@article{Maher2015, author = {Maher, Stephen J.}, title = {Solving the integrated airline recovery problem using column-and-row generation}, volume = {50}, journal = {Transportation Science}, number = {1}, doi = {10.1287/trsc.2014.0552}, pages = {216 -- 239}, year = {2015}, abstract = {Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. To address this, there has been increasing interest in the development of efficient solution techniques to solve an integrated recovery problem. In this paper, an integrated airline recovery problem is proposed by integrating the schedule, crew and aircraft recovery stages. To achieve short runtimes and high quality solutions, this problem is solved using column-and-row generation. Column-and-row generation achieves an improvement in solution runtimes by reducing the problem size and thereby achieving a faster execution of each LP solve. Further, the results demonstrate that a good upper bound achieved early in the solution process, indicating an improved solution quality with the early termination of the algorithm. This paper also details the integration of the row generation procedure with branch-and-price, which is used to achieve integral optimal solutions. The benefits of applying column-and-row generation to solve the integrated recovery problem are demonstrated with a comparison to a standard column generation technique.}, language = {en} } @article{VigerskeGleixner2018, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, volume = {33}, journal = {Optimization Methods \& Software}, number = {3}, doi = {10.1080/10556788.2017.1335312}, pages = {563 -- 593}, year = {2018}, abstract = {This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.}, language = {en} } @article{MaherMurray2016, author = {Maher, Stephen J. and Murray, John M.}, title = {The unrooted set covering connected subgraph problem differentiating between HIV envelope sequences}, volume = {248}, journal = {European Journal of Operational Research}, number = {2}, doi = {doi:10.1016/j.ejor.2015.07.011}, pages = {668 -- 680}, year = {2016}, abstract = {This paper presents a novel application of operations research techniques to the analysis of HIV Env gene sequences, aiming to identify key features that are possible vaccine targets. These targets are identified as being critical to the transmission of HIV by being present in early transmitted (founder) sequences and absent in later chronic sequences. Identifying the key features of Env involves two steps: first, calculating the covariance of amino acid combinations and positions to form a network of related and compensatory mutations; and second, developing an integer program to identify the smallest connected subgraph of the constructed covariance network that exhibits a set covering property. The integer program developed for this analysis, labelled the unrooted set covering connected subgraph problem (USCCSP), integrates a set covering problem and connectivity evaluation, the latter formulated as a network flow problem. The resulting integer program is very large and complex, requiring the use of Benders' decomposition to develop an efficient solution approach. The results will demonstrate the necessity of applying acceleration techniques to the Benders' decomposition solution approach and the effectiveness of these techniques and heuristic approaches for solving the USCCSP.}, language = {en} } @article{GamrathKochMartinetal.2015, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in presolving for mixed integer programming}, volume = {7}, journal = {Mathematical Programming Computation}, number = {4}, doi = {10.1007/s12532-015-0083-5}, pages = {367 -- 398}, year = {2015}, abstract = {This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 \% on affected instances while not degrading the performance on the remaining problems.}, language = {en} } @article{BestuzhevaBesanconChenetal.2023, author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {Enabling research through the SCIP optimization suite 8.0}, volume = {49}, journal = {ACM Transactions on Mathematical Software}, number = {2}, doi = {10.1145/3585516}, pages = {1 -- 21}, year = {2023}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.}, language = {en} } @article{BestuzhevaChmielaMuelleretal.2023, author = {Bestuzheva, Ksenia and Chmiela, Antonia and M{\"u}ller, Benjamin and Serrano, Felipe and Vigerske, Stefan and Wegscheider, Fabian}, title = {Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-023-01345-1}, year = {2023}, abstract = {For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.}, language = {en} } @article{ChmielaMunozSerrano2025, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {Monoidal strengthening and unique lifting in MIQCPs}, volume = {210}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-024-02112-0}, pages = {189 -- 222}, year = {2025}, language = {en} } @article{ChmielaMunozSerrano2023, author = {Chmiela, Antonia and Mu{\~n}oz, Gonzalo and Serrano, Felipe}, title = {On the implementation and strengthening of intersection cuts for QCQPs}, volume = {197}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-022-01808-5}, pages = {549 -- 586}, year = {2023}, language = {en} } @article{WoodstockPokutta2025, author = {Woodstock, Zev and Pokutta, Sebastian}, title = {Splitting the conditional gradient algorithm}, volume = {35}, journal = {SIAM Journal on Optimization}, number = {1}, doi = {10.1137/24M1638008}, pages = {347 -- 368}, year = {2025}, language = {en} } @article{HalbigHoenGleixneretal.2025, author = {Halbig, Katrin and Hoen, Alexander and Gleixner, Ambros and Witzig, Jakob and Weninger, Dieter}, title = {A diving heuristic for mixed-integer problems with unbounded semi-continuous variables}, volume = {13}, journal = {EURO Journal on Computational Optimization}, doi = {10.1016/j.ejco.2025.100107}, year = {2025}, language = {en} }