Maximize the amount of zeros in continuous matrix (Python, docplex)

Question

I have an optimization problem with a continuous matrix variable (C), but:

My objective function is not about min/max the entries of C, but to maximize the amounts of 0 in C. My approach to model this, is to translate C to heaviside(C), which would make all non-zero entries equal to 1 and all zero entries stay 0. Then i could minimize the sum of these matrix entries, resulting a maximum of zero entries.

model.set_objective('min', sum(np.heaviside(C[k,j], 0) for k, j in itertools.product(range(M), range(P))))

Here I get errors of cplex, because C does not have defined values at this point. Any kind of casting the values of C to int or float fails as well.

TypeError: ufunc 'heaviside' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

I do not understand, why this is a problem, while e.g.

model.set_objective('min', sum(C[k,j] for k, j in itertools.product(range(M), range(P))))

works fine.

score 0 · Accepted Answer · answered Jun 06 '23 at 09:08

numpy functions are not allowed you should turn them into functions that are in docplex.

For instance you could rely on logical constraints

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*460 + nbbus30*360)

mdl.solve()

for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value)

print()
print("with the logical constraint")

nbKindOfBuses = mdl.integer_var(name='nbKindOfBuses')
mdl.add(nbKindOfBuses==(nbbus40>=1)+(nbbus30>=1))

mdl.minimize(nbbus40*460 + nbbus30*360+(nbKindOfBuses-1)*(500))

mdl.solve()

for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value)

Maximize the amount of zeros in continuous matrix (Python, docplex)

1 Answers1