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Rounding and Propagation Heuristics for Mixed Integer Programming [chapter]

Tobias Achterberg, Timo Berthold, Gregor Hendel
2012 Operations Research Proceedings  
C = N only continuous variables form a Linear Program (LP) I = N an Integer Program (IP) I = ∅ = C a Mixed Integer Program (MIP) B = N a Binary Program (BP) 12)and the integer infeasibility of the entire  ...  We start with the definition of a mixed integer program (MIP). Definition 1.  ... 
doi:10.1007/978-3-642-29210-1_12 dblp:conf/or/AchterbergBH11 fatcat:bl6w424lmzfjhcuvhvy64kq7kq

Shift-and-Propagate

Timo Berthold, Gregor Hendel
2014 Journal of Heuristics  
Further, with a slight abuse of notation, we will use the abbreviation MIP for mixed integer programming as well as for a MIP being a single mixed integer programming instance.  ...  When we use the term heuristics in this paper, we always refer to primal heuristics for mixed integer programming.  ...  Acknowledgements Many thanks to Christina Burt for her valuable comments.  ... 
doi:10.1007/s10732-014-9271-0 fatcat:73ptfr47xrfopfoy6gruqo3vgu

Structure-Based Primal Heuristics for Mixed Integer Programming [chapter]

Gerald Gamrath, Timo Berthold, Stefan Heinz, Michael Winkler
2015 Optimization in the Real World  
Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process.  ...  Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.  ...  Acknowledgements The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM).  ... 
doi:10.1007/978-4-431-55420-2_3 fatcat:rkcvhvcilfftvh2dscvdmdnaqm

Primal MINLP Heuristics in a Nutshell [chapter]

Timo Berthold
2014 Operations Research Proceedings 2013  
Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP).  ...  We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations.  ...  Gleixner for proof-reading a first draft of this paper.  ... 
doi:10.1007/978-3-319-07001-8_4 dblp:conf/or/Berthold13 fatcat:itwweszlbbdddfcmeoo6cvqvxe

Structure-driven fix-and-propagate heuristics for mixed integer programming

Gerald Gamrath, Timo Berthold, Stefan Heinz, Michael Winkler
2019 Mathematical Programming Computation  
Primal heuristics play an important role in the solving of mixed integer programs (MIPs).  ...  It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings.  ...  Acknowledgements The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM).  ... 
doi:10.1007/s12532-019-00159-1 fatcat:yky7cktstvd4jovquwahlyfys4

Feasibility Pump-like heuristics for mixed integer problems

M. De Santis, S. Lucidi, F. Rinaldi
2014 Discrete Applied Mathematics  
The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems.  ...  Mixed integer programming, Concave penalty functions, Frank-Wolfe algorithm, Feasibility Pump. MSC. 90C06, 90C10, 90C11, 90C30, 90C59  ...  In [12] , Fischetti and Salvagnin proposed a new rounding heuristic based on a diving-like procedure and constraint propagation.  ... 
doi:10.1016/j.dam.2013.06.018 fatcat:puuafw5eqjh2bg3545lflc5gqu

Feasibility pump 2.0

Matteo Fischetti, Domenico Salvagnin
2009 Mathematical Programming Computation  
Finding a feasible solution of a given Mixed-Integer Programming (MIP) model is a very important N P-complete problem that can be extremely hard in practice.  ...  In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics.  ...  CPDA051592 (project: Integrating Integer Programming and Constraint Programming) and by the Future and Emerging Technologies unit of the EC (IST priority), under contract no.  ... 
doi:10.1007/s12532-009-0007-3 fatcat:ldh62x2yhjgatpd7nmywefv7qu

Feasibility Pump Heuristics for Column Generation Approaches [chapter]

Pierre Pesneau, Ruslan Sadykov, François Vanderbeck
2012 Lecture Notes in Computer Science  
Primal heuristics have become an essential component in mixed integer programming (MIP).  ...  We show how such methods can be implemented in a context of dynamically defined variables, and we report on numerically testing "feasibility pump" for cutting stock and generalized assignment problems.  ...  Alternatively, if one makes heuristic decision on the variables of the original compact formulation, then the generic primal heuristics for mixed integer programming apply directly.  ... 
doi:10.1007/978-3-642-30850-5_29 fatcat:sygcbocuurb6jeyliwg22xhebe

Mixed Integer Programming Computation [chapter]

Andrea Lodi
2009 50 Years of Integer Programming 1958-2008  
The first 50 years of Integer and Mixed-Integer Programming have taken us to a very stable paradigm for solving problems in a reliable and effective way.  ...  Finally, we show that a lot of work must still be done for improving the solvers and extending their modeling capability. In memory of my friend and colleague Lorenzo Brunetta (  ...  Acknowledgements The writing of this chapter as well as the talk delivered in the Aussois meeting celebrating the 50 Years of Integer Programming have been challenging.  ... 
doi:10.1007/978-3-540-68279-0_16 fatcat:ud2aajvmzbdebpis6pm2sribma

Undercover: a primal MINLP heuristic exploring a largest sub-MIP

Timo Berthold, Ambros M. Gleixner
2013 Mathematical programming  
We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP.  ...  We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib.  ...  Acknowledgements Many thanks to Tobias Achterberg, Christina Burt, and Stefan Vigerske for their valuable comments.  ... 
doi:10.1007/s10107-013-0635-2 fatcat:ifnqoxkwijba5b4rkiw3xqp5cq

Recent Advancements in Commercial Integer Optimization Solvers for Business Intelligence Applications [chapter]

Cheng Seong Khor
2021 E-Business - Higher Education and Intelligence Applications  
The chapter focuses on the recent advancements in commercial integer optimization solvers as exemplified by the CPLEX software package particularly but not limited to mixed-integer linear programming (  ...  The chapter also covers heuristic-based algorithms, which include preprocessing and probing strategies as well as the more advanced methods of local or neighborhood search for polishing solutions toward  ...  programming, and mixed-integer quadratically-constrained programming.  ... 
doi:10.5772/intechopen.93416 fatcat:hwlnyiuvsfdmpd3hz7zjp3cxv4

SCIP: solving constraint integer programs

Tobias Achterberg
2009 Mathematical Programming Computation  
Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques.  ...  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.  ...  Acknowledgments I thank the referees of this paper for their thorough reviews. Their suggestions helped significantly to improve the quality of the paper.  ... 
doi:10.1007/s12532-008-0001-1 fatcat:elsjugcawndjvlt2lf3e5vgtbq

Extending a CIP Framework to Solve MIQCPs [chapter]

Timo Berthold, Stefan Heinz, Stefan Vigerske
2011 IMA Volumes in Mathematics and its Applications  
This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP).  ...  Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently.  ...  Pfetsch for contributing the implementation of the linear outer approximation for second-order cones and Ambros M. Gleixner for his valuable comments on the paper.  ... 
doi:10.1007/978-1-4614-1927-3_15 fatcat:pngauiqh3vfl5g3dzvsje7vyhi

Boosting the feasibility pump

Natashia L. Boland, Andrew C. Eberhard, Faramroze G. Engineer, Matteo Fischetti, Martin W. P. Savelsbergh, Angelos Tsoukalas
2014 Mathematical Programming Computation  
The Feasibility Pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems.  ...  FP iterates between a rounding procedure and a projection procedure, which together provide a sequence of points alternating between LP feasible but fractional solutions, and integer but LP relaxed infeasible  ...  Acknowledgements We thank Domenico Salvagnin for providing the source code of his implementation of the feasibility pump with constraint propagation and for answering all of our questions promptly, elaborately  ... 
doi:10.1007/s12532-014-0068-9 fatcat:c6evkoirerdbbax263yjedqx5y

Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs [chapter]

Gerald Gamrath, Marco E. Lübbecke
2010 Lecture Notes in Computer Science  
algorithms for solving mixed integer linear programs" as described in [11] .  ...  That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user's specification, and solves the resulting re-formulation via branch-and-price.  ...  We thank Alberto Ceselli and Enrico Malaguti for providing us with the p-median and RAP instances from Sections 4.1 and 4.3, respectively.  ... 
doi:10.1007/978-3-642-13193-6_21 fatcat:cfe5e2d4enar3brmryxqbnoaam
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