How to assign value to a matrix in an indicator constraint

Specific Domains Optimization (Mathematical)
1

Is it possible and how to assign values to POSITION[R,C] matrix in the indicator constraint


    @variable(premex, ROLNA[R in keys(_ROWS), C in keys(_COLS), i_k in keys(_IMAGES_ALL)], Bin)
    @variable(premex, POSITION[R in keys(_ROWS), C in keys(_COLS)], Bin)
    @constraint(
      premex,
      SOMETHING[R in _ROWS, C in _COLS, i_k in keys(_IMAGES_ALL)],
      ROLNA[R, C, i_k]  => {
        POSITION[R1 + R - 1, C1 + C - 1]
        # for R1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["ROWS"])), C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
          # if (R1 + R - 1 <= length(_ROWS)) 
            # for C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
              # if  (C1 + C - 1 <= length(_ROWS))
        == 1
      }
    )

My goal is to assign 1 to some values in POSITION matrix when ROLNA[R, C, i_k] = 1

2

What are these objects? Are ROLNA and POSITION both arrays of Variables?

3

I’ve updated my question by adding their definitions.

4

So it looks like they’re both arrays of binary variables. In that case, at the index of interest, can you simply say p == 1 and r == 1?

Also, I think it is better to omit the constraint name entirely than to name it something like dsadasd… unless that actually means something. I hope it isn’t rude to suggest there could be improvement to readability here :stuck_out_tongue_winking_eye:

5

Ok let me write this in C#

      int[] _ROWS = new int[10];
      int[] _COLS = new int[10];
      int[] _IMAGES = new int[10];
      int[,] POSITION = new int[10, 10];
      int[,,] ROLNA = new int[10, 10, 10];

      int R, C, i_k, R1, C1;

      for (R = 0; R < _ROWS.Length; R++)
      {
        for (C = 0; C < _COLS.Length; C++)
        {
          for (i_k = 0; i_k < _IMAGES.Length; i_k++)
          {
            if (ROLNA[R,C,i_k] == 1)
            {
              for (R1 = 0; R1 < 4; R1++)
              {
                for (C1 = 0; C1 < 4; C1++)
                {
                  if (R1 + R - 1 <= _ROWS.Length && C1 + C - 1 <= _COLS.Length)
                    POSITION[R1 + R - 1,C1 + C - 1] = 1;
                }
              }
            }
          }
        }
      }

So, iterate through all ROLNA and if one point is == 1 then assign 1 (ones) to a square in the POSITION matrix that way that upper left point matches the coordinates and add 4 x 4 to the right and down from that point - but really I don;t care this coordinates calculation, I need someone to help me how to assign values to a multidimensional array in indicator constraint and that is it, nothing more .

How to write this in Julia / Jump indicator constraint?

6

Is this an accurate translation?

for cartesian_index in eachindex(ROLNA)
    r, c, i = Tuple(cartesian_index)
    if value(ROLNA[r, c, i]) == 1
        @constraint(premex, [r1 = 0:3, c1 = 0:3], POSITION[r+r1, c+c1] == 1)
    end
end

Even if not, the point is you can write all of the logic outside the @constraint macro and do the @constraint in the same place you seem to be doing it in the C# code. (I did a bit of a hybrid; one of the loops is external and the other is internal, but they can both be internal or both be external and that works too.)

edit: with both loops external and accounting for the bounds, it now looks like this

for cartesian_index in eachindex(ROLNA)
    r, c, i = Tuple(cartesian_index)
    if value(ROLNA[r, c, i]) == 1
        for r′ in r:min(r+3, size(ROLNA, 1)),
            c′ in c:min(c+3, size(ROLNA, 2))

            @constraint(premex, POSITION[r′, c′] == 1)
        end
    end
end

It’s a bit suspicious though that we’re iterating over the last index (i, above) and not using it anywhere. If for each (r, c), if any i leads to a 1 constraint the rest don’t matter anymore, you could iterate on each coordinate (R, C, I) in a separate loop (like your C# code) and break the i loop if you encounter a 1 after setting the constraint. Could save you a tiny bit of repeated constraint setting :man_shrugging:. You could also use this to inform the loops on r, and c, since they should skip in increments of 4 in those cases… too complicated for me right now.

1 Like
7

Thanks, @tomerarnon that is exactly what I’ve needed → so it is quite possible to iterate and then add it to the @constraint macro. Great! I will try this now.

8

Indeed it is! That is my preferred method, personally.

9

Thanks for your assistance, you’ve opened just another gate for me so I can move on :smile:

1 Like
10

This advice is incorrect, because it will be based on the previously solved value of ROLNA.

Since both are binary, use

for r′ in r:min(r+3, size(ROLNA, 1))
    for c′ in c:min(c+3, size(ROLNA, 2))
        @constraint(premex, POSITION[r′, c′] >= ROLNA[r, c, i])
    end
end
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11

I assumed this was the intention. The fact that the constraint was described as an “indicator” should have suggested that was not so, but I didn’t think through that.

1 Like
12

No worries. It’s useful to see different examples of more advanced things you can do with JuMP (adding constraints conditionally in a loop based on a previous solution).

13

I’ve tried what have @tomerarnon advised but I didn’t get the correct results. Let me explain what I am trying to do here. I want to allow ROLNA to hold only the top-left coordinate of an image from a set of images. Then I would assign all 1 to the remaining points of that image to POSITION matrix, So if POSITION has a value on x,y ROLNA cannot. How to write that.

Here is what I’ve tried from the last suggestion:

    @timeit to "02. this should put ones to POSITION matrix" begin
      for R in _ROWS, C in _COLS, i_k in keys(_IMAGES_ALL)
        if ROLNA[R, C, i_k] == 1
          for R1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["ROWS"])),
            C1 in collect(UnitRange(1, _IMAGES_ALL[i_k]["COLS"])) 
            if (R1 == 1 && C1 == 1)
              @constraint(premex, ROLNA[R, C, i_k] => {POSITION[R, C] == 0})
            elseif (R1 + R - 1 <= length(_ROWS)) && (C1 + C - 1 <= length(_COLS))
              @constraint(premex, ROLNA[R, C, i_k] => {POSITION[R1 + R - 1, C1 + C - 1] == 1})
            end            
          end            
        end
      end
    end

    @timeit to "03.this will prohibit ROLNA to take place that POSITION already holds" begin
      for i_k in keys(_IMAGES_ALL)
        @constraint(
          premex,
          [R in _ROWS, C in _COLS],
          POSITION[R, C] => {ROLNA[R, C, i_k] == 0}
        )
      end
    end
14

I think the way to do this is:

1 - POSITION[R, C] >= ROLNA[R, C, I_k]

so when p == 1 you get 0 >= r (ROLNA is 0), and when p == 0, 1 >= r, which does nothing to a binary variable.

15

Yes, that is a good idea too, so the thing here is to build a huge amount of constraints (predefined) with all possible indexes, is that the way this works?

So if I have an image, let’s say 500 x 200 mm and I divide ROLE to mm grid, so to assign all 1 (ones) to POSITION system will have to create 500 x 200 constraints, is that?

16

Honestly, I don’t know… Maybe? I think posing this problem (I looked at the previous threads) as an MIP like you’re doing is more intuitive to conceptualize, but computationally will be difficult to solve. I have been wondering if the problem can be posed as e.g. a geometric program (and solved with Convex.jl), but I don’t know of some simple mapping that will make it so. Anyway, for me this is uncharted territory, so I can’t predict what the results of this approach will be :sweat_smile:
Good luck!

1 Like