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Mathematical Modeling for Optimization and Machine Learning

Created by Hassan Hijazi -


Gravity is licensed under the BSD 3-Clause License. Please see the LICENSE file for details.


The original paper was presentend at the Machine Learning Open Source Software Workshop at NeurIPS 2018, a longer version of the paper can be downloaded here.

Bibtex ref: @article{Gravity, title={Gravity: A Mathematical Modeling Language for Optimization and Machine Learning}, author={Hassan Hijazi and Guanglei Wang and Carleton Coffrin}, journal={Machine Learning Open Source Software Workshop at NeurIPS 2018}, year={2018}, note = {Available at \url{}.}, publisher={The Thirty-second Annual Conference on Neural Information Processing Systems (NeurIPS)} }


See the list of contributors here

Getting Started

First, you will need to install an IDE, I recommend to choose among the following:

|| || ||

Then, follow the instructions presented in

After building, the Gravity library can be found under Gravity/lib, and the executables (from Gravity/examples) can be found under Gravity/bin/Release

The model below was implemented in Xcode:


Some Numerical Results:

Performance Profile on ACOPF

The first figure below is a performance profile illustrating percentage of instances solved as a function of time. The figure compares Gravity, JuMP and AMPL's NL interface (used by AMPL and Pyomo) on all standard instances found in the PGLIB benchmark library.

Performance Profile on ACOPF

The figure below compares model build time between Gravity and JuMP on the PGLIB benchmarks.

Model Build Time on ACOPF

Performance Profile on Inverse Ising Model

Performance Profile on Inverse Ising

Click here for more details.