PyCSP³

PyCSP³ is a Python library that allows us to write models of combinatorial constrained problems in a declarative manner. Currently, with PyCSP³, you can write models of constraint satisfaction and optimization problems. More specifically, you can build models for:

• CSP (Constraint Satisfaction Problem)
• COP (Constraint Optimization Problem)

In this website, you will find all that you need to know about Constraint Programming (CP) and PyCSP³, with more than 60 Jupyter Notebooks:

• find the 25 popular constraints , with dedicated Jupyter Notebooks
• discover, step by step, more than 30 models of classical problems (Sport Scheduling, Social Golfers , Warehouse Location , ...), with dedicated Jupyter Notebooks

You can also read this guide.

As an illustration, below, you can find two simple examples of PyCSP³ models:

from pycsp3 import *

n = data or 8

# x[i] is the ith note of the series
x = VarArray(size=n, dom=range(n))

satisfy(
   # notes must occur once, and so form a permutation
   AllDifferent(x),

   # intervals between neighbouring notes must form a permutation
   AllDifferent(abs(x[i] - x[i + 1]) for i in range(n - 1)),

   # tag(symmetry-breaking)
   x[0] < x[n - 1]
)

from pycsp3 import *

n = data or 10

# x[i] is the position of the ith tick
x = VarArray(size=n, dom=range(n * n))

satisfy(
   # all distances are different
   AllDifferent(abs(x[i] - x[j]) for i, j in combinations(range(n), 2)),

   # tag(symmetry-breaking)
   [x[0] == 0, Increasing(x, strict=True)]
)

minimize(
   # minimizing the position of the rightmost tick
   x[-1]
)

Requirements

• For building and compiling models, you need:
  • Python 3.6 (at least) to be installed
  • Python package PyCSP³ to be installed, for example from PyPi: pip install pycsp3
• For running the embedded solvers (ACE and Choco), you need Java 11 to be installed

Importantly, there is a complete separation between the modeling and solving phases: you write a model, you compile it (while providing some data) in order to generate an XCSP³ instance (file), and you solve that problem instance by means of a constraint solver. You can also directly pilot the solving procedure in PyCSP³ possibly conducting an incremental solving strategy.

In a nutshell, the main ingredients of the complete tool chain we propose for handling combinatorial constrained problems are:

• PyCSP³: a Python library for modelling constrained problems, which is described in this document (or equivalently, JvCSP3, a Java-based API)
• XCSP³: an intermediate format used to represent problem instances while preserving structure of models

A shown in the figure below, the user who wishes to solve a combinatorial constrained problem has to:

• write a model using the Python library PyCSP³ (i.e., write a Python file), or the Java modeling API JvCSP3 (i.e., write a Java file)
• provide a data file (in JSON format) for a specific problem instance to be solved
• compile both files (model and data) so as to generate an XCSP³ instance (file)
• solve the XCSP³ file (problem instance under format XCSP³) by using a constraint solver as, e.g., ACE, Choco, OscaR or PicatSAT

This approach has many advantages:

• Python (and Java), JSON, and XML are robust mainstream technologies
• using JSON for data permits to have a unified notation, easy to read for both humans and computers
• using Python 3 for modeling allows the user to avoid learning again a new programming language
• using a coarse-grained XML structure permits to have compact and readable problem instances

Note that using JSON instead of XML for representing instances would have been possible but has some drawbacks, as explained in an appendix of XCSP³ Specifications

.