OptiCL is an end-to-end framework for mixed-integer optimization (MIO) with data-driven learned constraints. We address a problem setting in which a practitioner wishes to optimize decisions according to some objective and constraints, but that we have no known functions relating our decisions to the outcomes of interest. We propose to learn predictive models for these outcomes using machine learning, and to subsequently optimize decisions by embedding the learned models in a larger MIO formulation.

The framework and full methodology are detailed in our manuscript, Mixed-Integer Optimization with Constraint Learning.

You can install the OptiCL package locally by cloning the repository and running pip install . within the home directory of the repo. This will allow you to load opticl in Python; see the example notebooks for specific usage of the functions.

Our pipeline requires two inputs from a user:

• Training data, with features classified as contextual variables, decisions, and outcomes.
• An initial conceptual model, which is defined by specifying the decision variables and any domain-driven fixed constraints or deterministic objective terms.

Given these inputs, we implement a pipeline that:

1. Learns predictive models for the outcomes of interest by using a moel training and selection pipeline with cross-validation.
2. Efficiently charactertizes the feasible decision space, or "trust region," using the convex hull of the observed data.
3. Embeds the learned models and trust region into a MIO formulation, which can then be solved using a Pyomo-supported MIO solver (e.g., Gurobi).

OptiCL requires no manual specification of a trained ML model, although the end-user can optionally restrict to a subset of model types to be considered in the selection pipeline. Furthermore, we expose the underlying trained models within the pipeline, providing transparency and allowing for the predictive models to be externally evaluated.

We illustrate the full OptiCL pipeline in three notebooks:

• A case study on food basket optimization for the World Food Programme (notebooks/WFP/The Palatable Diet Problem.ipynb): This notebook presents a simplified version of the case study in the manuscript. It shows how to train and select models for a single learned outcome, define a conceptual model with a known objective and constraints, and solve the MIO with an additional learned constraint.
• A general pipeline overview (notebooks/Pipeline/Model_embedding.ipynb): This notebook demonstrates the general features of the pipleine, including the procedure for training and embedding models for multiple outcomes, the specification of each outcome as either a constraint or objective term, and the incorporation of contextual features and domain-driven constraints.
• Model verification (notebooks/Pipeline/Model_Verification_Regression.ipynb, notebooks/Pipeline/Model_Verification_Classification.ipynb): These notebooks shows the training and embedding of a single model and compares the sklearn predictions to the MIO predictions to verify the MIO embeddings. The classification notebook also provides details on how we linearize constraints for the binary classification setting.

The package currently fully supports model training and embedding for continuous outcomes across all ML methods, as demonstrated in the example notebooks. Binary classification is fully supported for learned constraints. Multi-class classification support is in development.

Our software can be cited as:

  @misc{OptiCL,
    author = "Donato Maragno and Holly Wiberg",
    title = "OptiCL: Mixed-integer optimization with constraint learning",
    year = 2021,
    url = "https://github.com/hwiberg/OptiCL/"
  }

Our package is under active development. We welcome any questions or suggestions. Please submit an issue on Github, or reach us at d.maragno@uva.nl and hwiberg@mit.edu.