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BCP-MAPF – branch-and-cut-and-price for multi-agent path finding
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BCP is an implementation of a branch-and-cut-and-price model of the multi-agent path finding problem. It is described in the following papers:

  • Branch-and-Cut-and-Price for Multi-Agent Pathfinding. E. Lam, P. Le Bodic, D. Harabor, P. J. Stuckey. IJCAI 2019.
  • New Valid Inequalities in Branch-and-Cut-and-Price for Multi-Agent Path Finding. E. Lam, P. Le Bodic. ICAPS 2020.

If you use this code, please cite these articles.


BCP is released under the GPL version 3. See LICENSE.txt for further details.


BCP is implemented in C++17 and is compiled using CMake, so you will need a recent compiler and a recent version of CMake. It is tested with Clang 9 on Mac and GCC 8 on Linux. It has not been tested on Windows.

BCP calls SCIP for branch-and-bound and calls CPLEX for solving the linear relaxation.

Source code to SCIP is available free (as in beer) strictly for academic use. BCP is tested with SCIP 6.0.2. Download the SCIP Optimization Suite 6.0.2 and extract it into the root of this repository. You should find the subdirectory scipoptsuite-6.0.2/scip/src.

CPLEX is commercial software but has binaries available free under an academic license. BCP is tested with CPLEX 12.9. You should find the subdirectory cplex.

If CPLEX is not available, SoPlex from the SCIP Optimization Suite can be used instead but this option is not supported.


Download the source code by cloning this Git repository and all its submodules:

git clone --recurse-submodules

Locate the cplex subdirectory inside wherever you downloaded the CPLEX binaries. Compile BCP using CMake:

cd bcp-mapf
mkdir build
cd build
cmake --build .

If you use a custom compiler, you will need to tell CMake where the compiler is:


If you have a multi-core CPU with N cores, you can perform a parallel compile by running the following command instead, replacing N with the number of cores:

cmake --build . -j N


After compiling, run BCP with:

./bcp-mapf {PATH TO INSTANCE}

You can also set a time limit in seconds:

./bcp-mapf —-time-limit={TIME LIMIT} {PATH TO INSTANCE}

Benchmark instances can be found in the 2018_instances and 2019_instances directories. Example:

./bcp-mapf --time-limit=30 ../instances/movingai_2018/dao_maps/lak503dmap-100agents-49.scen

The 2019 instances are organised differently. There is (usually) a total of 1000 agents in each instance file, and the user can specify how many of the first N agents to run. For example, you can run an instance with only the first 50 agents:

./bcp-mapf --time-limit=30 --agents-limit=50 ../instances/movingai_2019/den520d-random-1.scen

The optimal solution (or feasible solution if timed out) will be saved into the outputs directory.


We welcome code contributions and scientific discussion subject to Monash University’s equal opportunity and harassment policies.


BCP is invented by Edward Lam with assistance from Pierre Le Bodic, Daniel Harabor and Peter J. Stuckey. Edward can be reached at

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