Minizinc - solve minimize does not minimize properly - minizinc

Question

My minizinc program does not minimize properly. It seems to maximize.
The program tries to find the minimum sum of times in which a given number of couriers ( in .dzn),
deliver the packages.
This is
.dzn
n = 5;
c = 2;
times = [| 0, 4, 2, 7, 9
| 4, 0, 4, 8, 9
| 2, 4, 0, 1, 6
| 7, 8, 1, 0, 2
| 9, 9, 6, 2, 0|];
place_names = ["H","A","B","C","D"];
This is
.mzn
include "globals.mzn";
int: n; % total number of places
int: c; % total number of couriers
set of int: num_deliveries = 1..n-1;
int: headquarter = 1;
set of int: num_places = 1..n;
set of int: deliveries = 2..n;
set of int: couriers = 1..c;
set of int: num_max_deliveries = 1..n+2;
set of int: schedule_domain = 0..n;
int: first_place_idx = 1;
int: last_place_idx = n+2;
array[num_places, num_places] of int: times; % estimate of the times needed to reach a place_b from place_a
array[num_places] of string: place_names; % names of places
array[couriers,num_max_deliveries] of var schedule_domain: schedule; % scheduling deliveries with 0 padding
constraint forall(i in couriers)(schedule[i,first_place_idx] == headquarter /\ schedule[i,last_place_idx] == headquarter)
/\ forall(a in couriers, b in num_max_deliveries where b != first_place_idx /\ b != last_place_idx)(schedule[a,b] !=1)
/\ forall(i in couriers)(sum(j in num_max_deliveries)(schedule[i,j]) > 2)
/\ forall(z in deliveries)(count([deopt(el)| el in [ k | k in [schedule[i,j]|i in couriers, j in num_max_deliveries where j != first_place_idx /\ j!= last_place_idx] where k != 0]],z,1))
/\ sum([ k | k in [schedule[i,j]|i in couriers, j in num_max_deliveries where j != first_place_idx /\ j!= last_place_idx] where k != 0]) == sum(2..n);
array[couriers] of var int : total_times = [ sum([times[[schedule[i,j] |j in num_max_deliveries where schedule[i,j] != 0][z], [schedule[i,j] |j in num_max_deliveries where schedule[i,j] != 0][z+1]]
| z in 1..length([schedule[i,j] |j in num_max_deliveries where schedule[i,j] != 0]) -1]) | i in couriers];
var int : sum_time = sum(total_times);
solve minimize sum_time;
output ["schedule = \(schedule)\n"];
output ["total_times = \(total_times)\n"];
output[ "courier_" ++ "\(i) " ++ "\([ place_names[fix(schedule[i,j])] ++ "->" | j in num_max_deliveries where schedule[i,j] != 0])\n" | i in couriers];
This is the output
output
schedule = [1, 5, 4, 3, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1]
total_times = [14, 8]
courier_1 ["H->", "D->", "C->", "B->", "H->"]
courier_2 ["H->", "A->", "H->"]
----------
schedule = [1, 3, 5, 4, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1]
total_times = [17, 8]
courier_1 ["H->", "B->", "D->", "C->", "H->"]
courier_2 ["H->", "A->", "H->"]
----------
schedule = [1, 3, 4, 5, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1]
total_times = [14, 8]
courier_1 ["H->", "B->", "C->", "D->", "H->"]
courier_2 ["H->", "A->", "H->"]
----------
schedule = [1, 0, 5, 4, 3, 0, 1, 1, 2, 0, 0, 0, 0, 1]
total_times = [14, 8]
courier_1 ["H->", "D->", "C->", "B->", "H->"]
courier_2 ["H->", "A->", "H->"]
----------
schedule = [1, 0, 5, 0, 4, 0, 1, 1, 3, 2, 0, 0, 0, 1]
total_times = [18, 10]
courier_1 ["H->", "D->", "C->", "H->"]
courier_2 ["H->", "B->", "A->", "H->"]
----------
schedule = [1, 0, 5, 0, 4, 3, 1, 1, 0, 2, 0, 0, 0, 1]
total_times = [14, 8]
courier_1 ["H->", "D->", "C->", "B->", "H->"]
courier_2 ["H->", "A->", "H->"]
----------
schedule = [1, 0, 4, 0, 5, 0, 1, 1, 3, 0, 2, 0, 0, 1]
total_times = [18, 10]
courier_1 ["H->", "C->", "D->", "H->"]
courier_2 ["H->", "B->", "A->", "H->"]
----------
schedule = [1, 0, 2, 0, 5, 0, 1, 1, 0, 4, 3, 0, 0, 1]
total_times = [22, 10]
courier_1 ["H->", "A->", "D->", "H->"]
courier_2 ["H->", "C->", "B->", "H->"]
----------
schedule = [1, 0, 3, 0, 5, 0, 1, 1, 0, 4, 0, 2, 0, 1]
total_times = [17, 19]
courier_1 ["H->", "B->", "D->", "H->"]
courier_2 ["H->", "C->", "A->", "H->"]
----------
==========
Finished in 422msec
It should stop after the first optimal solution, but it seems that the first solution is the optimal one.
Thanks in advance!

Answer 1

Please, note that the only variable that a solver outputs is schedule. All other are computed using information in own file. I have made an experiment, using JaCoP (I guess similar can be done with Gecode). I compile your problem to flatzinc (option -c), annotated variable sum_time with ":: output_var" and run fan_jacop (you can try fun_gecode) and got the following output.
sum_time = 16;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 3, 4, 5, 1]);
sum_time = 14;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 4, 5, 3, 1]);
sum_time = 9;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 5, 4, 3, 1]);
sum_time = 7;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 0, 2, 1, 1, 0, 3, 4, 5, 0, 1]);
sum_time = 5;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 5, 4, 3, 1]);
sum_time = 3;
schedule = array2d(1..2, 1..7, [1, 0, 0, 0, 2, 0, 1, 1, 0, 3, 4, 5, 0, 1]);
sum_time = 2;
schedule = array2d(1..2, 1..7, [1, 0, 0, 2, 0, 3, 1, 1, 0, 4, 0, 5, 0, 1]);
sum_time = 1;
schedule = array2d(1..2, 1..7, [1, 0, 0, 3, 4, 0, 1, 1, 0, 2, 0, 5, 0, 1]);
sum_time = 0;
schedule = array2d(1..2, 1..7, [1, 0, 2, 0, 3, 0, 1, 1, 0, 4, 0, 5, 0, 1]);
==========
It indicates that the objective variable is correctly minimized and the problem is in minizinc output program.