PL EN


2019 | 29 | 4 | 23-40
Article title

Application of the polyblock method to special integer chance constrained problem

Content
Title variants
Languages of publication
EN
Abstracts
EN
The focus in this paper is on a special integer stochastic program with a chance constraint in which, with a given probability, a sum of independent and normally distributed random variables is bounded below. The objective is to maximize the expectation of a linear function of the random variables. The stochastic program is first reduced to an equivalent deterministic integer nonlinear program with monotonic objective and constraints functions. The resulting deterministic problem is solved using the discrete polyblock method which exploits its special structure. A numerical example is included for illustration and comparisons with LINGO, COUENNE, BONMIN and BARON solvers are performed.
Year
Volume
29
Issue
4
Pages
23-40
Physical description
Contributors
  • LAROMAD Laboratory, Faculty of Sciences, Mouloud Mammeri University, BP 17 RP, 15000 Tizi- -Ouzou, Algeria, belfat.ummto@gmail.com
References
  • ABHISHEK K., LEYFFER S., LINDEROTH J., FilMINT. An outer approximation-based solver for convex mixed-integer nonlinear programs, INFORMS J. Comp., 2010, 22, 555–567.
  • BELOTTI P., Couenne. A user’s manual, https://projects.coin-or.org/Couenne
  • BONAMI P., BIEGLER L.T., CONN A.R., CORNUJOLS G., GROSSMANN I.E., LAIRD C.D., LEE J., LODI A., MARGOT F., SAWAYA N., WACHTER A., An algorithmic framework for convex mixed integer nonlinear programs, Disc. Opt., 2008, 5, 186–204.
  • BONAMI P., KILINC M., LINDEROTH J.T., Algorithms and software for solving convex mixed integer nonlinear programs, mixed integer nonlinear programming, IMA Vol. Math. Appl., 2012, 154, 1–39.
  • CHARNES A., COOPER W.W., Deterministic equivalents for optimizing and satisfying under chance constraints, Oper. Res., 1963, 11, 18–39.
  • COIN-OR. https://www.coin-or.org › Bonmin
  • DURAN M.A., GROSSMANN I., An outer-approximation algorithm for a class of mixed-integer nonlinear programs, Math. Progr., 1986, 36, 307–339.
  • FLETCHER R., LEYFFER S., Solving mixed integer nonlinear programs by outer approximation, Math. Progr., 1994, 66, 327–349.
  • GEOFFRION A., Generalized benders decomposition, J. Opt. Theory Appl., 1972, 10, 237–260.
  • HOAI-PHUONG N.T., TUY H., A unified monotonic approach to generalized linear fractional programming, J. Global Opt., 2003, 26, 229–259.
  • KELLEY J.E., The cutting plane method for solving convex programs, J. SIAM, 1960, 8, 703–712.
  • KILINÇ M.R., SAHINIDIS N.V., Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON, Opt. Meth. Soft., 2018, 33 (3), 540–562.
  • LINDO Systems, Inc., LINGO. The modeling language and optimizer, 2017. http://www.lindo.com
  • LINDO Systems, Inc., Optimization modeling with LINGO, Technical Support in China, 2015. http://www.lindochina.com
  • LI D., SUN X.L., BISWAL M.P., GAO F., Convexification, concavification and monotonization in global optimization, Ann. Oper. Res., 2001, 105, 213–226.
  • Neos-server. https://neos-server.org/neos/solvers/go:ANTIGONE
  • QUESADA I., GROSSMANN I.E., An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems, Com. Chem. Eng., 1992, 16, 937–947.
  • SUN X.L., LI J.L., Nonlinear integer programming, Springer, 2006.
  • TAWARMALANI M., SAHINIDIS N.V., Global optimization of mixed integer nonlinear programs. A theoretical and computational study, Math. Progr., 2004, 99, 563–591.
  • TUY H., Monotonic optimization. Problems and solution approaches, SIAM J. Opt., 2000, 11 (2), 464–494.
  • TUY H., THACH P.T., KONNO H., Optimization of polynomial fractional functions, J. Global Opt., 2004, 29, 19–44.
  • TUY H., MINOUX M., HOAI-PHUONG N.T., Discrete monotonic optimization with application to a discrete location problem, SIAM J. Opt., 2006, 17 (1), 78–97.
  • VIGERSKE S., GLEIXNER A., SCIP. Global optimization of mixed-integer nonlinear programs in a branch-and-cut framework, Opt. Meth. Soft., 33 (3), 2018, 536–539.
  • WESTERLUND T., PETTERSSON F., A cutting plane method for solving convex MINLP problems, Comp. Chem. Eng., 1995, 19, 131–136.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-3b20f19d-8974-42f3-a491-c26ba0b37244
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.