MiniZinc. Discrete knapsack problem. Аn incomprehensible solution - knapsack-problem

Question

Solve (from https://www.minizinc.org/doc-2.5.5/en/modelling2.html#set-constraints):
enum ITEM = { I1, I2, I3, I4, I5 };
int: capacity = 5;
array[ITEM] of int: profits = [1,2,3,4,5];
array[ITEM] of int: weights = [1,2,3,4,5];
int: maxProfit = sum (profits);
var set of ITEM: knapsack;
var int: weight = sum ([weights[i] | i in knapsack]);
var int: profit = sum ([profits[i] | i in knapsack]);
constraint weight <= capacity;
solve maximize profit;
output ["knapsack = \(knapsack)\n",
"weight = \(weight)/\(capacity)\n",
"profit = \(profit)"]
Output:
knapsack = {I1, I2}
weight = 3/5
profit = 3
----------
knapsack = {I1, I3}
weight = 4/5
profit = 4
----------
knapsack = {I1, I4}
weight = 5/5
profit = 5
----------
==========
Please tell me why the output is like this?
I expected an answer of the form:
% profit 5 for all
{ I1, I4 }
{ I2, I3 }
{ I5 }
Solver: Gecode 6.3.0

Answer 1

If I understand your question correctly, you are expecting that the output should show all optimal solutions. Is that correct?
However, this is an optimization problem which only shows one optimal solution. The two first "solutions" are the intermediate solutions with increasing value of profit (3 and 4). The last solution (profit = 5) is the optimal solution: {I1, I4}.
If you want all optimal solutions (with profit = 5), you have to add that as a constraint and change solve maximize profit to solve satisfy:
constraint profit = 5;
% solve maximize profit;
solve satisfy;
Then the output will be:
knapsack = {I1, I4}
weight = 5/5
profit = 5
----------
knapsack = {I2, I3}
weight = 5/5
profit = 5
----------
knapsack = {I5}
weight = 5/5
profit = 5
----------
==========
I am not aware of any flag to MiniZinc (or the FlatZinc solver) that will print all the optimal solutions directly (i.e. without the manual handling as above). However, this would be possible using the Python interface MiniZinc Python (https://minizinc-python.readthedocs.io/en/latest/ )
Update
Here is a Python model (using MiniZinc-Python) for showing all optimal solutions. The MiniZinc model is the same as stated except that there is no solve line. This is added by the Python program and is the key to getting all optimal solutions.
from minizinc import Instance, Model, Solver
gecode = Solver.lookup("gecode")
model = Model("./discrete_knapsack.mzn")
instance = Instance(gecode, model)
with instance.branch() as opt:
opt.add_string("solve maximize profit;\n")
res = opt.solve()
obj = res["objective"]
instance.add_string(f"constraint sum ([profits[i] | i in knapsack]) = {obj};\n")
result = instance.solve(all_solutions=True)
for sol in result.solution:
print(sol)
print()
The output is:
knapsack = {I1, I4}
weight = 5/5
profit = 5
knapsack = {I2, I3}
weight = 5/5
profit = 5
knapsack = {I5}
weight = 5/5
profit = 5
(This program was much inspired by the MiniZinc-Python example https://minizinc-python.readthedocs.io/en/latest/basic_usage.html#finding-all-optimal-solutions )