illustrate the use of this function:

using CP;

int NB_ELEMENTS = 7;
range elements_idx = 0..NB_ELEMENTS;
int elements_list[elements_idx] = [1, 3, 5, 17, 21, 13, 7, 11];

dvar int idx in elements_idx;
dvar int element_val;

maximize element_val;

subject to {
  element_val == element(elements_list, idx);
}

which would result in the following solution:

// solution with objective 21
element_val = 21;
idx = 4;

In the case of a MIP model, a similar approach could be used by creating as many boolean decision variables as there are elements to choose from, and to enforce that the sum over all these binary variables is equal to 1.
The actual value for the desired decision variable is then a dot product between the vector of boolean decision variables and the list of values.

Regards,

Hi,
The first idea that comes to my mind is that you need some form of indirection.
In the case of a combinatorial problem using CP, this can be implemented using the "element" function.

Here is a simple OPL example to illustrate the use of this function:

using CP;int NB_ELEMENTS = 7;range elements_idx = 0..NB_ELEMENTS;int elements_list[elements_idx] = [1, 3, 5, 17, 21, 13, 7, 11];dvar int idx in elements_idx;dvar int element_val;maximize element_val;subject to {  element_val == element(elements_list, idx);}

which would result in the following solution:

// solution with objective 21element_val = 21;idx = 4;

In the case of a MIP model, a similar approach could be used by creating as many boolean decision variables as there are elements to choose from, and to enforce that the sum over all these binary variables is equal to 1.
The actual value for the desired decision variable is then a dot product between the vector of boolean decision variables and the list of values.

Regards,

Hi Nourredine,
I'm a bit confused...

In the example of my previous e-mail, the decision variable element_val can only take values in {1, 3, 5, 17, 21, 13, 7, 11} because of the "element" constraint. This is the formulation in the OPL language (if CP is used as a solver).
Then, constraints in your model would be formulated using this element_val decision variable.
I thought this was the purpose of your question.

I'm certainly misunderstanding what you are asking for.
Can you please give more details about your context? Are you using a MIP or a CP model ? Which modelling language are you using (OPL, docplex, Cplex API... ?)
Thanks,

Hi Nourredine,
I'm a bit confused...

In the example of my previous e-mail, the decision variable element_val can only take values in {1, 3, 5, 17, 21, 13, 7, 11} because of the "element" constraint. This is the formulation in the OPL language (if CP is used as a solver).
Then, constraints in your model would be formulated using this element_val decision variable.
I thought this was the purpose of your question.

I'm certainly misunderstanding what you are asking for.
Can you please give more details about your context? Are you using a MIP or a CP model ? Which modelling language are you using (OPL, docplex, Cplex API... ?)
Thanks,

Hi,
The first idea that comes to my mind is that you need some form of indirection.
In the case of a combinatorial problem using CP, this can be implemented using the "element" function.

Here is a simple OPL example to illustrate the use of this function:

using CP;int NB_ELEMENTS = 7;range elements_idx = 0..NB_ELEMENTS;int elements_list[elements_idx] = [1, 3, 5, 17, 21, 13, 7, 11];dvar int idx in elements_idx;dvar int element_val;maximize element_val;subject to {  element_val == element(elements_list, idx);}

which would result in the following solution:

// solution with objective 21element_val = 21;idx = 4;

In the case of a MIP model, a similar approach could be used by creating as many boolean decision variables as there are elements to choose from, and to enforce that the sum over all these binary variables is equal to 1.
The actual value for the desired decision variable is then a dot product between the vector of boolean decision variables and the list of values.

Regards,

using CP;

{int} S={1, 3, 5, 17, 21, 13,  7, 11};

int n=card(S);
range r=1..n;

int v[i in r]=item(S,i-1);

dvar int x[r];
dvar int perm[r] in r;

subject to
{
  allDifferent(perm);
  forall(i in r) x[i]==v[perm[i]];
}​

gives

perm = [6 4 1 2 3 8 7 5];
x = [13 17 1 3 5 11 7 21];

but could also give other results

Hi Nourredine,
I'm a bit confused...

In the example of my previous e-mail, the decision variable element_val can only take values in {1, 3, 5, 17, 21, 13, 7, 11} because of the "element" constraint. This is the formulation in the OPL language (if CP is used as a solver).
Then, constraints in your model would be formulated using this element_val decision variable.
I thought this was the purpose of your question.

I'm certainly misunderstanding what you are asking for.
Can you please give more details about your context? Are you using a MIP or a CP model ? Which modelling language are you using (OPL, docplex, Cplex API... ?)
Thanks,