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Pivot, Cut, and Dive: a heuristic for 0-1 mixed integer programming

Jonathan Eckstein, Mikhail Nediak
2007 Journal of Heuristics  
ØÓ ÔÖÓÚ ×Ù ×ÓÐÙØ ÓÒ׺ ÁÒ Ø Ð ×Ø ¸Ø Ö × Ð×Ó Ò × Ò ¬ ÒØ ÔÖÓ Ö ×× Ò Ù Ñ ÒØ Ò Ø ÔÓÛ Ö Ó Ö Ò ¹ Ò ¹ ÓÙÒ Ð ÓÖ Ø Ñ× Ø ÖÓÙ Ô Ö ÐÐ Ð ÓÑÔÙØ Ò º ÁÒ Ô Ö ÐÐ Ð Ö Ò ¹ Ò ¹ ÓÙÒ Ò¹ Ú ÖÓÒÑ ÒØ׸ ÓÓ ÙÖ ×Ø × Ö Ú Ò ÑÓÖ ÑÔÓÖØ  ...  Ü ¾ ¼ ½ ¾ Á ´ µ Û Ö × Ñ ¢ Ò Ñ ØÖ Ü¸Á ½ Ò × × Ø Ó Ò ÖÝ Ú Ö Ð × Ò Ð ¼ Ù ½ ÓÖ ÐÐ ¾ Áº ÓÖ ÙØÙÖ Ö Ö Ò ¸Û ÒÓØ Ý È Ø × Ø Ó ÐÐ Ü ¾ Ê Ò × Ø × Ý Ò ´¾µ Ò ´¿µº ÇÙÖ ÙÖ ×Ø × ÒØ Ò ØÓ Ù× Ò Ø ÓÒØ ÜØ Ó Ð Ö ¹× Ð Ô Ö ÐÐ Ð  ... 
doi:10.1007/s10732-007-9021-7 fatcat:fs5qdbfxhvhmleihwpbpsq2nci

Design and Implementation of an Heuristic-Enhanced Branch-and-Bound Solver for MILP [article]

Warley Almeida Silva, Federico Bobbio, Flore Caye, Defeng Liu, Justine Pepin, Carl Perreault-Lafleur, William St-Arnaud
2022 arXiv   pre-print
We present a solver for Mixed Integer Programs (MIP) developed for the MIP competition 2022.  ...  Our Branch-and-Bound algorithm is effective on a small portion of the training data set, and it manages to find an incumbent feasible solution for an instance that we could not solve with the Diving heuristics  ...  In this paper, we focus on mixed-integer linear programs (MILP) of the form (P ) min c T x s.t.  ... 
arXiv:2206.01857v2 fatcat:23hlyx6jvfbvdm2dn5hcsvkdc4

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 (  ...  I would like to thank the editors for challenging me and a number of friends and colleagues for very beneficial discussions on the subject and comments on preliminary versions of this chapter.  ... 
doi:10.1007/978-3-540-68279-0_16 fatcat:ud2aajvmzbdebpis6pm2sribma

Computational Study of Cutting Planes for a Lot-Sizing Problem in Branch-and-Cut Algorithm
Branch-and-Cut 알고리즘에서 Lot-Sizing 문제에 대한 Cutting Planes의 전산 성능 연구

Kwanghun Chung
2015 Journal of the Korean Operations Research and Management Science Society  
To use three families of cutting planes in Branch-and-Cut framework, we develop separation algorithms for each cut and implement them in CPLEX.  ...  In this paper, we evaluate the strength of three families of cutting planes for a lot-sizing problem.  ...  Lifted Mixed Cover Inequalities Since constraints (4) are 0-1 mixed integer knapsack inequalities, we next consider as a relaxation of (P) a generic 0-1 knapsack polyhedron S of the form:       ... 
doi:10.7737/jkorms.2015.40.3.023 fatcat:thqc7ilqs5berd564s74wmd24y

Exploring relaxation induced neighborhoods to improve MIP solutions

Emilie Danna, Edward Rothberg, Claude Le Pape
2004 Mathematical programming  
Given a feasible solution to a Mixed Integer Programming (MIP) model, a natural question is whether that solution can be improved using local search techniques.  ...  The metrics we consider are quality of the best integer solution produced within a time limit, ability to improve a given integer solution (of both good and poor quality), and time required to diversify  ...  We wish to thank the two anonymous referees for their helpful comments. References  ... 
doi:10.1007/s10107-004-0518-7 fatcat:jr3tstvb7zhejlkierpmiuvpoq

Objective Scaling Ensemble Approach for Integer Linear Programming [article]

Weili Zhang, Charles Nicholson
2018 arXiv   pre-print
The objective scaling ensemble approach is a novel two-phase heuristic for integer linear programming problems shown to be effective on a wide variety of integer linear programming problems.  ...  The technique identifies and aggregates multiple partial solutions to modify the problem formulation and significantly reduce the search space.  ...  If C and I = {B, G} are non-empty, the problem is a mixed integer linear program (MILP). If C = ∅ and G = ∅, the problem is a pure integer problem.  ... 
arXiv:1808.10263v1 fatcat:tp2qrgihcvc5njzew5zmxqduf4

Proximity search for 0-1 mixed-integer convex programming

Matteo Fischetti, Michele Monaci
2014 Journal of Heuristics  
In this paper we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program (MIP) with a "proximity" one, with the aim of enhancing the heuristic behavior of a black-box  ...  The relationship of this approach with primal integer methods is also addressed.  ...  Acknowledgements This research was supported by the Progetto di Ateneo on "Computational Integer Programming" of the University of Padova, and by MiUR, Italy (PRIN project "Integrated Approaches to Discrete  ... 
doi:10.1007/s10732-014-9266-x fatcat:y6rmorr2jzamxiam3z66wf6lni

Mixed-integer nonlinear optimization

Pietro Belotti, Christian Kirches, Sven Leyffer, Jeff Linderoth, James Luedtke, Ashutosh Mahajan
2013 Acta Numerica  
In (Stubbs and Mehrotra, 2002) , a step toward nonlinear cutting planes is taken and convex quadratic inequalities are derived as cuts for convex mixed 0-1 integer programs.  ...  Disjunctive Cutting Planes for MINLP Disjunctive cuts for use in a branch-and-cut procedure were first discussed by Stubbs and Mehrotra (1999) for convex mixed 0-1 nonlinear programs, based on Balas  ... 
doi:10.1017/s0962492913000032 fatcat:drrzy4alsvflbgs6gospgsgnaa

A relax-and-cut framework for Gomory mixed-integer cuts

Matteo Fischetti, Domenico Salvagnin
2011 Mathematical Programming Computation  
Gomory Mixed-Integer Cuts (GMICs) are widely used in modern branch-and-cut codes for the solution of Mixed-Integer Programs.  ...  In this paper we analyze a different scheme for the generation of rank-1 GMICs read from a basis of the original LP-the one before the addition of any cut.  ...  Acknowledgements This work was partially supported by the "Progetto di Ateneo" on "Computational Integer Programming" of the University of Padova; the second author was also partially supported by the  ... 
doi:10.1007/s12532-011-0024-x fatcat:pc2epekcrzafnl6aao3td2sgqe

Active-constraint variable ordering for faster feasibility of mixed integer linear programs

Jagat Patel, John W. Chinneck
2006 Mathematical programming  
The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or integer linear program.  ...  Empirical experiments demonstrate a significant improvement compared to a state-of-the art commercial MIP solver.  ...  Acknowledgements Thanks are due to Ed Klotz and Ed Rothberg at Ilog Inc. for advice and discussions while working with the Cplex solver.  ... 
doi:10.1007/s10107-006-0009-0 fatcat:j7lnluv3i5g3tc4hxyyg5ofp6e

The stable set problem: some structural properties and relaxations

Carla Michini
2012 4OR  
For a review of the state of the art heuristics for mixed integer and binary programs we recommend [2] and [19] .  ...  Acknowledgements The literature shows a very rich variety of heuristics for 0-1 MILPs, including the pivot-and-complement method of Balas and Martin [6] , the tabu-search-based method of Løkkentagen and  ...  Concave heuristics for 0-1 mixed integer programming In [30] Eckstein and Nediak presented a heuristic for 0-1 mixed integer programming based on the use of a concave merit function to measure integrality  ... 
doi:10.1007/s10288-012-0218-8 fatcat:fvnfrmlqtrcqliq5owka6tdl7m

Combinatorial optimization: Current successes and directions for the future

Karla L. Hoffman
2000 Journal of Computational and Applied Mathematics  
The availability of reliable software, extremely fast and inexpensive hardware and high-level languages that make the modeling of complex problems much faster have led to a much greater demand for optimization  ...  We note that each section of this paper will include only a limited number of survey references. These survey papers contain the references to the much larger body of work in each area.  ...  = x 0 for j = 1; : : : ; m.  ... 
doi:10.1016/s0377-0427(00)00430-1 fatcat:wn5662mjbvemfco4iepj2m2ddy

Noncommercial Software for Mixed-Integer Linear Programming [chapter]

Ted Ralphs, Jeffrey Linderoth
2005 Integer Programming  
We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs).  ...  We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open-source or other  ...  Acknowledgment The authors would like to thank Kjell Eikland, John Forrest, Matthew Galati, Lou Hafer, and Matthew Saltzman for their insightful comments that helped to improve the presentation.  ... 
doi:10.1201/9781420039597.ch10 fatcat:5ppou24dgzctlalgpugjs5envy

Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition

Ellis L. Johnson, George L. Nemhauser, Martin W.P. Savelsbergh
2000 INFORMS journal on computing  
This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically.  ...  Finally, we discuss the relatively new research areas of parallel integer programming and stochastic integer programming.  ...  A PIP in which all variables have to be equal to 0 or 1 is called a binary integer program (BIP), and a MIP in which all integer variables have to be equal to 0 or 1 is called a mixed binary integer program  ... 
doi:10.1287/ijoc. fatcat:zticaywmezc4rl7uji44l7u6tu

Branching on nonchimerical fractionalities

Matteo Fischetti, Michele Monaci
2012 Operations Research Letters  
In this paper we address methods for selecting the branching variable in an enumerative exact algorithm for Mixed-Integer Programs-a crucial step for the effectiveness of the resulting method.  ...  In this paper we present heuristics to speed-up the strong branching computation, and also to reduce the set of candidate branching variables by removing the variables whose fractionality is just chimerical  ...  Acknowledgments This research was supported by the Progetto di Ateneo on "Computational Integer Programming" of the University of Padova, and by MiUR, Italy (PRIN project "Integrated Approaches to Discrete  ... 
doi:10.1016/j.orl.2012.01.008 fatcat:wnwg2d344rd6bcynbaskmu2i6a
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