最大连续数值（Minizinc）

Question

I'm trying to model the next constraint in Minizinc:

Suppose S is an array of decision variables of size n. I want my decision variables to take a value between 1-k, but there is a maximum 'Cons_Max' on the number of consecutive values used.

For example, suppose Cons_Max = 2, n = 8 and k = 15, then the sequence [1,2,4,5,7,8,10,11] is a valid sequence , while eg [1,2,3,5,6,8,9,11] is not a valid sequence because the max number of consecutive values is equal to 3 here (1,2,3). Important to mention is that sequence [1,3,5,7,9,10,12,14] is also valid, because the values don't need to be consecutive but the max number of consectuive values is fixed to 'Cons_Max'.

Any recommendations on how to model this in Minizinc?

Answer 1

Suppose you use array x to represent your decision variable.

array[1..n] of var 1..k: x;

then you can model the constraint like this.

constraint not exists (i in 1..n-1)(
                       forall(j in i+1..min(n, i+Cons_Max))
                             (x[j]=x[i]+1)
                      );

Answer 2

Here's a model with a approach that seems to work. I also added the two constraints all_different and increasing since they are probably assumed in the problem.

include "globals.mzn";
int: n = 8;
int: k = 15;
int: Cons_Max = 2;
% decision variables
array[1..n] of var 1..k: x;

constraint 
   forall(i in 1..n-Cons_Max) (
      x[i+Cons_Max]-x[i] > Cons_Max
   )
;

constraint 
  increasing(x) /\
  all_different(x)
;

%% test cases
% constraint 
%    % x = [1,2,4,5,7,8,10,11] % valid solution
%    % x = [1,3,5,7,9,10,12,14] % valid valid solution

%    % x = [1,2,3,5,6,8,9,11] % -> not valid solution (-> UNSAT)
%  ;


solve satisfy;
output ["x: \(x)\n" ];