Embedding Trained Machine Learning Models into Mixed-Integer Programs: A Primer

In recent years, machine learning (ML) has become increasingly popular in various fields due to its ability to handle complex data and make predictions. However, integrating ML models into mathematical optimization frameworks can be challenging, especially when dealing with large-scale datasets. This paper presents PySCIPOpt-ML, an open-source tool that simplifies the process of formulating trained ML predictors as mixed-integer programming (MIP) problems.

Challenges in MIP Optimization

Traditional MIP approaches rely on precise definitions of constraints and the objective function, making it difficult to incorporate ML models with complex relationships. The growing popularity of different ML architectures has created a need for a systematic way to formulate these models into MIPs.

Embedding ML Models in MIP

PySCIPOpt-ML addresses this challenge by directly interfacing with various ML frameworks, including scikit-learn, XGBoost, and PyTorch. By embedding trained ML predictors as surrogate models within the MIP framework, it becomes possible to leverage the strengths of both paradigms.

How PySCIPOpt-ML Works

PySCIPOpt-ML consists of three main components: (1) an interface for connecting with popular ML frameworks, (2) a module for approximating non-linear relationships using piecewise linear functions, and (3) a solver for solving the resulting MIPs. By combining these components, PySCIPOpt-ML enables users to tackle complex optimization problems that were previously unsolvable.

Advantages of PySCIPOpt-ML

PySCIPOpt-ML offers several advantages over traditional MIP approaches, including:

1. Automatic formulation: PySCIPOpt-ML automatically converts trained ML predictors into MIPs, eliminating the need for manual formulation.
2. Scalability: The tool is designed to handle large-scale datasets and can efficiently solve complex optimization problems.
3. Flexibility: PySCIPOpt-ML supports a wide range of ML frameworks, making it possible to leverage different architectures depending on the specific application.
4. Ease of use: By providing an intuitive interface, PySCIPOpt-ML simplifies the process of integrating ML models into MIP optimization problems.

Real-World Applications

PySCIPOpt-ML has numerous applications in various fields, including:

1. Healthcare: PySCIPOpt-ML can be used to optimize drug development and personalize treatment plans based on patient data.
2. Finance: The tool can help optimize portfolio management and risk assessment by integrating ML models into MIP optimization problems.
3. Energy: PySCIPOpt-ML can aid in the optimization of energy systems, such as scheduling energy production and distribution while taking into account complex constraints and uncertainties.

Conclusion

In summary, PySCIPOpt-ML is a powerful tool that simplifies the process of formulating trained ML predictors as MIPs. By leveraging the strengths of both paradigms, it becomes possible to tackle complex optimization problems that were previously unsolvable. With its ability to handle large-scale datasets and support for various ML frameworks, PySCIPOpt-ML has numerous applications in various fields, including healthcare, finance, and energy.