AMPL nonquadratic nonlinear constraints with cplex

Question

I'm working on an optimization project and I faced a small problem. For my project, I'm using AMPL and CPLEX as a solver. In my code, I have some elements indicated by e1, e2, ..., en. I also have a set which contains tuples within these elements. I must assign a number between 1 and 'n' to each element such that I maximize the distance between every 2 elements in 1 tuple in the moveTuples set (I need to order them but try to keep a distance between elements in the same tuple).

Every element MUST have ONLY 1 assigned number and each number should be given to ONLY 1 element. For this purpose, I wrote the following code:

set Elements;
set moveTuples dimen 2;
set Numbers;

var assign {Elements,Numbers} binary; 
var maximizer{moveTuples} integer >= 0; 

maximize obj: sum {(A,B) in moveTuples} maximizer[A,B];

subject to assign1NumberPerElement {i in Element}: sum {c in Numbers} assign[i,c] = 1;
subject to assign1ElementPerNumber {c in Numbers}: sum {i in Element} assign[i,c] = 1;


subject to moveApart {(A,B) in moveTuples}:  abs(sum{i in Numbers}(assign[A,i]*i) - (sum{j  in Numbers}x[B,j]*j)) - maximizer[A,B] = 0  ;

data;

set Elements:= e1 e2 e3;
set Numbers:= 1 2 3;
set moveTuples: e1 e2 e3:= 
(e1, e2);


solve;

display assign;

Now the problem is clear and for the previous example, the output must be either:

e1 -> 1

e2 -> 3

e3 -> 2

or

e1 -> 3

e2 -> 1

e3 -> 2

since it is required to only move e1 from e2 using the tuple (e1,e2). When running the previous code, I get the error: ... contains a non-quadratic non-linear constraint (definitely the "moveApart" constraint). Can you please guide me on how to solve this problem? Thanks in advance.

Answer 1

The constraint moveApart is nonlinear (and non-quadratic) because it contains a call to abs. However, since your problem is purely integer, you can solve it with CPLEX CP Optimizer (ilogcp).