pycombina: An Open-Source Tool for Solving Combinatorial Approximation Problems Arising in Mixed-Integer Optimal Control

Abstract Application of Model Predictive Control (MPC) for nonlinear switched systems often leads via discretization to Mixed-Integer Non-Linear Programs (MINLPs), which in a real-time setting can be solved approximately using a dedicated decomposition approach. One stage within this approach is the solution of a so-called Combinatorial Integral Approximation (CIA) problem, which is a Mixed-Integer Linear Program (MILP) that can be solved either approximately or to global optimality. The applicability of these decomposition methods depends strongly on efficient implementations, while many practical applications also require the consideration of a variety of additional and complex combinatorial constraints. In this work, we provide a comprehensive introduction to the open-source software tool pycombina, which enables users to automatically formulate CIA problems and provides methods for fast and efficient solution of these problems. In a case study, the usage of the tool is exemplified for input data from a real-life MPC application.