Modeling Constrained Combinatorial Problems in Python
Project description
PyCSP3 v2.4 _{(August 28, 2024)}
This is Version 2.4 of PyCSP3, a library in Python (version 3.10 or later) for modeling combinatorial constrained problems; see www.pycsp.org. With PyCSP3, it is possible to generate instances of:
 CSP (Constraint Satisfaction Problem)
 COP (Constraint Optimization Problem)
in format XCSP3; see www.xcsp.org. Currently, PyCSP3 is targeted to XCSP3core, which allows us to use integer variables (with finite domains) and popular constraints. Note that:
 a dedicated website with more than 60 Jupyter notebooks is available
 a welldocumented guide is available
 PyCSP3 is available as a PyPi package
 a GitHub repository with more than 340 models is available at pycsp3models
At this stage, one can run two embedded solvers:
 the constraint solver ACE, with the option solve or the option solver=ace
 the constraint solver Choco, with the option solver=choco
Of course, it is possible to launch on generated XCSP3 instances (files) any solver that recognizes the XCSP3 format.
For example, see the solvers involved in the 2022 and 2023 Competitions.
It is also immediate to run ACE or Choco on XCSP3 instances (files) as the respective executables (jar files) are present in directories pycsp3/solvers/ace
and pycsp3/solvers/choco
.
For example, for running ACE on the XCSP3 instance 'zebra.xml', just execute:
java jar ACEYYMM.jar zebra.xml
while replacing YY and MM with the current values that are present in the name of the jar file.
Note that it is also possible to pilot solvers with Python; see PyCSP3 Solving Process.
0) Zero Installation from Google Colab
This is an immediate solution for using PyCSP3, with no installation required (you are ready to work in exactly 2 minutes). What you have to do is:
 build a new notebook on Google colab
 insert a first code cell for being able to use PyCSP3 in your notebook:
pip install pycsp3
 test a very basic model by inserting in a second code cell something like:
from pycsp3 import * x = VarArray(size=5, dom=range(5)) satisfy( AllDifferent(x) ) if solve() is SAT: print(values(x))
Here, we have an array with 5 variables, we enforce them to be all different, and we display the first solution found by the underlying solver.
Just execute these cell codes on Colab. It should return [0, 1, 2, 3, 4]
.
That's it. However, note that for intensive use, it is better to install PyCSP3 on your computer; see next section.
1) Installation from PyPi
This is the second easiest way of installing PyCSP3.
Note that you need first Python (version 3.10, or later) to be installed. You can do it, for example, from python.org
Installing PyCSP3 (Linux)
Check if 'pip3' is installed. If it is not the case, execute:
sudo apt install python3pip
Then, install PyCSP3 with the command 'pip3':
sudo pip3 install pycsp3
For using the solve or solver options, you need to have Java (at least, version 11) installed:
sudo aptget install openjdk11jdk
Installing PyCSP3 (Mac OS)
If Python 3 is installed on your system, the command 'pip3' should already be present.
Install PyCSP3 with the command 'pip3':
sudo pip3 install pycsp3
For using the solve or solver options, you need to have Java (at least, version 11) installed.
Installing PyCSP3 (Windows)
You may need to upgrade 'pip'. Open the console and type:
python m pip install upgrade pip
Then, for installing pycsp3, type:
python m pip install pycsp3
For using the solve or solver options, you need to install (at least) Java version 11:
https://www.oracle.com/java/technologies/javasedownloads.html
And add in the PATH the java command, for example, temporally, with the command:
set path=%path%;C:/Program Files/Java/jdk14.0.1/bin/
You can check the java command by typing in your console:
java version
Updating the Version of PyCSP3 (for PyPi)
For updating your version of PyCSP3, simply execute:
For linux/Mac:
sudo pip3 install upgrade pycsp3
For Windows:
python m pip install upgrade pycsp3
Working with a Pool of Models
A GitHub repository is now available with more than 340 models at pycsp3models.
And you can test the compilation of one of these models. For example, at the root of the directory pycsp3models:
python single/Zebra/Zebra.py (For Linux/Mac)
python single\Zebra\Zebra.py (For Windows)
2) Installation (alternative) by Cloning from GitHub
An alternative to PyPi is to clone the code from GitHub.
Here is an illustration for MAC OS.
We assume that Python 3 is installed (otherwise, type port install python38
for example), and consequently 'pip3' is also installed.
In a console, type:
git clone https://github.com/xcsp3team/pycsp3.git
pip3 install lxml
You may need to update the environment variable 'PYTHONPATH', by typing for example:
export PYTHONPATH=$PYTHONPATH:.
3) Compilation and Examples
We succinctly introduce a few PyCSP3 models, showing how to compile them with different options. However, note that many illustrations are available on www.pycsp.org, notably many models with Jupyter notebooks.
First, we give some general information about compilation.
Compiling PyCSP3 Models
For generating an XCSP3 instance from a PyCSP3 model, you have to execute:
python3 <file> [options]
with:
 <file>: a Python file to be executed, describing a model in PyCSP3
 [options]: possible options to be used when compiling
Among the options, we find:

data=<data_value>
: allows us to specify the data to be used by the model. It can be: elementary: data=5
 a simple list: data=[9,0,0,3,9]
 a JSON file: data=Bibd346.json
Data can then be directly used in the PyCSP3 model by means of a predefined variable
data
. 
dataparser=<file>
: a Python file for reading/parsing data given under any arbitrary form (e.g., by a text file). See Example Nonogram below, for an illustration. 
dataexport
: exports (saves) the data in JSON format. See Example Nonogram below, for an illustration. 
variant=<variant_name>
: the name of a variant, to be used with functionvariant()
. See Example AllInterval below, for an illustration. 
solve
: attempts to solve the instance with the embedded solver 'Ace'. It requires that Java version 8 (at least) is installed. 
solver=<solver_name>
: attempts to solve the instance with the solver whose name is given. Currently, it can be 'ace' or 'choco'. Important: it requires that Java version 8 (at least) is installed. Information about how piloting these embedded solvers can be found in this document. 
output=<file_name>
: sets the filename of the generated XCSP3 instance (think about the extension .xml)
By default, a file containing the XCSP3 instance is generated, unless you use the option:
display
: displays the XCSP3 instance in the system standard output, instead of generating an XCSP3 file
Example 1: in console mode
Our first example shows how you can build basic models in console mode. In this example, we just post two variable and two simple binary constraints.
$ python3
Python 3.5.2
>>> from pycsp3 import *
>>> x = Var(range(10))
>>> y = Var(range(10))
>>> satisfy(
x < y,
x + y > 15
)
>>> compile()
>>> if solve() is SAT:
print(value(x),value(y))
Note that to get an XCSP3 file, we call compile()
.
Example 2: Send+More=Money
This example shows how you can define a model when no data is required from the user. This is the classical cryptoarithmetic puzzle 'Send+More=Money'.
File SendMore.py
from pycsp3 import *
# letters[i] is the digit of the ith letter involved in the equation
s, e, n, d, m, o, r, y = letters = VarArray(size=8, dom=range(10))
satisfy(
# letters are given different values
AllDifferent(letters),
# words cannot start with 0
[s > 0, m > 0],
# respecting the mathematical equation
[s, e, n, d] * [1000, 100, 10, 1]
+ [m, o, r, e] * [1000, 100, 10, 1]
== [m, o, n, e, y] * [10000, 1000, 100, 10, 1]
)
To generate the XCSP3 instance (file), the command is:
python3 SendMore.py
To generate and solve (with ACE) the XCSP3 instance, the command is:
python3 SendMore.py solve
To generate and solve with Choco the XCSP3 instance, the command is:
python3 SendMore.py solver=choco
Example 3: AllInterval Series
This example shows how you can simply specify an integer (as unique data) for a model. For our illustration, we consider the problem AllInterval Series.
A classical model is:
File AllInterval.py
(version 1)
from pycsp3 import *
n = data
# 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(symmetrybreaking)
x[0] < x[n  1]
)
Note the presence of a tag symmetrybreaking
that will be directly integrated into the XCSP3 file generated by the following command:
python3 AllInterval.py data=5
Suppose that you would prefer to declare a second array of variables for representing successive distances. This would give:
File AllInterval.py
(version 2)
from pycsp3 import *
n = data
# x[i] is the ith note of the series
x = VarArray(size=n, dom=range(n))
# y[i] is the distance between x[i] and x[i+1]
y = VarArray(size=n  1, dom=range(1, n))
satisfy(
# notes must occur once, and so form a permutation
AllDifferent(x),
# intervals between neighbouring notes must form a permutation
AllDifferent(y),
# computing distances
[y[i] == abs(x[i]  x[i + 1]) for i in range(n  1)],
# tag(symmetrybreaking)
[
x[0] < x[n  1],
y[0] < y[1]
]
)
However, sometimes, it may be relevant to combine different variants of a model in the same file. In our example, this would give:
File AllInterval.py
(version 3)
from pycsp3 import *
n = data
# x[i] is the ith note of the series
x = VarArray(size=n, dom=range(n))
if not variant():
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(symmetrybreaking)
x[0] < x[n  1]
)
elif variant("aux"):
# y[i] is the distance between x[i] and x[i+1]
y = VarArray(size=n  1, dom=range(1, n))
satisfy(
# notes must occur once, and so form a permutation
AllDifferent(x),
# intervals between neighbouring notes must form a permutation
AllDifferent(y),
# computing distances
[y[i] == abs(x[i]  x[i + 1]) for i in range(n  1)],
# tag(symmetrybreaking)
[
x[0] < x[n  1],
y[0] < y[1]
]
)
For compiling the main model (variant), the command is:
python3 AllInterval.py data=5
For compiling the second model variant, using the option variant
, the command is:
python3 AllInterval.py data=5 variant=aux
To generate and solve (with ACE) the instance of order 10 and variant 'aux', the command is:
python3 AllInterval.py data=10 variant=aux solve
Example 4: BIBD
This example shows how you can specify a list of integers to be used as data for a model.
For our illustration, we consider the problem BIBD.
We need five integers v, b, r, k, l
for specifying a unique instance (possibly, b
and r
can be set to 0, so that these values are automatically computed
according to a template for this problem).
The model is:
File Bibd.py
from pycsp3 import *
v, b, r, k, l = data
b = (l * v * (v  1)) // (k * (k  1)) if b == 0 else b
r = (l * (v  1)) // (k  1) if r == 0 else r
# x[i][j] is the value of the matrix at row i and column j
x = VarArray(size=[v, b], dom={0, 1})
satisfy(
# constraints on rows
[Sum(row) == r for row in x],
# constraints on columns
[Sum(col) == k for col in columns(x)],
# scalar constraints with respect to lambda
[row1 * row2 == l for (row1, row2) in combinations(x, 2)]
)
To generate an XCSP3 instance (file), we can for example execute a command like:
python3 Bibd.py data=[9,0,0,3,9]
With some command interpreters (shells), you may have to escape the characters '[' and ']', which gives:
python3 Bibd.py data=\[9,0,0,3,9\]
Example 5: Rack Configuration
This example shows how you can specify a JSON file to be used as data for a model. For our illustration, we consider the problem Rack Configuration. The data (for a specific instance) are then initially given in a JSON file, as for example:
File Rack_r2.json
{
"nRacks": 10,
"models": [
[150, 8, 150],
[200, 16, 200]
],
"cardTypes": [
[20, 20],
[40, 8],
[50, 4],
[75, 2]
]
}
In the following model, we directly unpack the components of the variable data
(because it is automatically given under the form of a named tuple) whose
fields are exactly those of the main object in the JSON file.
File Rack.py
from pycsp3 import *
nRacks, models, cardTypes = data
models.append([0, 0, 0]) # we add first a dummy model (0,0,0)
powers, sizes, costs = zip(*models)
cardPowers, cardDemands = zip(*cardTypes)
nModels, nTypes = len(models), len(cardTypes)
T = {(i, powers[i], sizes[i], costs[i]) for i in range(nModels)}
# m[i] is the model used for the ith rack
m = VarArray(size=nRacks, dom=range(nModels))
# p[i] is the power of the model used for the ith rack
p = VarArray(size=nRacks, dom=powers)
# s[i] is the size (number of connectors) of the model used for the ith rack
s = VarArray(size=nRacks, dom=sizes)
# c[i] is the cost (price) of the model used for the ith rack
c = VarArray(size=nRacks, dom=costs)
# nc[i][j] is the number of cards of type j put in the ith rack
nc = VarArray(size=[nRacks, nTypes], dom=lambda i, j: range(min(max(sizes), cardDemands[j]) + 1))
satisfy(
# linking rack models with powers, sizes and costs
[(m[i], p[i], s[i], c[i]) in T for i in range(nRacks)],
# connectorcapacity constraints
[Sum(nc[i]) <= s[i] for i in range(nRacks)],
# powercapacity constraints
[nc[i] * cardPowers <= p[i] for i in range(nRacks)],
# demand constraints
[Sum(nc[:, j]) == cardDemands[j] for j in range(nTypes)],
# tag(symmetrybreaking)
[
Decreasing(m),
If(
m[0] == m[1],
Then=nc[0][0] >= nc[1][0]
)
]
)
minimize(
# minimizing the total cost being paid for all racks
Sum(c)
)
To generate an XCSP3 instance (file), we execute the command:
python3 Rack.py data=Rack_r2.json
One might want to have the data in the JSON file with another structure, as for example:
File Rack_r2b.json
{
"nRacks": 10,
"rackModels": [
{"power": 150, "nConnectors": 8, "price": 150},
{"power": 200, "nConnectors": 16, "price": 200}
],
"cardTypes": [
{"power": 20, "demand": 20},
{"power": 40, "demand": 8},
{"power": 50, "demand": 4},
{"power": 75, "demand": 2}
]
}
We only need to modify one line from the previous model:
File Rack2.py
models.append(models[0].__class__(0, 0, 0)) # we add first a dummy model (0,0,0) ; we get the class of the used named tuples to build a new one
To generate an XCSP3 instance (file), we execute the command:
python3 Rack2.py data=Rack_r2b.json
Example 6: Nonogram
This example shows how you can use an auxiliary Python file for parsing data that are not initially given under JSON format. For our illustration, we consider the problem Nonogram. The data (for a specific Nonogram puzzle) are initially given in a text file as follows:
 a line stating the numbers of rows and columns,
 then, for each row a line stating the number of blocks followed by the sizes of all these blocks (on the same line),
 then, for each column a line stating the number of blocks followed by the sizes of all these blocks (on the same line).
Below, here is an example of such a text file.
File Nonogram_example.txt
24 24
0
1 5
2 3 3
2 1 2
2 2 1
2 1 1
2 3 3
3 1 5 1
3 1 1 1
3 2 1 1
3 1 1 2
3 3 1 3
3 1 3 1
3 1 1 1
3 2 1 2
3 1 1 1
1 5
3 1 1 1
3 1 1 1
3 1 1 1
3 5 1 1
2 1 2
3 2 2 4
2 4 9
0
0
0
1 1
1 2
1 2
2 6 1
3 3 1 3
3 1 1 4
4 2 1 1 7
5 1 1 1 1 1
3 1 12 1
5 1 1 1 1 1
4 2 1 1 7
4 1 1 4 1
4 2 1 2 2
2 8 3
2 1 1
2 1 2
1 4
1 3
1 2
1 1
0
First, we need to write a piece of code in Python for building a dictionary data
that will be then used in our model (after having been automatically
converted to a named tuple).
We have first to import everything (*) from pycsp3.problems.data.parsing
.
We can then add any new arbitrary item to the dictionary data
(which is initially empty).
This is what we do below with two items whose keys are called rowPatterns
and colPatterns
.
The values associated with these two keys are defined as twodimensional arrays (lists) of integers, defining the sizes of blocks.
The function next_int()
can be called for reading the next integer in a text file, which will be specified on the command line (see later).
File Nonogram_Parser.py
from pycsp3.problems.data.parsing import *
nRows, nCols = next_int(), next_int()
data["rowPatterns"] = [[next_int() for _ in range(next_int())] for _ in range(nRows)]
data["colPatterns"] = [[next_int() for _ in range(next_int())] for _ in range(nRows)]
Then, we just write the model by getting data from the variable data
.
The model is totally independent of the way data were initially given (from a text file or a JSON file, for example).
In the code below, note how an object Automaton
is defined from a specified pattern (list of blocks).
Also, for a regular
constraint, we just write something like scope in automaton
.
Finally, x[:, j]
denotes the jth column of x
.
File Nonogram.py
from pycsp3 import *
rows, cols = data # patterns for row and columns
nRows, nCols = len(rows), len(cols)
def automaton(pattern):
q = Automaton.q # for building state names
transitions = []
if len(pattern) == 0:
n_states = 1
transitions.append((q(0), 0, q(0)))
else:
n_states = sum(pattern) + len(pattern)
num = 0
for i, size in enumerate(pattern):
transitions.append((q(num), 0, q(num)))
transitions.extend((q(num + j), 1, q(num + j + 1)) for j in range(size))
transitions.append((q(num + size), 0, q(num + size + (1 if i < len(pattern)  1 else 0))))
num += size + 1
return Automaton(start=q(0), final=q(n_states  1), transitions=transitions)
# x[i][j] is 1 iff the cell at row i and col j is colored in black
x = VarArray(size=[nRows, nCols], dom={0, 1})
satisfy(
[x[i] in automaton(rows[i]) for i in range(nRows)],
[x[:, j] in automaton(cols[j]) for j in range(nCols)]
)
To generate the XCSP3 instance (file), we just need to specify the name of the text file (option data
) and the name of the Python parser (
option dataparser
).
python3 Nonogram.py data=Nonogram_example.txt dataparser=Nonogram_Parser.py
Maybe, you think that it would be simpler to have directly the data in JSON file.
You can generate such a file with the option dataexport
.
The command is as follows:
python3 Nonogram.py data=Nonogram_example.txt dataparser=Nonogram_Parser.py dataexport
A file Nonogram_example.json
is generated, whose content is:
{
"colPatterns": [
[],
[],
[],
[1],
[2],
[2],
[6, 1],
[3, 1, 3],
[1, 1, 4],
[2, 1, 1, 7],
[1, 1, 1, 1, 1],
[1, 12, 1],
[1, 1, 1, 1, 1],
[2, 1, 1, 7],
[1, 1, 4, 1],
[2, 1, 2, 2],
[8, 3],
[1, 1],
[1, 2],
[4],
[3],
[2],
[1],
[]
],
"rowPatterns": [
[],
[5],
[3, 3],
[1, 2],
[2, 1],
[1, 1],
[3, 3],
[1, 5, 1],
[1, 1, 1],
[2, 1, 1],
[1, 1, 2],
[3, 1, 3],
[1, 3, 1],
[1, 1, 1],
[2, 1, 2],
[1, 1, 1],
[5],
[1, 1, 1],
[1, 1, 1],
[1, 1, 1],
[5, 1, 1],
[1, 2],
[2, 2, 4],
[4, 9]
]
}
With this new file, you can directly generate the XCSP3 file with:
python3 Nonogram.py data=Nonogram_example.json
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