AMPL, selecting data from two sets

Question

I have two sets which are:

set s1 := 0 1 5 6 ;
set s2 := 3 4 8 9 ;

I need to have a constraint which selects the data from these sets like the following line:

subject to sym1{i in 0..3 , j in 0..3 : i=j } : x[0,s1[i],0] = x[1,s1[j],0];

It means selecting data from s1 and s2 should be like: x[0,0,0] = x[1,3,0]; x[0,1,0] = x[1,4,0]; x[0,5,0] = x[1,8,0]; x[0,6,0] = x[1,9,0];

But the code I wrote has a syntax error. Would you please help me

Thanks

Answer 1

One way to do this is by declaring sets as ordered and using the member function to an element of a set by its index:

set s1 ordered := {0, 1, 5, 6};
set s2 ordered := {3, 4, 8, 9};

subject to sym1{i in 1..4}: x[0, member(i, s1), 0] = x[1, member(i, s2), 0];

Alternatively, you can replace sets with parameters:

param s1{1..4};
param s2{1..4};

subject to sym1{i in 1..4}: x[0, s1[i], 0] = x[1, s2[i], 0];

data;

param s1 :=
 1 0
 2 1
 3 5
 4 6;

param s2 :=
 1 3
 2 4
 3 8
 4 9;