Constrained sum of elements

From a shuffled set of integers, find the numbers that minimize the sum of 5 (five) elements, so that the result is also an odd number

In this case, since the objective function is the sum of the elements, the order doesn’t matter, so we use the Combination optimizer.

Out:

Iteration 0:
   global_best: 17.000   iteration_best: 17.000
Iteration 1:
   global_best: 15.000   iteration_best: 15.000

Iteration completed
==========================
Exit code 2: Algorithm has reached the value threshold of 15
Elapsed time 0.011
1 iterations
Best selection: [1, 5, 4, 3, 2]
Best evaluation: 15.0
Solution:  [1, 5, 4, 3, 2]

import random
from psopt import Combination


def main():
    # define objective function: f([a, b, c, ...]) = a + b + c + ...
    def obj_func(x):
        return sum(x)

    # list of possible candidates
    random.seed(0)
    candidates = random.sample(list(range(1, 12)), 11)

    # constraint: sum of values cannot be even
    def mod(x):
        return sum(x) % 2

    constraint = {"fn": mod, "type": "==", "value": 1}

    # instantiate the optimizer
    opt = Combination(obj_func, candidates, constraints=constraint)

    # define a threshold of acceptance for early convergence
    threshold = 15

    # minimize the obj function
    results = opt.minimize(selection_size=5, threshold=threshold, seed=0, verbose=1)
    print("Solution: ", results.solution)

    results.history.plot(["global_best", "iteration_best"])


if __name__ == "__main__":
    main()