RENS: The optimal rounding

Mathematical Programming Computation

Volumn 6, Issue 1, 2014, Pages 33-54

  Berthold, Timo ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Large neighborhood search; Mixed integer nonlinear programming; Mixed integer programming; Primal heuristic; Rounding

Indexed keywords

LARGE NEIGHBORHOOD SEARCH; MIXED INTEGER PROGRAMMING; MIXED-INTEGER NONLINEAR PROGRAMMING; PRIMAL HEURISTIC; ROUNDING;

ALGORITHMS; NONLINEAR PROGRAMMING; OPTIMAL SYSTEMS; OPTIMIZATION; SOFTWARE TESTING;

INTEGER PROGRAMMING;

EID: 84898076987     PISSN: 18672949     EISSN: 18672957     Source Type: Journal    
DOI: 10.1007/s12532-013-0060-9     Document Type: Article

References (63)

1. Achterberg, T.; Koch, T.; Martin, A.: MIPLIB 2003. Oper. Res. Lett. 34(4), 1-12 (2006). http://miplib.zib.de/miplib2003/
2. Achterberg, T.: Constraint Integer Programming. PhD thesis, Technische Universität Berlin, 2007
3. Achterberg, T.; Berthold, T.: Improving the feasibility pump. Discret Optim. 4(1), 77-86 (2007). (Special Issue) (Pubitemid 46186193)
4. Achterberg, T.: SCIP: solving constraint integer programs. Math. Program. Comput. 1(1), 1-41 (2009)
5. Balas, E.: Facets of the knapsack polytope. Math. Program. 8, 146-164 (1975)
6. Balas, E.; Ceria, S.; Dawande, M.; Margot, F.; Pataki, G.: Octane: a new heuristic for pure 0-1 programs. Operat. Res. 49, 207-225 (2001) (Pubitemid 32508827)
7. Balas, E.; Schmieta, S.; Wallace, C.: Pivot and shift - a mixed integer programming heuristic. Discret. Optim. 1(1), 3-12 (2004) (Pubitemid 40266105)
8. Belotti, P.; Lee, J.; Liberti, L.; Margot, F.; Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24, 597-634 (2009)
9. Bertacco, L.; Fischetti, M.; Lodi, A.: A feasibility pump heuristic for general mixed-integer problems. Discret. Optim. 4(1), 77-86 (2007). (Special Issue) (Pubitemid 46186196)
10. Berthold, T.; Feydy, T.; Stuckey, P.J.: Rapid learning for binary programs. In: Lodi, A.; Milano, M.; Toth, P. (eds.) Proceedings of CPAIOR 2010, vol 6140 of LNCS, pp. 51-55. Springer, Berlin (2010)
11. Berthold, T.; Gleixner, A.M.: Undercover - a primal heuristic for MINLP based on sub-MIPs generated by set covering. In: Bonami, P.; Liberti, L.; Miller, A.J.; Sartenaer, A. (eds.) Proceedings of the EWMINLP, pp. 103-112 (2010)
12. Berthold, T.; Gleixner, A.M.: Undercover - a primal MINLP heuristic exploring a largest sub-MIP. Math. Program. A (2013). doi: 10.1007/s10107-013- 0635-2
13. Berthold, T.; Heinz, S.; Pfetsch, M.E.; Vigerske, S.: Large neighborhood search beyond MIP. In: Gaspero, L.D.; Schaerf, A.; Stützle, T. (eds.) Proceedings of the 9th Metaheuristics International Conference (MIC 2011), pp. 51-60 (2011)
14. Berthold, T.: Measuring the impact of primal heuristics. Oper. Res. Lett. 41(6), 611-614 (2013)
15. Berthold, T.: Primal heuristics for mixed integer programs. Technische Universität Berlin, Diploma thesis (2006)
16. Berthold, T.: Heuristics of the branch-cut-and-price-framework SCIP. In: Kalcsics, J.; Nickel, S. (eds.) Operations Research Proceedings 2007, pp. 31-36. Springer-Verlag, Berlin (2008)
17. Berthold, T.; Heinz, S.; Vigerske, S.: Extending a CIP framework to solve MIQCPs. In: Lee, J.; Leyffer, S. (eds.) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, pp. 427-444. Springer, Berlin (2011)
18. Berthold, T.; Gleixner, A.M.; Heinz, S.; Vigerske, S.: Analyzing the computational impact of MIQCP solver components. Numer. Algebra, Control Optim. 2(4), 739-748 (2012)
19. Bixby, R.E.; Ceria, S.; McZeal, C.M.; Savelsbergh, M.W.: An updated mixed integer programming library: MIPLIB 3.0. Optima 58, 12-15 (1998)
20. Bixby, R.E.; Fenelon, M.; Gu, Z.; Rothberg, E.; Wunderling, R.: MIP: theory and practice - closing the gap. In: Powell, M.; Scholtes, S. (eds.) Systems Modelling and Optimization: Methods, Theory, and Applications, pp. 19-49. Kluwer Academic Publisher, Dordrecht (2000)
21. Bonami, P.; Gonçalves, J.: Heuristics for convex mixed integer nonlinear programs. Comput. Optim. Appl. 51(2), 729-747 (2012)
22. Bonami, P.; Biegler, L.; Conn, A.; Cornuéjols, G.; Grossmann, I.; Laird, C.; Lee, J.; Lodi, A.; Margot, F.; Sawaya, N.; Wächter, A.: An algorithmic framework for convex mixed integer nonlinear programs. Disc. Opt. 5, 186-204 (2008) (Pubitemid 351443148)
23. Bonami, P.; Cornuéjols, G.; Lodi, A.; Margot, F.: A feasibility pump for mixed integer nonlinear programs. Math. Program. 119(2), 331-352 (2009)
24. Bussieck, M.; Drud, A.; Meeraus, A.: MINLPLib - a collection of test models for mixed-integer nonlinear programming. INFORMS J. Comput. 15(1), 114-119 (2003) (Pubitemid 39042736)
25. Bussieck, M.R.; Vigerske, S.: MINLP solver software. In: Cochran, J.J.; Cox, L.A.; Keskinocak, P.; Kharoufeh, J.P.; Smith, J.C. (eds.) Wiley Encyclopedia of Operations Research and Management Science. Wiley (2010)
26. CBC user guide - COIN-OR. http://www.coin-or.org/Cbc
27. CppAD. A Package for Differentiation of C++ Algorithms. http://www.coin-or.org/CppAD/
28. D'Ambrosio, C.; Frangioni, A.; Liberti, L.; Lodi, A.: Experiments with a feasibility pump approach for nonconvex MINLPs. In: Festa, P. (ed.) Experimental Algorithms. Lecture Notes in Computer Science, pp. 350-360. Springer, Berlin (2010)
29. D'Ambrosio, C.; Lodi, A.: Mixed integer nonlinear programming tools: a practical overview. 4OR: Q. J. Operat. Res. 9, 329-349 (2011)
30. D'Ambrosio, C.; Frangioni, A.; Liberti, L.; Lodi, A.: A storm of feasibility pumps for nonconvex MINLP. Math. Program. 136, 375-402 (2012)
31. Danna, E.; Rothberg, E.; Pape, C.L.: Exploring relaxation induced neighborhoods to improve MIP solutions. Math. Program. A 102(1), 71-90 (2004) (Pubitemid 40134692)
32. Fischetti, M.; Monaci, M.: Proximity search for 0-1 mixed-integer convex programming. Technical report, DEI, University of Padova (2012)
33. Fischetti, M.; Lodi, A.: Local branching. Mathematical Programming B 98(1-3), 23-47 (2003)
34. Fischetti, M.; Glover, F.; Lodi, A.: The feasibility pump. Math. Program. A 104(1), 91-104 (2005) (Pubitemid 41218556)
35. Fischetti, M.; Salvagnin, D.: Feasibility pump 2.0. Math. Program. C 1, 201-222 (2009)
36. Ghosh, S.: DINS, a MIP improvement heuristic. In: Fischetti, M.; Williamson, D.P. (eds.) Integer Programming and Combinatorial Optimization (IPCO 2007), volume 4513 of LNCS, pp. 310-323 (2007)
37. Glover, F.; Løkketangen, A.; Woodruff, D.L.: Scatter search to generate diverse MIP solutions. In: Laguna, M.; González-Velarde, J.L. (eds.) OR Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pp. 299-317. Kluwer Academic Publishers, Dordrecht (2000)
38. Glover, F.; Laguna, M.: General purpose heuristics for integer programming - part I. J. Heuristics 2(4), 343-358 (1997)
39. Glover, F.; Laguna, M.: General purpose heuristics for integer programming - part II. J. Heuristics 3(2), 161-179 (1997) (Pubitemid 127505779)
40. Hammer, P.L.; Johnson, E.L.; Peled, U.N.: Facets of regular 0-1 polytopes. Math. Program. 8, 179-206 (1975)
41. Hansen, P.; Mladenović, N.; Urošević, D.: Variable neighborhood search and local branching. Comput. Operat. Res. 33(10), 3034-3045 (2006) (Pubitemid 43199839)
42. Ipopt (Interior Point OPTimizer). http://www.coin-or.org/Ipopt/
43. Jones, E.; Oliphant, T.; Peterson, P.; et al.: SciPy: open source scientific tools for Python (2001)
44. Koch, T.; Achterberg, T.; Andersen, E.; Bastert, O.; Berthold, T.; Bixby, R.E.; Danna, E.; Gamrath, G.; Gleixner, A.M.; Heinz, S.; Lodi, A.; Mittelmann, H.; Ralphs, T.; Salvagnin, D.; Steffy, D.E.; Wolter, K.: MIPLIB 2010. Math. Program. Comput. 3(2), 103-163 (2011)
45. Land, A.H.; Doig, A.G.: An automatic method of solving discrete programming problems. Econometrica 28(3), 497-520 (1960)
46. Liberti, L.; Mladenović, N.; Nannicini, G.: A recipe for finding good solutions to MINLPs. Math. Program. Comput. 3(4), 349-390 (2011)
47. LindoGlobal. Lindo Systems, Inc. http://www.lindo.com
48. Løkketangen, A.: Heuristics for 0-1 mixed integer programming. In: Pardalos, P.M.; Resende, M.G.C. (eds.) Handbook of Applied, Optimization, pp. 474-477. Oxford University Press, New York (2002)
49. Løkketangen, A.; Glover, F.: Solving zero/one mixed integer programming problems using tabu search. Eur. J. Operat. Res. 106, 624-658 (1998) (Pubitemid 128399673)
50. Mittelmann, H.: Decision tree for optimization software: Benchmarks for optimization software. http://plato.asu.edu/bench.html
51. Nannicini, G.; Belotti, P.; Liberti, L.: A local branching heuristic for MINLPs. ArXiv e-prints (2008)
52. Nannicini, G.; Belotti, P.: Rounding-based heuristics for nonconvex MINLPs. Math. Program. Comput. 4(1), 1-31 (2012)
53. Rothberg, E.: An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS J. Comput. 19(4), 534-541 (2007)
54. Savelsbergh, M.W.P.: Preprocessing and probing techniques for mixed integer programming problems. ORSA J. Comput. 6, 445-454 (1994)
55. SBB. ARKI Consulting & Development A/S and GAMS Inc. http://www.gams.com/solvers/solvers.htm #SBB
56. SCIP. Solving Constraint Integer Programs. http://scip.zib.de/
57. SoPlex. An open source LP solver implementing the revised simplex algorithm. http://soplex.zib.de/
58. Tawarmalani, M.; Sahinidis, N.: Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Program. 99, 563-591 (2004) (Pubitemid 40871718)
59. Vigerske, S.: Decomposition in Multistage Stochastic Programming and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming. PhD thesis, Humboldt-Universität zu Berlin (2013)
60. Wächter, A.; Biegler, L.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25-57 (2006) (Pubitemid 41813168)
61. Wallace, C.: ZI round, a MIP rounding heuristic. J. Heuristics 16(5), 715-722 (2010)
62. Wolsey, L.A.: Faces for a linear inequality in 0-1 variables. Math. Program. 8, 165-178 (1975)
63. Wunderling, R.: Paralleler und objektorientierter Simplex-Algorithmus. PhD thesis, Technische Universität Berlin (1996)