TY - GEN A1 - Tjusila, Gennesaret A1 - Besancon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. T3 - ZIB-Report - 23-15 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90902 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu T1 - A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming N2 - The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set. T3 - ZIB-Report - 23-21 KW - cutting plane selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91691 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs N2 - A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML. T3 - ZIB-Report - 23-28 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93095 SN - 1438-0064 ER -