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

Branch-and-Cut-and-Price for Multi-Agent Path Finding. Edward Lam, Pierre Le Bodic, Daniel Harabor and Peter J. Stuckey. Computers & Operations Research, vol. 144, pp. 105809. 2022.

Please cite this article if you use this code for the multi-agent path finding problem or as a template for other branch-and-cut-and-price codes.

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 to run on Mac and Linux. It has not been tested on Windows.

BCP uses SCIP 7.0.3 for branch-and-bound. Source code to SCIP is available free (as in 🍺) for academic use. BCP calls Gurobi or CPLEX for solving the linear relaxation. Gurobi and CPLEX are commercial software but provide free binaries under an academic license. BCP is tested with Gurobi 10.0.1 and CPLEX 20.1.0.

1. Download the source code to BCP-MAPF by cloning this repository and all its submodules.

git clone --recurse-submodules https://github.com/ed-lam/bcp-mapf.git
cd bcp-mapf

2. Download the SCIP Optimization Suite 7.0.3 into the bcp-mapf directory and extract it. You should find the subdirectory scipoptsuite-7.0.3/scip/src.

tar xf scipoptsuite-7.0.3.tgz

3. Download the Boost C++ libraries if not already provided by your system.

wget https://boostorg.jfrog.io/artifactory/main/release/1.79.0/source/boost_1_79_0.tar.gz
tar xf boost_1_79_0.tar.gz

4. Compile BCP-MAPF.

   1. If using Gurobi, locate its directory, which should contain the include and lib subdirectories. Copy the main directory into the command below.

   cmake -DGUROBI_DIR={PATH TO GUROBI DIRECTORY} .
   cmake --build .
   

   2. If using CPLEX, locate the subdirectory cplex and copy this directory into the command below.

   cmake -DCPLEX_DIR={PATH TO cplex SUBDIRECTORY} .
   cmake --build .
   

   If Boost is missing, download Boost in step 3 and append -DBOOST_ROOT={PATH TO BOOST DIRECTORY} to the first cmake command above.

   To compile with a multi-core CPU with N cores, append -j N to the second cmake command above.

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}

BCP can be run as a bounded suboptimal algorithm by setting an optimality gap. For example, enter 0.1 for a 10% optimality gap.

./bcp-mapf —-gap-limit={OPTIMALITY GAP} {PATH TO INSTANCE}

The Moving AI benchmarks can be found in the instances/movingai directory. 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 --agent-limit=50 instances/movingai/Berlin_1_256-random-1.scen

The optimal solution (or feasible solution if a time limit or gap limit is reached) 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 ed-lam.com.