cpmpy 0.10.0

A numpy-based library for modeling constraint programming problems

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CPMpy: a Constraint Programming and Modeling library in Python, based on numpy, with direct solver access.

Documentation: https://cpmpy.readthedocs.io/

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Constraint solving at your finger tips

For combinatorial problems with Boolean and integer variables. With many high-level constraints that are automatically decomposed when not natively supported by the solver.

Lightweight, well-documented, used in research and industry.

Install simply with pip install cpmpy

🔑 Key Features

• Solver-agnostic: use and compare CP, ILP, SMT, PB and SAT solvers
• ML-friendly: decision variables are numpy arrays, with vectorized operations and constraints
• Incremental solving: assumption variables, adding constraints and updating objectives
• Extensively tested: large test-suite and actively fuzz-tested
• Tools: for parameter-tuning, debugging, explanation generation and XCSP3 benchmarking
• Flexible: easy to add constraints or solvers, also direct solver access

🔩 Solvers

CPMpy can translate to a wide variety of constraint solving paradigms, including both commercial and open-source solvers.

• CP Solvers: OR-Tools (default), IBM CP Optimizer (license required), Choco, Glasgow GCS, Pumpkin, MiniZinc+solvers
• ILP Solvers: Gurobi (license required), CPLEX (license required)
• GO Solvers: Hexaly (license required)
• SMT Solvers: Z3
• PB Solvers: Exact
• SAT Encoders and Solvers: PySAT+solvers, Pindakaas
• Decision Diagrams: PySDD

</> Example: flexible jobshop scheduling

An example that also demonstrates CPMpy's seamless integration into the scientific Python ecosystem:

# Simple flexible job-shop: a set of jobs (each 1 task) must be run, each can be run on any of the machines,
# with different duration and energy consumption. Minimize makespan and total energy consumption
import cpmpy as cp
import pandas as pd
import random; random.seed(1)

# --- Data definition ---
num_jobs = 15
num_machines = 3
# Generate some data: [job_id, machine_id, duration, energy]
data = [[jobid, machid, random.randint(2, 8), random.randint(5, 15)]
        for jobid in range(num_jobs) for machid in range(num_machines)]
df_data = pd.DataFrame(data, columns=['job_id', 'machine_id', 'duration', 'energy'])

# Compute maximal horizon (crude upper bound) and number of alternatives
horizon = df_data.groupby('job_id')['duration'].max().sum()
num_alternatives = len(df_data.index)
assert list(df_data.index) == list(range(num_alternatives)), "Index must be default integer (0,1,..)"


# --- Decision variables ---
start = cp.intvar(0, horizon, name="start", shape=num_alternatives)
end   = cp.intvar(0, horizon, name="end", shape=num_alternatives)
active = cp.boolvar(name="active", shape=num_alternatives)

# --- Constraints ---
model = cp.Model()

# Each job must have one active alternative
for job_id, group in df_data.groupby('job_id'):
    model += (cp.sum(active[group.index]) == 1)

# For all jobs ensure start + dur = end (also for inactives, thats OK)
model += (start + df_data['duration'] == end)

# No two active alternatives on the same machine may overlap; (ab)use cumulative with 'active' as demand.
for mach_id, group in df_data.groupby('machine_id'):
    sel = group.index
    model += cp.Cumulative(start[sel], group['duration'].values, end[sel], active[sel], capacity=1)

# --- Objectives ---
# Makespan: max over all active alternatives
makespan = cp.intvar(0, horizon, name="makespan")
for i in range(num_alternatives):
    model += active[i].implies(makespan >= end[i])  # end times of actives determines makespan

# Total energy consumption
total_energy = cp.sum(df_data['energy'] * active)

# Minimize makespan first, then total energy
model.minimize(100 * makespan + total_energy)


# --- solving and graphical visualisation ---
if model.solve():
    print(model.status())
    print("Total makespan:", makespan.value(), "energy:", total_energy.value())

    # Visualize with Plotly's excellent Gantt chart support
    import plotly.express as px
    df_solution = df_data[active.value() == True].copy()  # Select rows where active is True
    df_solution["start"] = pd.to_datetime(start[df_solution.index].value(), unit="m")
    df_solution["end"] = pd.to_datetime(end[df_solution.index].value(), unit="m")
    px.timeline(df_solution, x_start="start", x_end="end", y="machine_id", color="job_id", text="energy").show()
else:
    print("No solution found.")

You can then compare the runtime of all installed solvers, or much more...

for solvername in cp.SolverLookup.solvernames():
    try:
        model.solve(solver=solvername, time_limit=10)  # max 10 seconds
        print(f"{solvername}: {model.status()}")
    except Exception as e:
        print(f"{solvername}: Not run -- {str(e)}")

🌳 Ecosystem

CPMpy is part of the scientific Python ecosystem, making it easy to use in Jupyter notebooks, to add visualisations, or to use it in machine learning pipelines.

Other projects that build on CPMpy:

• XCP-explain: a library for explainable constraint programming
• PyConA: a library for constraint acquisition
• Fuzz-Test: fuzz testing of constraint solvers
• Sudoku Assistant: an Android app for sudoku scanning, solving and intelligent hints
• CHAT-Opt demonstrator: translates natural language problem descriptions into CPMpy models

Also, CPMpy participated in both the 2024 and 2025 XCSP3 competition, twice making its solvers win 3 gold and 1 silver medal.

🔧 Library development

CPMpy has the open-source Apache 2.0 license and is run as an open-source project. All discussions happen on Github, even between direct colleagues, and all changes are reviewed through pull requests.

Join us! We welcome any feedback and contributions. You are also free to reuse any parts in your own project. A good starting point to contribute is to add your models to the examples/ folder.

Are you a solver developer? We are keen to integrate solvers that have a Python API and are on pip. Check out our adding solvers documentation and contact us!

🙏 Acknowledgments

Part of the development received funding through Prof. Tias Guns' European Research Council (ERC) Consolidator grant, under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002802, CHAT-Opt).

You can cite CPMpy as follows: "Guns, T. (2019). Increasing modeling language convenience with a universal n-dimensional array, CPpy as python-embedded example. The 18th workshop on Constraint Modelling and Reformulation at CP (ModRef 2019).

@inproceedings{guns2019increasing,
    title={Increasing modeling language convenience with a universal n-dimensional array, CPpy as python-embedded example},
    author={Guns, Tias},
    booktitle={Proceedings of the 18th workshop on Constraint Modelling and Reformulation at CP (Modref 2019)},
    volume={19},
    year={2019}
}

If you work in academia, please cite us. If you work in industry, we'd love to hear how you are using it. The lab of Prof. Guns is open to collaborations and contract research.