Exact

Exact solves decision and optimization problems formulated as integer linear programs. Under the hood, it converts integer variables to binary (0-1) variables and applies highly efficient propagation routines and strong cutting-planes / pseudo-Boolean conflict analysis.

Exact is a fork of RoundingSat and improves upon its predecessor in reliability, performance and ease-of-use. In particular, Exact supports integer variables, reified linear constraints, multiplication constraints, and propagation and count inferences. The name "Exact" reflects that the answers are fully sound, as approximate and floating-point calculations only occur in heuristic parts of the algorithm. As such, Exact can soundly be used for verification and theorem proving, where its envisioned ability to emit machine-checkable certificates of optimality and unsatisfiability should prove useful.

Features

• Native conflict analysis over binary linear constraints, constructing full-blown cutting planes proofs.
• Highly efficient watched propagation routines.
• Fine-grained employment of arbitrary precision calculations - only when needed.
• Hybrid linear (top-down) and core-guided (bottom-up) optimization.
• Optional integration with the SoPlex LP solver.
• Core solver also compiles on macOS and Windows.
• Python interface with assumption solving and reuse of solver state (Linux only for now).
• Generation of certificates of optimality and unsatisfiability that can be automatically verified by VeriPB.
• Excellent performance, as showcased in 2024's PB competition.

Python interface

PyPI package

The easiest way is to use Exact's Python interfaces is on an x86_64 machine with Windows or Linux. In that case, install this precompiled PyPi package, e.g., by running pip install exact.

Compile your own Python package

To use the Exact Python interface with optimal binaries for your machine (and the option to include SoPlex in the binary), compile as a shared library and install it with your package manager. E.g., on Linux systems, running pip install . in Exact's root directory should do the trick. On Windows, uncomment the build options below # FOR WINDOWS and comment out those for # FOR LINUX. Make sure to have the Boost libraries installed (see dependencies).

Documentation

The header file Exact.hpp contains the C++ methods exposed to Python via Pybind11 as well as their description. This is probably the best place to start to learn about Exact's Python interface.

Next, python_examples contains instructive examples. Of particular interest is the knapsack tutorial, which is fully commented, starts simple, and ends with some of Exact's advanced features.

Command line usage

Exact takes as command line input an integer linear program and outputs a(n optimal) solution or reports that none exists. Either pipe the program

cat test/instances/opb/opt/stein15.opb | build/Exact

or pass the file as a parameter

build/Exact test/instances/opb/opt/stein15.opb

Use the flag --help to display a list of runtime parameters.

Exact supports five input formats (described in more detail in InputFormats.md):

• .opb pseudo-Boolean decision and optimization (equivalent to 0-1 integer linear programming)
• .wbo weighted pseudo-Boolean optimization (0-1 integer linear programming with weighted soft constraints)
• .cnf DIMACS Conjunctive Normal Form (CNF)
• .wcnf Weighted Conjunctive Normal Form (WCNF)
• .mps Mathematical Programming System (MPS) via the optional CoinUtils library
• .lp Linear Program (LP) via the optional CoinUtils library

Note that .mps and .lp allow rational variables, which are not supported by Exact. Additionally, these formats permit floating point values, which may lead to tricky issues. Rewrite constraints with fractional values to integral ones by multiplying with the lowest common multiple of the denominators.

By default, Exact decides on the format based on the filename extension, but this can be overridden with the --format option.

Compilation from source

In the root directory of Exact:

cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make

Replace make by cmake --build . on Windows. For more builds, similar build directories can be created.

For installing system-wide or to the CMAKE_INSTALL_PREFIX root, use make install (on Linux).

Dependencies

• A recent C++20 compiler (GCC, Clang or MSVC should do)
• Boost library, minimal version 1.65. On a Debian/Ubuntu system, install with sudo apt install libboost-dev. On Windows, follow the instructions on boost.org
• Optionally: CoinUtils library to parse MPS and LP file formats. Use CMake option -Dcoinutils=ON after installing the library.
• Optionally: SoPlex LP solver (see below).

SoPlex (on Linux)

Exact supports an integration with the LP solver SoPlex to improve its search routine. For this, checkout SoPlex from its git repository as a submodule, compile it in some separate directory, and configure the right CMake options when compiling Exact.

By default, the following commands in Exact's root directory should work with a freshly checked out repository:

    git submodule init
    git submodule update

    mkdir soplex_build
    cd soplex_build
    cmake ../soplex -DBUILD_TESTING="0" -DSANITIZE_UNDEFINED="0" -DCMAKE_BUILD_TYPE="Release" -DBOOST="0" -DGMP="0" -DCMAKE_WINDOWS_EXPORT_ALL_SYMBOLS="0" -DZLIB="0"
    make -j 8

    cd ../build
    cmake .. -DCMAKE_BUILD_TYPE="Release" -Dsoplex="ON"
    make -j 8

The CMake options soplex_src and soplex_build allow to look for SoPlex in a different location.

License

Exact is licensed under the AGPLv3. If this would hinder your intended usage, please contact @JoD.

Benchmarks

The current set of benchmarks which is used to assess performance is available here.

Citations

If you use Exact, please star and cite this repository and cite the RoundingSat origin paper (which focuses on cutting planes conflict analysis):
[EN18] J. Elffers, J. Nordström. Divide and Conquer: Towards Faster Pseudo-Boolean Solving. IJCAI 2018

Please cite any of the following papers if they are relevant.

Integration with SoPlex:
[DGN20] J. Devriendt, A. Gleixner, J. Nordström. Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search. CPAIOR 2020 / Constraints journal

Watched propagation:
[D20] J. Devriendt. Watched Propagation for 0-1 Integer Linear Constraints. CP 2020

Core-guided optimization:
[DGDNS21] J. Devriendt, S. Gocht, E. Demirović, J. Nordström, P. J. Stuckey. Cutting to the Core of Pseudo-Boolean Optimization: Combining Core-Guided Search with Cutting Planes Reasoning. AAAI 2021

Industrial use cases

After considering Gurobi and OR-tools to extract minimal unsatisfiable subsets for a workforce allocation problem, a big European airplane manufacturer decided Exact was the way to go! (mirror)