How Can I declare constraints in Xpress IVE?

Question

I am trying to write a model in Xpress IVE however I got error101: Incompatible types for operator ('mpvar' * 'mpvar' not defined). error.

I tried to write this constraint but I couldn't make it. The two consecutive characters on the string must be positioned to the neighboring nodes of the grid.

I think, my model is true and all of my decision variables is true.

Can anyone help me about this issue? Here is my code:

grid := 16
length := 8
!sample declarations section
declarations
    ! Declaring S and N array for the input
    S: array(1..length) of integer
    N: array(1..grid,1..grid) of integer
    ! Declaring decision variables
    X: array(1..length, 1..grid) of mpvar
    V: array(1..grid) of mpvar
    C: array(1..grid,1..grid) of mpvar
    W: real
    constraint1, constraint2,constraint3: linctr
end-declarations

! Decision Variable Declaration
forall(i in 1..length, k in 1..grid) X(i,k) is_binary
forall(k in 1..grid) V(k) is_binary
forall(l in 1..grid) V(l) is_binary
forall(k in 1..grid, l in 1..grid) C(k,l) is_binary

!Input String
S:: [ 1, 0, 0, 1, 0, 1, 1, 0 ]
! Neighbours in the grid. 
N:: [ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
     1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
     0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
     0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
     0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,
     0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0,
     0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0,
     0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1,
     0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]

! Finding consecutive 1's in the string
forall(i in 1..length-1) do
    if S(i) = 1 and S(i+1) = 1
    then W := W + 1
    end-if
end-do

! Declaring Constraints
! Constraint 1
forall(k in 1..grid) constraint1 := sum(i in 1..length) X(i,k) <= 1

! Constraint 2
forall(i in 1..length) constraint2 := sum(k in 1..grid) X(i,k) = 1

!Constraint 3
forall( i in 1..length - 1 ) constraint3 := (sum(j in 1..grid)(sum(k in 1..grid) N(k,j) * X(i,k) * X(i + 1,j))) = 1

Answer 1

Since you are creating the product of two variables in Constraint3, your problem is no longer linear but now quadratic (thus non-linear). This means you have to use the mmnl (non-linear) Mosel module. Putting

uses "mmnl"

at the top of your model should do that. It enables multiplication of decision variables.

Note that due to the quadratic terms in it, your Constraint3 will no longer be of type linctr. It will now be nlctr and you have to adjust this in the declaration.