[SOLVED] How to pick an element from matrix (list of list in python) based on decision variables (one for row, and one for column)

How to pick an element from matrix (list of list in python) based on decision variables (one for row, and one for column) | OR-Tools, Python

I am new to constraint programming and OR-Tools. A brief about the problem. There are 8 positions, for each position I need to decide which move of type A (move_A) and which move of type B (move_B) should be selected such that the value achieved from the combination of the 2 moves (at each position) is maximized. (This is only a part of the bigger problem though). And I want to use AddElement approach to do the sub setting.

Please see the below attempt

from ortools.sat.python import cp_model
model = cp_model.CpModel()

# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2nd move of type A and 3rd move of type B will give value = 2
value = [
            [ -1,  5,  3,  2,  2],
            [  2,  4,  2, -1,  1], 
            [  4,  4,  0, -1,  2],
            [  5,  1, -1,  2,  2],
            [  0,  0,  0,  0, 0],
            [  2,  1,  1,  2, 0]
       ]

# 6 moves of type A
num_moves_A = len(value)

# 5 moves of type B
num_moves_B = len(value[0])

num_positions = 8

type_move_A_position = [model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)]

type_move_B_position = [model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)]

value_position = [model.NewIntVar(0, 10, f"value_position[{i}]") for i in range(num_positions)]

# I am getting an error when I run the below
objective_terms = []
for i in range(num_positions):
    model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
    objective_terms.append(value_position[i])

The error is as follows:

Traceback (most recent call last):

  File "<ipython-input-65-3696379ce410>", line 3, in <module>
    model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])

TypeError: list indices must be integers or slices, not IntVar

In MiniZinc the below code would have worked

var int: obj = sum(i in 1..num_positions ) (value [type_move_A_position[i], type_move_B_position[i]])

I know in OR-Tools we will have to create some intermediary variables to store results first, so the above approach of minizinc will not work. But I am struggling to do so.

I can always create a 2 matrix of binary binary variables one for num_moves_A * num_positions and the other for num_moves_B * num_positions, add re;evant constraints and achieve the purpose

But I want to learn how to do the same thing via AddElement constraint

Any help on how to re-write the AddElement snippet is highly appreciated. Thanks.

Solution

AddElement is 1D only. The way it is translated from minizinc to CP-SAT is to create an intermediate variable p == index1 * max(index2) + index2 and use it in an element constraint with a flattened matrix.