Analyzing the computational impact of MIQCP solver components

Numerical Algebra, Control and Optimization

Volumn 2, Issue 4, 2012, Pages 739-748

  Berthold, Timo ^a   Gleixner, Ambros M ^a   Heinz, Stefan ^a   Vigerske, Stefan ^b  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Branch and cut; Global optimization; Mixed integer programming; Mixed integer quadratically constrained programming; Nonconvex; Software engineering

Indexed keywords

EID: 84892564561     PISSN: 21553289     EISSN: 21553297     Source Type: Journal    
DOI: 10.3934/naco.2012.2.739     Document Type: Article

References (29)

1. T. Achterberg, "Constraint Integer Programming, " PhD thesis, Technische Universitt Berlin, 2007.
2. T. Achterberg and T. Berthold, Hybrid branching, in "Proc. of CPAIOR 2009" (eds. W. J. van Hoeve and J. N. Hooker), Springer, 5547 (2009), 309-311.
3. T. Achterberg, T. Berthold, T. Koch and K. Wolter, Constraint integer programming: A new approach to integrate CP and MIP, in "Proc. of CPAIOR 2008" (eds. L. Perron and M. Trick), Springer, 5015 (2008), 6-20.
4. K. Abhishek, S. Leyffer and J. T. Linderoth, FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs, INFORMS J. Comput., 22 (2010), 555-567.
5. P. Belotti, J. Lee, L. Liberti, F. Margot and A. Wächter, Branching and bounds tightening technièues for non-convex MINLP, Optim. Methods Softw., 24 (2009), 597-634.
6. T. Berthold, "Primal Heuristics for Mixed Integer Programs, " Master's thesis, Technische Universitt Berlin, 2006.
7. T. Berthold and A. M. Gleixner, Undercover a primal MINLP heuristic exploring a largest sub-MIP, ZIB-Report 12-07, Zuse Institute Berlin, 2012. Available from: http://vs24.kobv.de/opus4-zib/frontdoor/index/index/docId/1463/.
8. T. Berthold, S. Heinz, M. E. Pfetsch and S. Vigerske, Large neighborhood search beyond MIP, in "Proceedings of the 9th Metaheuristics International Conference (MIC 2011)" (eds. L. D. Gaspero, A. Schaerf and T. Stützle), (2011), 51-60.
9. T. Berthold, S. Heinz and S. Vigerske, Extending a CIP framework to solve MIQCPs, in Lee and Leyffer [16], 427-444.
10. P. Bonami, L. T. Biegler, A. R. Conn, G. Cornuéjols, I. E. Grossmann, C. D. Laird, J. Lee, A. Lodi, F. Margot, N. W. Sawaya and A. Wächter, An algorithmic framework for convex mixed integer nonlinear programs, Discrete Optim., 5 (2008), 186-204.
11. P. Bonami, M. Kilinç and J. Linderoth, Algorithms and software for convex mixed integer nonlinear programs, in Lee and Leyffer [16], 1-40.
12. M. R. Bussieck, A. S. Drud and A. Meeraus, MINLPLib a collection of test models for mixed-integer nonlinear programming, INFORMS J. Comput., 15 (2003), 114-119.
13. M. R. Bussieck and S. Vigerske, MINLP solver software, in "Wiley Encyclopedia of Operations Research and Management Science" (eds. J. J. C. et. al.), Wiley & Sons, Inc., 2010.
14. F. Domes and A. Neumaier, Constraint propagation on èuadratic constraints, Constraints, 15 (2010), 404-429.
15. O. Günlük, J. Lee and R. Weismantel, MINLP strengthening for separable convex èuadratic transportation-cost UFL, IBM Research Report, RC23771, 2007.
16. J. Lee and S. Leyffer, "Mixed Integer Nonlinear Programming, " in "The IMA Volumes in Mathematics and its Applications, " Springer, 154 (2012).
17. Y. Lin and L. Schrage, The global solver in the LINDO API, Optim. Methods Softw., 24 (2009), 657-668.
18. G. P. McCormick, Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems, Math. Program., 10 (1976), 147-175.
19. R. Misener and C. A. Floudas, GloMIQO: Global mixed-integer èuadratic optimizer, J. Glob. Optim., to appear.
20. H. Mittelmann, "MIQP Test Instances, " http://plato.asu.edu/ftp/mièp.html.
21. N. Sawaya, "Reformulations, Relaxations and Cutting Planes for Generalized Disjunctive Programming, " PhD thesis, Carnegie Mellon University, 2006.
22. J. P. M. Silva and K. A. Sakallah, GRASP-A new search algorithm for satisfiability, in "ICCAD'96: Proceedings of the 1996 IEEE/ACM international conference on Computeraided design, " IEEE Computer Society, Washington, DC, USA, 1996, 220-227.
23. M. Tawarmalani and N. V. Sahinidis, "Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, " Kluwer Academic Publishers, 2002.
24. S. Vigerske, "Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming, " PhD thesis, Humboldt-Universität zu Berlin, 2012, to be published.
25. J. P. Vielma, S. Ahmed and G. L. Nemhauser, A lifted linear programming branch-and-bound algorithm for mixed-integer conic èuadratic programs, INFORMS J. Comput., 20 (2008), 438-450.
26. A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), 25-57.
27. K. Wolter, "Implementation of Cutting Plane Separators for Mixed Integer Programs, " Master's thesis, Technische Universitt Berlin, 2006.
28. T. Yunes, I. D. Aron and J. N. Hooker, An integrated solver for optimization problems, Oper. Res., 58 (2010), 342-356.
29. IBM, "CPLEX, " http://ibm.com/software/integration/optimization/cplex.