Abstract
Large-scale mixed-integer programs (MIPs) typically cannot be solved by standard solvers with reasonable computational cost. MIP-heuristics decompose large-scale monolithic mixed-integer programs into polylithic programs such that they can be solved with reasonable computational cost at the price of loosing their optimality certificate. The decomposition is steered by hyperparameters that impact the solution quality and the computational cost diametrically. The proper selection of the hyperparameter values is a black-box optimization problem which is mostly solved by grid search or random search. In previous publications the authors proposed a novel hyperparameter optimization method based on Bayesian optimization and studied a use case from the PSE domain. Computational studies showed that the BO-based algorithm is superior for objective functions with few optimal solutions.This contribution generalizes the description of the MIP-Heuristic Optimization Problem (MIP-HOP) and the computer implementation of the solution-method. It supports the transferability of the method to other use cases. The general mathematical description of the MIP-HOP comprises eight expressions covering the monolithic and the polylithic MIP-model, the heuristic decomposition and composition operator, and the MIP-HOP. The formulation is explained and linked to the computer implementation of the solution method. The Python-code integrates state-of-the-art tools for mathematical programming (Pyomo and CPLEX) and Bayesian optimization (SMAC3) and will be published on GitHub.