Model Magic Sequence (Magic Series) problem using MIP

[dusantrtica]

Hello everyone,
I am trying to model Magic Sequence (or Magic Series) problem using MIP. Here is how I get started but it just doesn't work.
Could you please tell me what I am doing wrong here? Thanks

# Generates magic series:
# Example: for n = 5, one of the series is S = [2, 1, 2, 0, 0]
# Magic series S is an array such that S[i] is a number of occurences of i in S
# and its elements sum to n
n = 5
magic_series = Model('magic-series')

variables = [magic_series.add_var("", var_type=INTEGER, lb=0, ub=n-1) for i in range(n)]

for i in range(n):
    magic_series.add_constr(variables[i] == len([variable for variable in variables if variable == i]))

magic_series.add_constr(xsum(variables) == n)

magic_series.optimize()

[sebheger]

Hi @dusantrtica We do not offer support for modeling questions in general. If you can specify more in detail what doesn't work, we might if it is a bug.

[rschwarz]

A good place to ask modeling questions would be the OR StackExchange.

PS: You can't use condititionals such as if variable == i in a MIP formulation. The boolean expression will be evaluated by Python, but the value of variable is not yet known. Instead of using integer variables, try using binary values, one for each possible assignment.