# Simple Constraint Programming Problem: docplex works but equivalent ortools model is infeasible

I have a simple constraint programming model which can be solved using the docplex library, however I am struggling to implement the same model using ortools (see the examples below).

Question: Is there a fundamental limitation of ortools which prevents implementing this solution, or is there a problem with my syntax?

Note: I am NOT interested in alternative problem formulations, e.g., reformulating this as an MIP. This is a toy problem and I know different formulations are possible. My goal is to understand the differences and limitations of different solvers when it comes to implementing a constraint like this.

# Problem

Given a series with indices 0...n, find integer values of the series such that the value for each index i corresponds to the number of occurrences of i in the series.

For example, a solution for n = 4 is:

0 1 2 3 4
2 1 2 0 0

For index i=0, the value is 2, which corresponds to the series "2, 1, 2, 0, 0" containing two occurrences of the value 0. Index i=1 has a value of 1, corresponding to the single occurrence of 1 in the series. And so on.

# Example input data

# Input: Series length
n = 5

# Define data
max_value = n - 1
NUMBERS = range(n)


# docplex implementation works!

from docplex.cp.model import CpoModel

# Model instance
model = CpoModel(name='find series')

# Decision variables
s = model.integer_var_list(n, 0, max_value, "series")

# Constraint: Value should equal the # of occurrences of the index in the series
for i in NUMBERS:
model.add(sum(s[j] == i for j in NUMBERS) == s[i])

# Solve
model.solve()


# ortools implementation does NOT work!

When attempting to run the code below, I get an error when I try to define the constraints:

TypeError: unsupported operand type(s) for +: 'int' and 'BoundedLinearExpression'.

I've tried adjusting the syntax a few different ways, but it never reads the constraint as I intend it to.

from ortools.sat.python import cp_model

# Model instance
model = cp_model.CpModel()

# Decision variables
X = {}
for i in NUMBERS:
X[i] = model.NewIntVar(0, max_value, f'X_{i}')

# Add constraints (CODE FAILS HERE)
for i in NUMBERS:
model.Add(X[i] == sum([X[j]==i for j in NUMBERS]))

# Solve
solver = cp_model.CpSolver()
solver.Solve(model)

# Solution
print('Solve status: %s' % solver.StatusName())
if solver.StatusName() in ['FEASIBLE', 'OPTIMAL']:
for i in NUMBERS:
print(f'  X_{i}: {solver.Value(X[i])}')
$$$$
`
• You are trying to do sumif in ORtools. I am no expert in Google language but have you double checked if sum in a constraint under a condition is implemented in that way? Does ORtools give an lp file that shows the model? Nov 22, 2022 at 18:28
• Per Laurent Perron's accepted answer, ORtools can implement a constraint like this using something called a "channeling constraint". It's not very intuitive to me, but it seems like the way to do a conditional sum Nov 22, 2022 at 20:47