Parallel Implementation

Parallel implementation in parmest is preliminary. To run parmest in parallel, you need the mpi4py Python package and a compatible MPI installation. If you do NOT have mpi4py or a MPI installation, parmest still works (you should not get MPI import errors).

For example, the following command can be used to run the semibatch model in parallel:

mpiexec -n 4 python

The file is shown below. Results are saved to file for later analysis.

#  ___________________________________________________________________________
#  Pyomo: Python Optimization Modeling Objects
#  Copyright (c) 2008-2022
#  National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________

The following script can be used to run semibatch parameter estimation in 
parallel and save results to files for later analysis and graphics.
Example command: mpiexec -n 4 python
import numpy as np
import pandas as pd
from itertools import product
from os.path import join, abspath, dirname
import pyomo.contrib.parmest.parmest as parmest
from pyomo.contrib.parmest.examples.semibatch.semibatch import generate_model

def main():
    # Vars to estimate
    theta_names = ['k1', 'k2', 'E1', 'E2']
    # Data, list of json file names
    data = [] 
    file_dirname = dirname(abspath(str(__file__)))
    for exp_num in range(10):
        file_name = abspath(join(file_dirname, 'exp'+str(exp_num+1)+'.out'))
    # Note, the model already includes a 'SecondStageCost' expression 
    # for sum of squared error that will be used in parameter estimation
    pest = parmest.Estimator(generate_model, data, theta_names)
    ### Parameter estimation with bootstrap resampling
    bootstrap_theta = pest.theta_est_bootstrap(100)
    ### Compute objective at theta for likelihood ratio test
    k1 = np.arange(4, 24, 3)
    k2 = np.arange(40, 160, 40)
    E1 = np.arange(29000, 32000, 500)
    E2 = np.arange(38000, 42000, 500)
    theta_vals = pd.DataFrame(list(product(k1, k2, E1, E2)), columns=theta_names)
    obj_at_theta = pest.objective_at_theta(theta_vals)

if __name__ == "__main__":


The mpi4py Python package should be installed using conda. The following installation instructions were tested on a Mac with Python 3.5.

Create a conda environment and install mpi4py using the following commands:

conda create -n parmest-parallel python=3.5
source activate parmest-parallel
conda install -c conda-forge mpi4py

This should install libgfortran, mpi, mpi4py, and openmpi.

To verify proper installation, create a Python file with the following:

from mpi4py import MPI
import time
rank = comm.Get_rank()
print('Rank = ',rank)

Save the file as and run the following command:

time mpiexec -n 4 python
time python

The first one should be faster and should start 4 instances of Python.