Maximize based on constraints - minizinc

Question

3 Arrays f1,f2 and f3 have child elements (f1a,f1b) ; (f2a,f2b,f2c) ; (f3a,f3b,f3c,f3d) respectively.They are all bool variables
I have a combination of these child elements in a list with 2 columns . The first column gives an ID and second col has the combination of child elements as shown below
row1 : 2345 | f1a , f2b
row2 : 2345 | f1a,f2a,f3c
row3 : 2346 | f2c, f3a
row4 : 2347 | f1b, f2c
.... ....
I need to choose one element of each of the arrays and form a selected array
if all elements of row are represented in selected array, I set 1 for that Row , else 0
So if selected array is [ f1a,f2a,f3c] , then ( using the above list example)
row1 is 0 ( as f2b is not in selected array)
row2 is 1 as all elements of row are in selected list
row3 is 0 as f2c and f3a is not in selected array
row4 is 0 as f2c is not present in selected array
I need to choose the selected array so as to maximize the sum of Row count (0+1+0+0 ...) for all Unique ID
for example if list is as shown below and selected array is [f1a,f2b,f3c] , though both rows are set 1 ,
I would only take 1 from both the rows as ID is same in both rows
row1 : 2345 | f1a , f2b
row2 : 2345 | f1a,f2b,f3c
Any help is appreciated as I am new to Minizinc and struggling to formulate the constraint with Minizinc

Answer 1

If your row variables are themselves also located in an array, then
solve maximize sum(row);
should set the activation of the rows to be the objective.
If you don't have them in an array you can still manually add them together to form an objective:
solve maximize row1 + row2 + row3 + row4;
I'm unsure if you were also asking about how the row activation itself works, but if a row only activates when all its elements are selected, then this would be enforced using a simple forall constraint:
constraint row1 = forall([...]);

Answer 2

I could finally get it working with this code. Here row1 and row2 have same ID and similarly row 3 and row4 have another common ID
array[1..2] of var bool: f1 ;
array[1..2] of var bool: f1 ;
array[1..3] of var bool: f2 ;
array[1..4] of var bool: f3 ;
var bool: row1;
var bool: row2 ;
var bool: row3 ;
var bool: row4 ;
constraint sum(f1) == 1;
constraint sum(f2) == 1;
constraint sum(f3) == 1;
constraint row1 = forall ( [(f1[1]) ] ) ;
constraint row2 = forall ( [(f1[2]) , (f2[2]) , (f3[3]) ] );
constraint row3 = forall ( [(f1[1]) , (f2[2]) , (f3[3]) ] ) ;
constraint row4 = forall ( [(f1[2]) , (f2[1]) , (f3[4]) ] ) ;
var int: rown1 = bool2int(row1) ;
var int: rown2 = bool2int(row2) ;
var int: rown2a = max(rown1,rown2) ;
var int: rown3 = bool2int(row3) ;
var int: rown4 = bool2int(row4) ;
var int: rown4a = max( rown3,rown4) ;
var int: rown = rown2a + rown4a ;
solve maximize rown;