TY - GEN A1 - Müller, Benjamin A1 - Muñoz, Gonzalo A1 - Gasse, Maxime A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Serrano, Felipe T1 - On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming N2 - The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments. T3 - ZIB-Report - 19-55 KW - surrogate relaxation KW - MINLP KW - nonconvex optimization Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75179 SN - 1438-0064 ER - TY - CHAP A1 - Müller, Benjamin A1 - Muñoz, Gonzalo A1 - Gasse, Maxime A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Serrano, Felipe T1 - On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming T2 - Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020 N2 - The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments. Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-45771-6_25 SP - 322 EP - 337 ER - TY - BOOK A1 - Hadjidimitriou, Natalia Selini A1 - Frangioni, Antonio A1 - Lodi, Andrea A1 - Koch, Thorsten ED - Hadjidimitriou, Natalia Selini ED - Frangioni, Antonio ED - Lodi, Andrea ED - Koch, Thorsten T1 - Mathematical Optimization for Efficient and Robust Energy Networks Y1 - 2020 SN - 978-3-030-57441-3 U6 - https://doi.org/10.1007/978-3-030-57442-0 VL - 4 PB - Springer ER - TY - JOUR A1 - Furini, Fabio A1 - Traversi, Emiliano A1 - Belotti, Pietro A1 - Frangioni, Antonio A1 - Gleixner, Ambros A1 - Gould, Nick A1 - Liberti, Leo A1 - Lodi, Andrea A1 - Misener, Ruth A1 - Mittelmann, Hans A1 - Sahinidis, Nikolaos V. A1 - Vigerske, Stefan A1 - Wiegele, Angelika T1 - QPLIB: A Library of Quadratic Programming Instances JF - Mathematical Programming Computation N2 - This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-018-0147-4 VL - 11 IS - 2 SP - 237 EP - 265 ER - TY - JOUR A1 - Müller, Benjamin A1 - Muñoz, Gonzalo A1 - Gasse, Maxime A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Serrano, Felipe T1 - On generalized surrogate duality in mixed-integer nonlinear programming JF - Mathematical Programming N2 - The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global ϵ-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments. Y1 - 2022 U6 - https://doi.org/10.1007/s10107-021-01691-6 VL - 192 IS - 1 SP - 89 EP - 118 ER - TY - JOUR A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 JF - Mathematical Programming Computation Y1 - 2011 UR - http://mpc.zib.de/index.php/MPC/article/view/56 U6 - https://doi.org/10.1007/s12532-011-0025-9 VL - 3 IS - 2 SP - 103 EP - 163 ER - TY - GEN A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 N2 - This paper reports on the fifth version of the Mixed Integer Programming Library. The MIPLIB 2010 is the first MIPLIB release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today's codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic. T3 - ZIB-Report - 10-31 KW - Mixed Integer Programming KW - Problem Instances KW - IP KW - MIP KW - MIPLIB Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12953 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Khalil, Elias B. A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Pokutta, Sebastian T1 - Learning to Schedule Heuristics in Branch and Bound T2 - Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021 N2 - Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances. Y1 - 2021 ER - TY - CHAP A1 - Gasse, Maxime A1 - Bowly, Simon A1 - Cappart, Quentin A1 - Charfreitag, Jonas A1 - Charlin, Laurent A1 - Chételat, Didier A1 - Chmiela, Antonia A1 - Dumouchelle, Justin A1 - Gleixner, Ambros A1 - Kazachkov, Aleksandr M. A1 - Khalil, Elias A1 - Lichocki, Pawel A1 - Lodi, Andrea A1 - Lubin, Miles A1 - Maddison, Chris J. A1 - Christopher, Morris A1 - Papageorgiou, Dimitri J. A1 - Parjadis, Augustin A1 - Pokutta, Sebastian A1 - Prouvost, Antoine A1 - Scavuzzo, Lara A1 - Zarpellon, Giulia A1 - Yang, Linxin A1 - Lai, Sha A1 - Wang, Akang A1 - Luo, Xiaodong A1 - Zhou, Xiang A1 - Huang, Haohan A1 - Shao, Shengcheng A1 - Zhu, Yuanming A1 - Zhang, Dong A1 - Quan, Tao A1 - Cao, Zixuan A1 - Xu, Yang A1 - Huang, Zhewei A1 - Zhou, Shuchang A1 - Binbin, Chen A1 - Minggui, He A1 - Hao, Hao A1 - Zhiyu, Zhang A1 - Zhiwu, An A1 - Kun, Mao T1 - The Machine Learning for Combinatorial Optimization Competition (ML4CO): results and insights T2 - Proceedings of Conference on Neural Information Processing Systems Y1 - 2022 ER -