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SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

Stefan Vigerske, Ambros Gleixner
2017 Optimization Methods and Software  
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  ...  The combination of discrete decisions, nonlinearity, and possible nonconvexity of the nonlinear functions in MINLP combines the areas of mixed-integer linear programming, nonlinear programming, and global  ...  This work has been supported by the DFG Research Center MATHEON Mathematics for key technologies in Berlin, the Berlin Mathematical School, and the Research Campus Modal Mathematical Optimization and Data  ... 
doi:10.1080/10556788.2017.1335312 fatcat:3l2viypjinbxtcwadxszfayc3y

SCIP: solving constraint integer programs

Tobias Achterberg
2009 Mathematical Programming Computation  
In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and non-commercial use and can be downloaded in source code.  ...  Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques.  ...  Finally, I thank all of my colleagues that worked on SCIP during the recent years.  ... 
doi:10.1007/s12532-008-0001-1 fatcat:elsjugcawndjvlt2lf3e5vgtbq

The SCIP Optimization Suite 8.0 [article]

Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, Leona Gottwald, Christoph Graczyk (+23 others)
2021 arXiv   pre-print
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP.  ...  Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints  ...  The Matlab-SCIP(-SDP) interface was set up with the big help of Nicolai Simon.  ... 
arXiv:2112.08872v1 fatcat:fqkdhu4bhngcblzaaaasqneplm

An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-Libraries

Yuji Shinano, Daniel Rehfeldt, Tristan Gally
2019 2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)  
In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel.  ...  Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems.  ...  Acknowledgment The authors would like to thank Chuen Teck See for first experimenting with a parallel version of SCIP-SDP, and Marc E.  ... 
doi:10.1109/ipdpsw.2019.00095 dblp:conf/ipps/ShinanoRG19 fatcat:k3d3t4rhsvfu3d3m7yfft2d5d4

Packing of Circles on Square Flat Torus as Global Optimization of Mixed Integer Nonlinear problem [article]

Sergey A. Smirnov, Vladimir V. Voloshinov
2018 arXiv   pre-print
It is formulated as Mixed-Integer Nonlinear Problem with linear and non-convex quadratic constraints.  ...  The main result is a confirmation of the conjecture on optimal packing for N=9 that was published in 2012 by O. Musin and A. Nikitenko.  ...  Acknowledgements Authors are grateful to Alexey Tarasov for recommendation to try Flat Torus Packing problem in our experiments with distributed implementations of B&B.  ... 
arXiv:1809.10525v2 fatcat:pbwvblimlbajzbhg5pogre4pje

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

Ruth Misener, Christodoulos A. Floudas
2014 Journal of Global Optimization  
This manuscript introduces ANTIGONE, Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework.  ...  The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program (MIQCQP) and mixed-integer signomial  ...  Fig. 8: 1116 Fig. 9 : 11169 introduces ANTIGONE, a general mixed-integer nonlinear global optimization framework.  ... 
doi:10.1007/s10898-014-0166-2 fatcat:qgz6usfohna7hdkn3h7ybbofby

Analyzing the computational impact of MIQCP solver components

Stefan Vigerske, Stefan Heinz, Ambros Gleixner, Timo Berthold
2012 Numerical Algebra, Control and Optimization  
The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality.  ...  We provide a computational study of the performance of a state-of-theart solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs).  ...  State-of-the-art solvers for MINLP comprise a variety of algorithmic techniques from several related fields such as nonlinear programming, mixed-integer linear programming (MILP), global optimization (  ... 
doi:10.3934/naco.2012.2.739 fatcat:346zbghdfnflvnzfx5b7abzmhq

Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling [chapter]

Andreas Bley, Ambros M. Gleixner, Thorsten Koch, Stefan Vigerske
2012 Modeling, Simulation and Optimization of Complex Processes  
We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations.  ...  This paper investigates the performance of several out-ofthe-box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints  ...  Ltd. 7 for providing us with the necessary data sets to conduct this study, and GAMS Development Corp. 8 for providing us with evaluation licenses for BARON and SBB.  ... 
doi:10.1007/978-3-642-25707-0_3 dblp:conf/hpsc/BleyGKV09 fatcat:eymdh7v7cnevjptn2vysomgztq

A Branch-and-Cut Algorithm for Mixed-Integer Bilinear Programming

Matteo Fischetti, Michele Monaci
2019 European Journal of Operational Research  
In this paper we consider the Mixed-Integer Bilinear Programming problem, a widely-used reformulation of the classical mixed-integer quadratic programming problem.  ...  Our results show that our method, even without intersection cuts, is competitive with a state-of-the-art mixed-integer nonlinear solver.  ...  We thank the organizers of Dagstuhl Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" (Pierre Bonami, Ambros M.  ... 
doi:10.1016/j.ejor.2019.09.043 fatcat:dbpm42yrtrg5pdysgz4g6yzkp4

Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization (Dagstuhl Seminar 18081)

Pierre Bonami, Ambros M. Gleixner, Jeff Linderoth, Ruth Misener, Michael Wagner
2018 Dagstuhl Reports  
These mixed-integer nonlinear programs (MINLP) may be used to optimize the energy use of large industrial plants, integrate renewable sources into energy networks, design biological and biomedical systems  ...  Mathematical models for optimal decisions often require both nonlinear and discrete components.  ...  Intersecting Mixed-Integer & Nonlinear Programming MINLP is a superset of both mixed integer linear optimization and nonlinear optimization, so we leveraged the best methods from both by incorporating  ... 
doi:10.4230/dagrep.8.2.64 dblp:journals/dagstuhl-reports/BonamiGLM18 fatcat:fn6llvricbevzjsm4teuf5xuha

GloMIQO: Global mixed-integer quadratic optimizer

Ruth Misener, Christodoulos A. Floudas
2012 Journal of Global Optimization  
This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality.  ...  To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure.  ...  Acknowledgements We are sincerely grateful to: Alex Meeraus and Michael Bussieck for freely providing us a GAMS license and the GAMS Modeling Object API, Stefan Vigerske for suggesting routines in the  ... 
doi:10.1007/s10898-012-9874-7 fatcat:bo4va2ic2zh3lbmc3zlpio5ody

On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming [article]

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2019 arXiv   pre-print
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.  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
arXiv:1912.00356v1 fatcat:f3hmuz6vajb23pp2apnd4sdc4a

Convex integer optimization with Frank-Wolfe methods [article]

Deborah Hendrych and Hannah Troppens and Mathieu Besançon and Sebastian Pokutta
2022 arXiv   pre-print
Mixed-integer nonlinear optimization is a broad class of problems that feature combinatorial structures and nonlinearities.  ...  In particular, we will study the algorithmic consequences of optimizing with a branch-and-bound approach where the subproblem is solved over the convex hull of the mixed-integer feasible set thanks to  ...  Acknowledgments Research reported in this paper was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund numbers 05M14ZAM,05M20ZBM  ... 
arXiv:2208.11010v4 fatcat:xne4wzi5jjfqhfwpho7f6seyz4

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Fani Boukouvala, Ruth Misener, Christodoulos A. Floudas
2016 European Journal of Operational Research  
This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO).  ...  This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and  ...  Figure 2 illustrates the domain of the contributions in the context of a global optimization branch-and-cut framework.  ... 
doi:10.1016/j.ejor.2015.12.018 fatcat:jwe7b7ivrzhrjbttdl74eff2pe

A computational study of global optimization solvers on two trust region subproblems

Tiago Montanher, Arnold Neumaier, Ferenc Domes
2018 Journal of Global Optimization  
We focus on numerical aspects of branch-and-bound solvers with three goals in mind.  ...  The following solvers were selected for the experiments: Antigone 1.1, Baron 16.12.7, Lindo Global 10.0, Couenne 0.5 and SCIP 3.2.  ...  In the Global Mixed-Integer Quadratic Optimizer GloMIQO [32] , Floudas and Misener developed the branch and bound framework so that the solution of QCQPs benefits from dynamically generated cutting planes  ... 
doi:10.1007/s10898-018-0649-7 pmid:30956397 pmcid:PMC6417392 fatcat:cxgztn7xvng3lbdcyl5a7o5fcu
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