Arithmetic constraints

In the previous sections we have already seen several examples of linear constraints over finite domain variables. Linear constraints may be regarded as a special case of arithmetic constraints, that is, equations or inequality relations involving expressions over decision variables formed with the operators +, -, /, *, ^, sum, prod and arithmetic functions like abs or ln. For a complete list of arithmetic functions supported by the solver the reader is refered to the Xpress Kalis reference manual.

Arithmetic constraints in Xpress Kalis may be defined over finite domain variables (type cpvar), continuous variables (type cpfloatvar), or mixtures of both. Notice, however, that arithmetic constraints involving continuous variables cannot be defined as strict inequalities, that means, only the relational operators >=, <=, and = may be used.

Here are a few examples of (nonlinear) arithmetic constraints that may be defined with Xpress Kalis.

model "Nonlinear constraints"
 uses "kalis"

 setparam("KALIS_DEFAULT_LB", 0)
 setparam("KALIS_DEFAULT_UB", 5)
 setparam("KALIS_DEFAULT_CONTINUOUS_LB", -10)
 setparam("KALIS_DEFAULT_CONTINUOUS_UB", 10)

 declarations
  a,b,c: cpvar
  x,y,z: cpfloatvar
 end-declarations

 x = ln(y)
 y = abs(z)
 x*y <= z^2
 z = -a/b
 a*b*c^3 >= 150

 while (cp_find_next_sol)
  writeln("a:", getsol(a), ", b:", getsol(b), ", c:", getsol(c),
         ", x:", getsol(x), ", y:", getsol(y), ", z:", getsol(z))

end-model