Rhodium is an open source Python library for robust decision making (RDM) and multiobjective robust decision making (MORDM), and exploratory modelling (EM).
Please cite the following paper (PDF) if using this project in your own works:
Hadjimichael A, et al. 2020 Rhodium: Python Library for Many-Objective Robust Decision Making and Exploratory Modeling. Journal of Open Research Software, 8: 12. DOI: https://doi.org/10.5334/jors.293
To install the latest Rhodium release, run the following command:
pip install rhodium
To install the latest development version of Rhodium, run the following commands:
pip install -U build setuptools
git clone https://github.com/Project-Platypus/Rhodium.git
cd Rhodium
python -m build
python -m pip install --editable .
Rhodium has several optional dependencies that enable additional graphical and analytical capabilities.
- GraphViz - Required for CART figures (
Cart#show_tree) pip install pywin32- Required to connect to Excel models (ExcelModel)pip install openmdao- Required to connect to OpenMDAO models (OpenMDAOModel)pip install pyper- Required to connect to R models (RModel)pip install images2gif- Required to produce 3D animated GIFs (animate3d)- J3Py - Interactive 3D visualizations
Robust Decision Making (RDM) is an analytic framework developed by Robert Lempert and his collaborators at RAND Corporation that helps identify potential robust strategies for a particular problem, characterize the vulnerabilities of such strategies, and evaluate trade-offs among them [2]. Multiobjective Robust Decision Making (MORDM) is an extension of RDM to account for problems with multiple competing performance objectives, enabling the exploration of performance tradeoffs with respect to robustness [3, 4].
Rhodium is an open source Python library providing methods for RDM and MORDM. It follows a declarative design, where you tell Rhodium the actions or analyses you wish to perform and it determines the necessary calculations. Rhodium can interface with models written in a variety of languages, including Python, C and Fortran, R, and Excel. One begins by creating a Rhodium model:
from rhodium import *
def lake_problem(pollution_limit,
b = 0.42, # decay rate for P in lake (0.42 = irreversible)
q = 2.0, # recycling exponent
mean = 0.02, # mean of natural inflows
stdev = 0.001, # standard deviation of natural inflows
alpha = 0.4, # utility from pollution
delta = 0.98, # future utility discount rate
nsamples = 100): # monte carlo sampling of natural inflows
# add body of function
return (max_P, utility, inertia, reliability)
model = Model(lake_problem)
model.parameters = [Parameter("pollution_limit"),
Parameter("b"),
Parameter("q"),
Parameter("mean"),
Parameter("stdev"),
Parameter("delta")]
model.responses = [Response("max_P", Response.MINIMIZE),
Response("utility", Response.MAXIMIZE),
Response("inertia", Response.MAXIMIZE),
Response("reliability", Response.MAXIMIZE)]
model.constraints = [Constraint("reliability >= 0.95")]
model.levers = [RealLever("pollution_limit", 0.0, 0.1, length=100)]
model.uncertainties = [UniformUncertainty("b", 0.1, 0.45),
UniformUncertainty("q", 2.0, 4.5),
UniformUncertainty("mean", 0.01, 0.05),
UniformUncertainty("stdev", 0.001, 0.005),
UniformUncertainty("delta", 0.93, 0.99)]A Rhodium model consists of 6 parts:
-
The underlying model (in this case, the Python function
lake_problem). -
model.parameters- the parameters of interest. -
model.responses- the model responses or outputs. -
model.constraints- any hard constraints that must be satisfied. -
model.levers- parameters that we have direct control over. -
model.uncertainties- parameters that represent exogeneous uncertainties.
Once the Rhodium model is defined, you can then perform any analysis. For example, if we want to optimize the model and display the Pareto front:
output = optimize(model, "NSGAII", 10000)
scatter3d(model, output)
plt.show()Check out the examples folder to see Rhodium in action!
To publish a new version to PyPI, use:
python3 -m build
python3 -m pip install --upgrade twine
# The following command publishes the build. Add `--repository testpypi` for testnig.
# Use `__token__` for the username and the PyPI token to authenticate.
python3 -m twine upload dist/*- Rhodium logo by Tyler Glaude, Creative Commons License, https://thenounproject.com/term/knight/30912/
- Lempert, R. J., D. G. Groves, S. W. Popper, and S. C. Bankes (2006). A General, Analytic Method for Generating Robust Strategies and Narrative Scenarios. Management Science, 52(4):514-528.
- Kasprzyk, J. R., S. Nataraj, P. M. Reed, and R. J. Lempert (2013). Many objective robust decision making for complex environmental systems undergoing change. Environmental Modelling & Software, 42:55-71.
- Hadka, D., Herman, J., Reed, P.M., Keller, K. An Open Source Framework for Many-Objective Robust Decision Making. Environmental Modelling & Software, 74:114-129, 2015. DOI:10.1016/j.envsoft.2015.07.014. (View Online)
- Hadjimichael A, et al. 2020 Rhodium: Python Library for Many-Objective Robust Decision Making and Exploratory Modeling. Journal of Open Research Software, 8: 12. DOI: https://doi.org/10.5334/jors.293
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