ParMOO is a parallel multiobjective optimization solver that seeks to exploit simulation-based structure in objective and constraint functions.

To exploit structure, ParMOO models simulations separately from objectives and constraints. In our language:

• a design variable is an input to the problem, which we can directly control;
• a simulation is an expensive or time-consuming process, including real-world experimentation, which is treated as a blackbox function of the design variables and evaluated sparingly;
• an objective is an algebraic function of the design variables and/or simulation outputs, which we would like to optimize; and
• a constraint is an algebraic function of the design variables and/or simulation outputs, which cannot exceed a specified bound.

To solve a multiobjective optimization problem (MOOP), we use surrogate models of the simulation outputs, together with the algebraic definition of the objectives and constraints.

ParMOO is implemented in Python. In order to achieve scalable parallelism, we use libEnsemble to distribute batches of simulation evaluations across parallel resources.

ParMOO has been tested on Unix/Linux and MacOS systems.

ParMOO's base has the following dependencies:

• Python 3.9+
• jax -- for algorithmic differentiation and just-in-time (jit) compilation
• numpy -- for data structures and performant numerical linear algebra
• scipy -- for scientific calculations needed for specific modules
• pandas -- for exporting the resulting databases

Additional dependencies are needed to use the additional features in parmoo.extras:

• libEnsemble -- for managing parallel simulation evaluations

And for using the Pareto front visualization library in parmoo.viz:

• plotly -- for generating interactive plots
• dash -- for hosting interactive plots in your browser
• kaleido -- for exporting static plots post-interaction

The easiest way to install ParMOO is via the Python package index, PyPI (commonly called pip):

pip install < --user > parmoo

where the braces around < --user > indicate that the --user flag is optional.

To install all dependencies (including libEnsemble) use:

pip install < --user > "parmoo[extras]"

Note that the full feature set for libEnsemble and kaleido may require you to separately install an MPI implementation (such as Open_MPI) and Google chrome (e.g., via kaleido_get_chrome), respectively.

You can also clone this project from our GitHub and pip install it in-place, so that you can easily pull the latest version or checkout the develop branch for pre-release features. On Debian-based systems with a bash shell, this looks like:

git clone https://github.com/parmoo/parmoo
cd parmoo
pip install -e .

Alternatively, the latest release of ParMOO (including all required and optional dependencies) can be installed from the conda-forge channel using:

conda install --channel=conda-forge parmoo

Before doing so, it is recommended to create a new conda environment using:

conda create --name channel-name
conda activate channel-name

Note that in order to run the unit tests, you must first install the parmoo[extras], as described above. This may include the additional steps such as kaleido_get_chrome.

You can install pytest with the pytest-cov plugin and flake8 using the tests extension, then you can lint the project with flake8 and run the unit tests for your installation using pytest. After running unit tests, you can view the coverage report using the coverage report command.

pip install -e ".[tests]"
flake8 parmoo
pytest
coverage report

Running the regression tests and libensemble tests is a bit more involved and is usually accomplished via the -l flag for the parmoo/tests/run-tests.sh script.

To run all the linter, unit tests, regression tests, and generate the coverage report in a single command, run the script with all 4 flags set.

These tests are run regularly using GitHub Actions.

ParMOO uses numpy and jax in an object-oriented design, based around the MOOP class.

Before getting started, note that jax runs in single (32-bit) precision by default. To run in double precision, the following code is needed at startup:

import jax
jax.config.update("jax_enable_x64", True)

This will be done automatically when importing certain modules in ParMOO, which are only compatible with double precision. However, in many use cases, 32-bit precision may be enough and provides substantial speedup in iteration tasks.

Once the precision is set, to get started, create a MOOP object.

from parmoo import MOOP
from parmoo.optimizers import LocalGPS

my_moop = MOOP(LocalGPS)

To summarize the framework, in each iteration ParMOO models each simulation using a computationally cheap surrogate, then solves one or more scalarizations of the objectives, which are specified by acquisition functions. Read more about this framework at our ReadTheDocs page. In the above example, LocalGPS is the class of optimizers that the my_moop will use to solve the scalarized surrogate problems.

Next, add design variables to the problem as follows using the MOOP.addDesign(*args) method. In this example, we define one continuous and one categorical design variable. Other options include integer, custom, and raw (using raw variables is not recommended except for expert users).

# Add a single continuous design variable in the range [0.0, 1.0]
my_moop.addDesign({'name': "x1", # optional, name
                   'des_type': "continuous", # optional, type of variable
                   'lb': 0.0, # required, lower bound
                   'ub': 1.0, # required, upper bound
                   'tol': 1.0e-8 # optional tolerance
                  })
# Add a second categorical design variable with 3 levels
my_moop.addDesign({'name': "x2", # optional, name
                   'des_type': "categorical", # required, type of variable
                   'levels': ["good", "bad"] # required, category names
                  })

Next, add simulations to the problem as follows using the MOOP.addSimulation method. In this example, we define a toy simulation sim_func(x).

import numpy as np
from parmoo.searches import LatinHypercube
from parmoo.surrogates import GaussRBF

# Define a toy simulation for the problem, whose outputs are quadratic
def sim_func(x):
   if x["x2"] == "good":
      return np.array([(x["x1"] - 0.2) ** 2, (x["x1"] - 0.8) ** 2])
   else:
      return np.array([99.9, 99.9])
# Add the simulation to the problem
my_moop.addSimulation({'name': "MySim", # Optional name for this simulation
                       'm': 2, # This simulation has 2 outputs
                       'sim_func': sim_func, # Our sample sim from above
                       'search': LatinHypercube, # Use a LHS search
                       'surrogate': GaussRBF, # Use a Gaussian RBF surrogate
                       'hyperparams': {}, # Hyperparams passed to internals
                       'sim_db': { # Optional dict of precomputed points
                                  'search_budget': 10 # Set search budget
                                 },
                      })

Now we can add objectives and constraints using MOOP.addObjective(*args) and MOOP.addConstraint(*args). In this example, there are 2 objectives (each corresponding to a single simulation output) and one constraint.

# First objective just returns the first simulation output
def f1(x, s): return s["MySim"][0]
my_moop.addObjective({'name': "f1", 'obj_func': f1})
# Second objective just returns the second simulation output
def f2(x, s): return s["MySim"][1]
my_moop.addObjective({'name': "f2", 'obj_func': f2})
# Add a single constraint, that x[0] >= 0.1
def c1(x, s): return 0.1 - x["x1"]
my_moop.addConstraint({'name': "c1", 'constraint': c1})

Finally, we must add one or more acquisition functions using MOOP.addAcquisition(*args). These are used to scalarize the surrogate problems. The number of acquisition functions typically determines the number of simulation evaluations per batch. This is useful to know if you are using a parallel solver.

from parmoo.acquisitions import RandomConstraint

# Add 3 acquisition functions
for i in range(3):
   my_moop.addAcquisition({'acquisition': RandomConstraint,
                           'hyperparams': {}})

Finally, the MOOP is solved using the MOOP.solve(budget) method, and the results can be viewed using MOOP.getPF() method.

import pandas as pd

my_moop.solve(5) # Solve with 5 iterations of ParMOO algorithm
results = my_moop.getPF(format="pandas") # Extract the results as pandas df

After executing the above block of code, the results variable points to a pandas dataframe, each of whose rows corresponds to a nondominated objective value in the my_moop object's final database. You can reference individual columns in the results array by using the name keys that were assigned during my_moop's construction, or plot the results by using the viz library.

Congratulations, you now know enough to get started solving MOOPs with ParMOO!

Next steps:

• Learn more about all that ParMOO has to offer (including saving and checkpointing, INFO-level logging, advanced problem definitions, and different surrogate and solver options) at our ReadTheDocs page.
• Explore the advanced examples (including a libEnsemble example) in the examples directory.
• Install libEnsemble and get started solving MOOPs in parallel.
• See some of our pre-built solvers in the parmoo_solver_farm.
• To interactively explore your solutions, install its extra dependencies and use our built-in viz tool.
• For more advice, consult our FAQs.

To seek support or report issues, e-mail:

• parmoo@lbl.gov

Our full documentation is hosted on:

• ReadTheDocs

Recent versions of ParMOO are also incorporated in:

• BANDFramework

Please read our LICENSE and CONTRIBUTING files.

Please use one or more of the following to cite ParMOO.

Our JOSS paper:

@article{parmoo,
    author={Chang, Tyler H. and Wild, Stefan M.},
    title={{ParMOO}: A {P}ython Library for Parallel Multiobjective Simulation Optimization},
    journal = {Journal of Open Source Software},
    volume = {8},
    number = {82},
    pages = {4468},
    year = {2023},
    doi = {10.21105/joss.04468}
}

Our online documentation:

@techreport{parmoo-docs,
    title       = {{ParMOO}: {P}ython Library for Parallel Multiobjective Simulation Optimization},
    author      = {Chang, Tyler H. and Wild, Stefan M. and Dickinson, Hyrum},
    institution = {Argonne National Laboratory},
    number      = {Version 0.5.1},
    year        = {2026},
    url         = {https://parmoo.readthedocs.io/en/latest}
}

Our design principles paper:

@article{ParMOODesign25,
    title = {Designing a Framework for Solving Multiobjective Simulation Optimization Problems},
    author = {Tyler H. Chang and Stefan M. Wild},
    journal = {INFORMS Journal on Computing},
    year = {2026},
    doi = {10.1287/ijoc.2023.0250},
    arxivnumber = {2304.06881},
    note = {To appear}
}