# Distributed Mixed-Integer Programming (MIP) optimization with Cplex and Gurobi

Cplex is an optimization software for mathematical programming. The Cplex optimizer can solve:

• Mixed-Integer programming problems (MIP)
• Very large linear programming problems (LP)
• Non-convex quadratic programming problems (QP)
• Convex quadratically constrained problems (QCP)

Gurobi is a powerful optimization software and an alternative to Cplex for solving. Gurobi has some additionnal features compared to Cplex. For example, it can perform Mixed-Integer Quadratic Programming (MIQP) and Mixed-Integer Quadratic Constrained Programming (MIQCP).

In this tutorial, we are going to see how to leverage distributed optimization on a High Computing Platform such as Slurm.

## Mathematical programming

Decision and optimization problems can be representend as mathematical models called programs.

It exists several formats used by Cplex and Gurobi to provide your problems to these solvers:

## Using both optimization software on the ULHPC platform

The cplex optimizer can be accessed throught the module command once ressources have been requested through the SLURM scheduler.

module load math/CPLEX/12.8-foss-2018a


The Gurobi optimizer can be accessed throught the module command once ressources have been requested through the SLURM scheduler.

module load math/Gurobi/8.1.1-intel-2018a-Python-3.6.4


The resolution of optmization problem can be either done using the command line interface (CLI) or by using the different APis (e.g. C/C++, Python, Java). In this tutorial, we only consider the CLI for each optimizer.

## Ressources for this tutorial

In order to test cplex and gurobi, we need an optimization instance. Hereafter, we are going to rely on instances from the miplib. For example, let us the following instance ex10.mps.gz described in details here for the interested readers.

If you did not already clone the tutorial repository, enter the following commands in your HOME directory:

# cd into scratch and clone tutorial repository
cd $SCRATCH git clone https://github.com/ULHPC/tutorials.git # cd into the scripts folder cd tutorials/maths/Cplex-Gurobi/scripts  ## Cplex ### Multi-threaded optimization with Cplex In order to solve mathematical programs, cplex allows users to define a command line script that can be passed to the executable. On the Iris cluster, the following launcher can be used to perform multi-threaded MIP optimzation. A good practice is to request as many threads as available cores on the node. If you need more computing power, you have to consider a distributed version. #!/bin/bash -l #SBATCH -J Multi-threaded_cplex #SBATCH --ntasks=1 #SBATCH --cpus-per-task=28 #SBATCH --time=0-01:00:00 #SBATCH -p batch #SBATCH --qos=normal # Load cplex module load math/CPLEX/12.8-foss-2018a # Some variable MPS_FILE=$1
RES_FILE=$2 CPLEX_COMMAND_SCRIPT="command_job${SLURM_JOBID}.lst"

# Create cplex command script
cat << EOF > ${CPLEX_COMMAND_SCRIPT} set threads${SLURM_CPUS_PER_TASK}
read ${MPS_FILE} mipopt write "${RES_FILE}.sol"
quit
EOF
chmod +x ${CPLEX_COMMAND_SCRIPT} # Cplex will access use the required number of thread cplex -f${CPLEX_COMMAND_SCRIPT}
rm ${CPLEX_COMMAND_SCRIPT}  Use the script cplex_mtt.slurm and launch a batch job using the sbatch command as follows sbatch cplex_mtt.slurm ex10.mps.gz cplex_mtt. ### Distributed optimization with Cplex When you require more computing power (e.g. more cores), distributed computations is the way to go. The cplex optimization software embeds a feature that allows you to perform distributed MIP. Using the Message Passing Interface (MPI), cplex will distribute the exploration of the tree search to multiple workers. The below launcher is an example showing how to reserve ressources on multiple nodes through the Slurm scheduler. In this example, 31 tasks will be distributed over 2 nodes. #!/bin/bash -l #SBATCH -J Distrbuted_cplex #SBATCH --nodes=2 #SBATCH --ntasks=14 #SBACTH --cpus-per-task=2 #SBATCH --time=0-01:00:00 #SBATCH -p batch #SBATCH --qos=normal module load math/CPLEX/12.8-foss-2018a # Some variables MPS_FILE=$1
RES_FILE=$2 CPLEX_COMMAND_SCRIPT="command_job${SLURM_JOBID}.lst"

# Create cplex command script
cat << EOF > ${CPLEX_COMMAND_SCRIPT} set distmip config mpi set threads${SLURM_CPUS_PER_TASK}
read ${MPS_FILE} mipopt write "${RES_FILE}.sol"
quit
EOF
chmod +x ${CPLEX_COMMAND_SCRIPT} # Start Cplex with MPI # On first host, the master is running mpirun -np 1 cplex -f${CPLEX_COMMAND_SCRIPT} -mpi : -np $((SLURM_NTASKS - 1)) cplex -mpi rm${CPLEX_COMMAND_SCRIPT}


Use the script cplex_dist.slurm and launch a batch job using the sbatch command as follows sbatch cplex_dist.slurm ex10.mps.gz cplex_dist.

## Gurobi

The script below allows you to start multi-threaded MIP optimization with Gurobi.

#!/bin/bash -l
#SBATCH --time=0-01:00:00
#SBATCH -p batch
#SBATCH --qos=normal

# Some variable
MPS_FILE=$1 RES_FILE=$2

# Gurobi will access use the required number of thread
gurobi_cl Threads=${SLURM_CPUS_PER_TASK} ResultFile="${RES_FILE}.sol" ${MPS_FILE}  Use the script gurobi_mtt.slurm and launch a batch job using the sbatch command as follows sbatch gurobi_mtt.slurm ex10.mps.gz gurobi_mtt. ### Distributed optimization with Gurobi #!/bin/bash -l #SBATCH -J Distrbuted_gurobi #SBATCH --ntasks=3 #SBATCH --ntasks-per-node=1 #SBATCH --cpus-per-task=5 #SBATCH --time=00:15:00 #SBATCH -p batch #SBATCH --qos normal #SBATCH -o %x-%j.log # Load personal modules mu # Load gurobi module load math/Gurobi/8.1.1-intel-2018a-Python-3.6.4 export MASTER_PORT=61000 export SLAVE_PORT=61000 export MPS_FILE=$1
export RES_FILE=$2 export GUROBI_INNER_LAUNCHER="inner_job${SLURM_JOBID}.sh"

if [[ -f "grb_rs.cnf" ]];then
sed -i "s/^THREADLIMIT.*$/THREADLIMIT=${SLURM_CPUS_PER_TASK}/g" grb_rs.cnf
else
$GUROBI_REMOTE_BIN_PATH/grb_rs init echo "THREADLIMIT=${SLURM_CPUS_PER_TASK}" >> grb_rs.cnf
fi

cat << 'EOF' > ${GUROBI_INNER_LAUNCHER} #!/bin/bash MASTER_NODE=$(scontrol show hostname ${SLURM_NODELIST} | head -n 1) ## Load configuration and environment if [[${SLURM_PROCID} -eq 0 ]]; then
## Start Gurobi master worker in background
$GUROBI_REMOTE_BIN_PATH/grb_rs --worker --port${MASTER_PORT} &
wait
elif [[ ${SLURM_PROCID} -eq 1 ]]; then sleep 5 grbcluster nodes --server${MASTER_NODE}:${MASTER_PORT} gurobi_cl Threads=${SLURM_CPUS_PER_TASK} ResultFile="${RES_FILE}.sol" Workerpool=${MASTER_NODE}:${MASTER_PORT} DistributedMIPJobs=$((SLURM_NNODES -1)) ${MPS_FILE} else sleep 2 ## Start Gurobi slave worker in background$GUROBI_REMOTE_BIN_PATH/grb_rs --worker --port ${MASTER_PORT} --join${MASTER_NODE}:${MASTER_PORT} & wait fi EOF chmod +x${GUROBI_INNER_LAUNCHER}

## Launch Gurobi and wait for it to start
srun ${GUROBI_INNER_LAUNCHER} & while [[ ! -e "${RES_FILE}.sol" ]]; do
sleep 5
done
rm \${GUROBI_INNER_LAUNCHER}


Use the script gurobi_dist.slurm and launch a batch job using the sbatch command as follows sbatch gurobi_dist.slurm ex10.mps.gz gurobi_dist.

## Next

1. Download and try to solve other miplib instances using Cplex and/or Gurobi
2. Modify the number of parallel tasks