Michael Winkler

Mark Turner, Antonia Chmiela, Thorsten Koch et al.

A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it difficult or even impossible to model the problem directly. To overcome these hurdles, machine learning (ML) predictors are often used to represent these relationships and are then embedded in the MIP as surrogate models. Due to the large amount of available ML frameworks and the complexity of many ML predictors, formulating such predictors into MIPs is a highly non-trivial task. In this paper, we introduce PySCIPOpt-ML, an open-source tool for the automatic formulation and embedding of trained ML predictors into MIPs. By directly interfacing with a broad range of commonly used ML frameworks and an open-source MIP solver, PySCIPOpt-ML provides a way to easily integrate ML constraints into optimisation problems. Alongside PySCIPOpt-ML, we introduce, SurrogateLIB, a library of MIP instances with embedded ML constraints, and present computational results over SurrogateLIB, providing intuition on the scale of ML predictors that can be practically embedded. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.

Mark Turner, Thorsten Koch, Felipe Serrano et al.

Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.