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Three enhancements for optimization-based bound tightening

Ambros M. Gleixner, Timo Berthold, Benjamin Müller, Stefan Weltge
2016 Journal of Global Optimization  
Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs).  ...  At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)-up to twice the number of variables many.  ...  Tobias Achterberg for creating SCIP and Stefan Vigerske for providing the MINLP core of SCIP.  ... 
doi:10.1007/s10898-016-0450-4 fatcat:qikuqf2tdjhaviipbl7nxpamdy

A Computational Comparison of Optimization Methods for the Golomb Ruler Problem [article]

Burak Kocuk, Willem-Jan van Hoeve
2019 arXiv   pre-print
We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies.  ...  The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms.  ...  Enhancements We propose several enhancements to the models presented above based on bound tightening and branching strategies.  ... 
arXiv:1902.08660v1 fatcat:fuhrpgrs2nan5nfksermtokxf4

Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow [article]

Mowen Lu, Harsha Nagarajan, Russell Bent, Sandra D. Eksioglu, Scott J. Mason
2018 arXiv   pre-print
Based on these approaches, we develop tight piecewise convex relaxations with convex-hull representations, an adaptive, multivariate partitioning algorithm with bound tightening that progressively improves  ...  Computational results show that our novel algorithm reduces the best-known optimality gaps for some hard ACOPF cases.  ...  In line 4, we sequentially tighten the bounds of the voltage magnitude, vi, and phase angle differences, θij, using optimization-based bound tightening (BT) [11] , [12] .  ... 
arXiv:1803.04633v1 fatcat:2wverrprfnaslb5n2jgftjbe5y

On handling indicator constraints in mixed integer programming

Pietro Belotti, Pierre Bonami, Matteo Fischetti, Andrea Lodi, Michele Monaci, Amaya Nogales-Gómez, Domenico Salvagnin
2016 Computational optimization and applications  
More generally, we argue that aggressive bound tightening is often overlooked in MIP, while it represents a significant building block for enhancing MIP technology when indicator constraints and disjunctive  ...  Inspired by this empirical and surprising observation, we show that aggressive bound tightening is the crucial ingredient for solving this class of instances, and we devise a pair of computationally effective  ...  The authors are grateful to Andrea Tramontani and Sven Wiese for many interesting discussions on the subject and to two anonymous referees for a careful reading and many useful comments that helped improving  ... 
doi:10.1007/s10589-016-9847-8 fatcat:wf5tm3jklfaxdgab7gq4wclmi4

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

Harsha Nagarajan, Mowen Lu, Site Wang, Russell Bent, Kaarthik Sundar
2019 Journal of Global Optimization  
Keywords Global optimization · Adaptive partitioning · MILP-based methods · Mixed-integer nonlinear programs · McCormick · Piecewise relaxations · Sequential optimization-based bound-tightening B Harsha  ...  Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm  ...  optimization solver".  ... 
doi:10.1007/s10898-018-00734-1 fatcat:m563ht7usveb5euz3aec7c476u

An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs [article]

Harsha Nagarajan, Mowen Lu, Site Wang, Russell Bent, Kaarthik Sundar
2019 arXiv   pre-print
Further, we discuss a few algorithmic enhancements based on the sequential bound-tightening procedure as a presolve step, where we observe the importance of solving piecewise relaxations compared to basic  ...  We also shrink the best known optimality gap for one of the hard, generalized pooling problem instance.  ...  optimization solver".  ... 
arXiv:1707.02514v4 fatcat:vmlhtypecbcrvjqzhm2ntfa2wi

Tightening Bounds for Bayesian Network Structure Learning

Xiannian Fan, Changhe Yuan, Brandon Malone
2014 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
This paperintroduces methods for tightening the bounds.  ...  A recent breadth-first branch and bound algorithm (BFBnB)for learning Bayesian network structures (Maloneet al. 2011) uses two bounds to prune the searchspace for better efficiency; one is a lower bound  ...  The basic breadth-first search can be enhanced with branch and bound, resulting in a breadth-first branch and bound algorithm (BFBnB).  ... 
doi:10.1609/aaai.v28i1.9061 fatcat:esxnab6dibdexpvbmslksyz4ki

The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights [article]

Maxime Gasse, Quentin Cappart, Jonas Charfreitag, Laurent Charlin, Didier Chételat, Antonia Chmiela, Justin Dumouchelle, Ambros Gleixner, Aleksandr M. Kazachkov, Elias Khalil, Pawel Lichocki, Andrea Lodi (+29 others)
2022 arXiv   pre-print
Based on this context, the ML4CO aims at improving state-of-the-art combinatorial optimization solvers by replacing key heuristic components.  ...  However, recent years have seen a surge of interest in using machine learning as a new approach for solving combinatorial problems, either directly as solvers or by enhancing exact solvers.  ...  We used the following three metrics for the evaluation.  ... 
arXiv:2203.02433v2 fatcat:ct6osucw6rfrvc3xvqjuf7emku

Optimal design of mixed AC–DC distribution systems for commercial buildings: A Nonconvex Generalized Benders Decomposition approach

Stephen M. Frank, Steffen Rebennack
2015 European Journal of Operational Research  
buildings, and (ii) describes a tailored global optimization algorithm based on Nonconvex Generalized Benders Decomposition.  ...  The results of three case studies demonstrate the strength of the decomposition approach compared to state-of-the-art general-purpose global solvers.  ...  Figure 7 : 7 Convergence of NGBD algorithm (with BARON) for three bus test case: (a) without bound tightening, (b) with bound tightening.  ... 
doi:10.1016/j.ejor.2014.10.008 fatcat:tg7kcfo2bzbkpa4tyi27scjrg4

Valid Inequalities Based on Demand Propagation for Chemical Production Scheduling MIP Models

Sara Velez, Arul Sundaramoorthy, Christos T. Maravelias
2013 AIChE Journal  
These bounds are then used to express three types of tightening constraints which greatly enhance the computational performance of the MIP scheduling model.  ...  We use lowercase italic letters for indices, uppercase bold letters for sets, lowercase Greek letters for parameters, and uppercase italics for optimization variables.  ...  i is the tightest bound for eqn. 25. In §3.1.2, we calculate i based on min j  . Since eqn. 25 is based on max j  , i does not provide a tight bound.  ... 
doi:10.1002/aic.14021 fatcat:qh2nf3d35rcinhydirb7klhmwu

Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization [chapter]

Carleton Coffrin, Hassan L. Hijazi, Pascal Van Hentenryck
2015 Lecture Notes in Computer Science  
This paper studies how bound tightening can improve convex relaxations for power network optimization.  ...  ., minimal network and bound consistency) to a relaxation framework and shows how bound tightening can dramatically improve power network optimization.  ...  Moreover, on the ubiquitous AC-OPF problem, the QC relaxation, enhanced by bound tightening, almost always outperforms the stateof-the-art SDP relaxation on the optimal power flow problem.  ... 
doi:10.1007/978-3-319-23219-5_4 fatcat:ic5pptrvzvg2pe6pr5hrn5soem

Improving QC Relaxations of OPF Problems via Voltage Magnitude Difference Constraints and Envelopes for Trilinear Monomials [article]

Mohammad Rasoul Narimani, Daniel K. Molzahn, Mariesa L. Crow
2018 arXiv   pre-print
Using "bound tightening" techniques, the bounds on the voltage magnitude difference variables can be significantly smaller than the bounds on the voltage magnitudes themselves, so constraints based on  ...  This paper proposes two methods for tightening the QC relaxation. The first method introduces new variables that represent the voltage magnitude differences between connected buses.  ...  Optimization-based bound tightening algorithms, e.g., [9] , [11] , [12] , are typically slower than analytical methods [10] but provide tighter bounds.  ... 
arXiv:1804.02735v1 fatcat:exia2oahgngbto5ipvbn7z2imi

Semilocal density functional obeying a strongly tightened bound for exchange

Jianwei Sun, John P. Perdew, Adrienn Ruzsinszky
2015 Proceedings of the National Academy of Sciences of the United States of America  
Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one-and twoelectron densities, and conjectured for all densities.  ...  Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound.  ...  This third ingredient permits accurate energies even with the drastically tightened bound. optimally tightened bound on the exchange energy was proved for one-and two-electron densities, and conjectured  ... 
doi:10.1073/pnas.1423145112 pmid:25561554 pmcid:PMC4311813 fatcat:5mpqnkvmpng75ftbsqgurn325e

Global optimization of generalized geometric programming

Yanjun Wang, Kecun Zhang, Yuelin Gao
2004 Computers and Mathematics with Applications  
Local optimization approaches for solving (GGP) problem include three kinds of methods in general.  ...  Clearly, this BTM technique will enhance the solution procedure. Based on the previous BTM technique, we construct the global optimization algorithm.  ... 
doi:10.1016/j.camwa.2004.07.008 fatcat:v5cuv4yaz5hdpcdipvmy3wzqhe

RMPC for Uncertain Nonlinear Systems with non-additive Dynamic Disturbances and Noisy Measurements

Sami El-Ferik
2020 IEEE Access  
An explicit bound on the maximum allowable disturbance for recursive feasibility is also derived based on optimization of the one-step ahead controllable set to the terminal region.  ...  To satisfy state constraints, the proposed algorithms adopt a constraints tightening approach using the restricted constraint sets computed online.  ...  Three main techniques exist for Robust MPC (RMPC) in the literature. The first is Min-Max optimization technique.  ... 
doi:10.1109/access.2020.2975535 fatcat:nvwvlnammzaz3bbqbbcax3vwqa
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