Surrogate model example

This GAMSPy example shows how to embed a trained neural network into a GAMSPy optimization model (a mixed-integer linear program in this case) by utilizing the new sub-package formulations in GAMSPy.

More infos and examples on machine learning related capabilities of GAMSPy can be found in the GAMSPy user guide section on GAMSPy and machine learning.

Quick start

If needed, setup a virtual environment or switch into a pre-existing one and install all packages from requirements.txt.

Spells to install from scratch with only a Python interpreter installed (tested with 3.12):

python -m venv venv
source venv/bin/activate # or use .ps1 script on Windows
pip install -r requirements.txt
python main.py

The NN is trained on the first run and saved to disk as rs.pth. Subsequent runs skip the training and only solve the optimization model.

Model formulation

The objective function computes the total cost incurred by the choice of reactor $r$ and selector $s$ plus the cost for the input material flow rate $F_a$. The first constraints ensure exactly one reactor and exactly one separator is chosen. Following equation links the auxiliary variable $V$ for the available volume with the volume of the chosen reactor. The next constraint uses the embedded NN to predict a feasibility probability for a given tuple of reactor volume $V$, input flow rate $F_a$ and output material flow rate demands $F_B$ and $F_E$. The feasibility prediction acquired through NN inference must be at least 99%. Subsequent equations make sure the input material flow rate is inside the operational bounds of the chosen selector using a bigM-formulation. The decision variable domains are declared such that the input material flow rate and available volume auxiliary variable are continuous, and the reactor- $y_r$ and selector-choice $y_s$ indicator variables are binary.

To solve the model with a MILP solver, the parameterized NN term $NN$ in must be expanded into a set of additional constraints and variables, such that the left-hand side of evaluates to the value acquired by doing a forward propagation of input vector $(V,F_a,F_B,F_E)$ through the network layers. The NN is sequential and consists of 4 linear layers connected with ReLU and sigmoid as activation functions for the inner layers and output layer respectively.