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Wampler, Joe F., and Stephen E. Newman. "Integer Programming." College Mathematics Journal 27, no. 2 (March 1996): 95. http://dx.doi.org/10.2307/2687396.
Wampler, Joe F., and Stephen E. Newman. "Integer Programming." College Mathematics Journal 27, no. 2 (March 1996): 95–100. http://dx.doi.org/10.1080/07468342.1996.11973758.
Kara, Imdat, and Halil Ibrahim Karakas. "Integer Programming Formulations For The Frobenius Problem." International Journal of Pure Mathematics 8 (December 28, 2021): 60–65. http://dx.doi.org/10.46300/91019.2021.8.8.
The Frobenius number of a set of relatively prime positive integers α1,α2,…,αn such that α1< α2< …< αn, is the largest integer that can not be written as a nonnegative integer linear combination of the given set. Finding the Frobenius number is known as the Frobenius problem, which is also named as the coin exchange problem or the postage stamp problem. This problem is closely related with the equality constrained integer knapsack problem. It is known that this problem is NP-hard. Extensive research has been conducted for finding the Frobenius number of a given set of positive integers. An exact formula exists for the case n=2 and various formulas have been derived for all special cases of n = 3. Many algorithms have been proposed for n≥4. As far as we are aware, there does not exist any integer programming approach for this problem which is the main motivation of this paper. We present four integer linear programming formulations about the Frobenius number of a given set of positive integers. Our first formulation is used to check if a given positive integer is the Frobenius number of a given set of positive integers. The second formulation aims at finding the Frobenius number directly. The third formulation involves the residue classes with respect to the least member of the given set of positive integers, where a residue table is computed comprising all values modulo that least member, and the Frobenius number is obtained from there. Based on the same approach underlying the third formulation, we propose our fourth formulation which produces the Frobenius number directly. We demonstrate how to use our formulations with several examples. For illustrative purposes, some computa-tional analysis is also presented.
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Freire, Alexandre S., Eduardo Moreno, and Juan Pablo Vielma. "An integer linear programming approach for bilinear integer programming." Operations Research Letters 40, no. 2 (March 2012): 74–77. http://dx.doi.org/10.1016/j.orl.2011.12.004.
He, Deng Xu, and Liang Dong Qu. "Population Migration Algorithm for Integer Programming and its Application in Cutting Stock Problem." Advanced Materials Research 143-144 (October 2010): 899–904. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.899.
For integer programming, there exist some difficulties and problems for the direct applications of population migration algorithm (PMA) due to the variables belonging to the set of integers. In this paper, a novel PMA is proposed for integer programming which evolves on the set of integer space. Several functions and cutting stock problem simulation results show that the proposed algorithm is significantly superior to other algorithms.
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Gomory, Ralph E. "Early Integer Programming." Operations Research 50, no. 1 (February 2002): 78–81. http://dx.doi.org/10.1287/opre.50.1.78.17793.
Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010. Committee Chair: Erera, Martin; Committee Chair: Nemhauser, George; Committee Chair: Savelsbergh, Martin; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Vigerske, Stefan. "Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16704.
Diese Arbeit leistet Beiträge zu zwei Gebieten der mathematischen Programmierung: stochastische Optimierung und gemischt-ganzzahlige nichtlineare Optimierung (MINLP). Im ersten Teil erweitern wir quantitative Stetigkeitsresultate für zweistufige stochastische gemischt-ganzzahlige lineare Programme auf Situationen in denen Unsicherheit gleichzeitig in den Kosten und der rechten Seite auftritt, geben eine ausführliche Übersicht zu Dekompositionsverfahren für zwei- und mehrstufige stochastische lineare und gemischt-ganzzahlig lineare Programme, und diskutieren Erweiterungen und Kombinationen des Nested Benders Dekompositionsverfahrens und des Nested Column Generationsverfahrens für mehrstufige stochastische lineare Programme die es erlauben die Vorteile sogenannter rekombinierender Szenariobäume auszunutzen. Als eine Anwendung dieses Verfahrens betrachten wir die optimale Zeit- und Investitionsplanung für ein regionales Energiesystem unter Einbeziehung von Windenergie und Energiespeichern. Im zweiten Teil geben wir eine ausführliche Übersicht zum Stand der Technik bzgl. Algorithmen und Lösern für MINLPs und zeigen dass einige dieser Algorithmen innerhalb des constraint integer programming Softwaresystems SCIP angewendet werden können. Letzteres erlaubt uns die Verwendung schon existierender Technologien für gemischt-ganzzahlige linear Programme und constraint Programme für den linearen und diskreten Teil des Problems. Folglich konzentrieren wir uns hauptsächlich auf die Behandlung der konvexen und nichtkonvexen nichtlinearen Nebenbedingungen mittels Variablenschrankenpropagierung, äußerer Approximation und Reformulierung. In einer ausführlichen numerischen Studie untersuchen wir die Leistung unseres Ansatzes anhand von Anwendungen aus der Tagebauplanung und des Aufbaus eines Wasserverteilungssystems und mittels verschiedener Vergleichstests. Die Ergebnisse zeigen, dass SCIP ein konkurrenzfähiger Löser für MINLPs geworden ist. This thesis contributes to two topics in mathematical programming: stochastic optimization and mixed-integer nonlinear programming (MINLP). In the first part, we extend quantitative continuity results for two-stage stochastic mixed-integer linear programs to include situations with simultaneous uncertainty in costs and right-hand side, give an extended review on decomposition algorithm for two- and multistage stochastic linear and mixed-integer linear programs, and discuss extensions and combinations of the Nested Benders Decomposition and Nested Column Generation methods for multistage stochastic linear programs to exploit the advantages of so-called recombining scenario trees. As an application of the latter, we consider the optimal scheduling and investment planning for a regional energy system including wind power and energy storages. In the second part, we give a comprehensive overview about the state-of-the-art in algorithms and solver technology for MINLPs and show that some of these algorithm can be applied within the constraint integer programming framework SCIP. The availability of the latter allows us to utilize the power of already existing mixed integer linear and constraint programming technologies to handle the linear and discrete parts of the problem. Thus, we focus mainly on the domain propagation, outer-approximation, and reformulation techniques to handle convex and nonconvex nonlinear constraints. In an extensive computational study, we investigate the performance of our approach on applications from open pit mine production scheduling and water distribution network design and on various benchmarks sets. The results show that SCIP has become a competitive solver for MINLPs.
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Shmonin, Gennady. "Parameterised integer programming, integer cones, and related problems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985786132.
Espinoza, Daniel G. "On Linear Programming, Integer Programming and Cutting Planes." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10482.
In this thesis we address three related topic in the field of Operations Research.
Firstly we discuss the problems and limitation of most common solvers for linear programming, precision.
We then present a solver that generate rational optimal solutions to linear programming problems by solving a succession of (increasingly more precise) floating point approximations of the original rational problem until the rational optimality conditions are achieved.
This method is shown to be (on average) only 20% slower than the common pure floating point approach, while returning true optimal solutions to the problems.
Secondly we present an extension of the Local Cut procedure introduced by Applegate et al, 2001, for the Symmetric Traveling Salesman Problem (STSP), to the general setting of MIP problems.
This extension also proves finiteness of the separation, facet and tilting procedures in the general MIP setting, and also provides conditions under which the separation procedure is guaranteed to generate cuts that separate the current fractional solution from the convex hull of the mixed-integer polyhedron.
We then move on to explore some configurations for local cuts, realizing extensive testing on the instances from MIPLIB.
Those results show that this technique may be useful in general MIP problems, while the experience of Applegate et al, shows that the ideas can be successfully applied to structures problems as well.
Thirdly we present an extensive computational experiment on the TSP and Domino Parity inequalities as introduced by Letchford, 2000.
This work also include a safe-shrinking theorem for domino parity inequalities, heuristics to apply the planar separation algorithm introduced by Letchford to instances where the planarity requirement does not hold, and several practical speed-ups.
Our computational experience showed that this class of inequalities effectively improve the lower bounds from the best relaxations obtained with Concorde, which is one of the state of the art solvers for the STSP.
As part of these experience, we solved to optimality the (up to now) largest two STSP instances, both of them belong to the TSPLIB set of instances and they have 18,520 and 33,810 cities respectively.
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Hooker, Kevin J. "Hypergraphs and integer programming polytopes /." Search for this dissertation online, 2005. http://wwwlib.umi.com/cr/ksu/main.
Integer Programming (IP) is a powerful and widely-used formulation for combinatorial problems. The study of IP over the past several decades has led to fascinating theoretical developments, and has improved our ability to solve discrete optimization problems arising in practice. This thesis makes progress on algorithmic solutions for IP by building on combinatorial, geometric and Linear Programming (LP) approaches.
We use a combinatorial approach to give an approximation algorithm for the feedback vertex set problem (FVS) in a recently developed Implicit Hitting Set framework. Our algorithm is a simple online algorithm which finds a nearly optimal FVS in random graphs. We also propose a planted model for FVS and show that an optimal hitting set for a polynomial number of subsets is sufficient to recover the planted subset.
Next, we present an unexplored geometric connection between integer feasibility and the classical notion of discrepancy of matrices. We exploit this connection to show a phase transition from infeasibility to feasibility in random IP instances. A recent algorithm for small discrepancy solutions leads to an efficient algorithm to find an integer point for random IP instances that are feasible with high probability.
Finally, we give a provably efficient implementation of a cutting-plane algorithm for perfect matchings. In our algorithm, cuts separating the current optimum are easy to derive while a small LP is solved to identify the cuts that are to be retained for later iterations. Our result gives a rigorous theoretical explanation for the practical efficiency of the cutting plane approach for perfect matching evident from implementations.
In summary, this thesis contributes to new models and connections, new algorithms and rigorous analysis of well-known approaches for IP.
This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem.
The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented
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Evans, G. M. "Parallel and distributed integer programming." Thesis, University of East Anglia, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267706.
Lee, Jon, and Sven Leyffer, eds. Mixed Integer Nonlinear Programming. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1927-3.
Poler, Raúl, Josefa Mula, and Manuel Díaz-Madroñero. "Integer Programming." In Operations Research Problems, 49–86. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5577-5_2.
Vanderbei, Robert J. "Integer Programming." In International Series in Operations Research & Management Science, 385–405. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-74388-2_23.
Bard, Jonathan F. "Integer Programming." In Nonconvex Optimization and Its Applications, 76–136. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2836-1_3.
Korte, Bernhard, and Jens Vygen. "Integer Programming." In Algorithms and Combinatorics, 101–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24488-9_5.
Awange, Joseph L., Béla Paláncz, Robert H. Lewis, and Lajos Völgyesi. "Integer Programming." In Mathematical Geosciences, 185–206. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-67371-4_7.
Vanderbei, Robert J. "Integer Programming." In International Series in Operations Research & Management Science, 389–414. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39415-8_23.
Korte, Bernhard, and Jens Vygen. "Integer Programming." In Algorithms and Combinatorics, 91–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-21708-5_5.
Korte, Bernhard, and Jens Vygen. "Integer Programming." In Algorithms and Combinatorics, 91–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-21711-5_5.
Тези доповідей конференцій з теми "Integer programming":
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Arnow, David, Ken McAloon, and Carol Tretkoff. "Parallel integer goal programming." In the 1995 ACM 23rd annual conference. New York, New York, USA: ACM Press, 1995. http://dx.doi.org/10.1145/259526.259536.
Deng, Changshou, Bingyan Zhao, Yanlin Yang, and Anyuan Deng. "Integer Encoding Differential Evolution Algorithm for Integer Programming." In 2010 2nd International Conference on Information Engineering and Computer Science (ICIECS). IEEE, 2010. http://dx.doi.org/10.1109/iciecs.2010.5677899.
Steffy, Daniel E. "Exact linear and integer programming." In the 38th international symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2465506.2465931.
Wonka, Peter. "Integer programming for layout problems." In SA '18: SIGGRAPH Asia 2018. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3277644.3277794.
Megerian, S., M. Drinic, and M. Potkonjak. "Watermarking integer linear programming solutions." In Proceedings of 39th Design Automation Conference. IEEE, 2002. http://dx.doi.org/10.1109/dac.2002.1012585.
Megerian, Seapahn, Milenko Drinic, and Miodrag Potkonjak. "Watermarking integer linear programming solutions." In the 39th conference. New York, New York, USA: ACM Press, 2002. http://dx.doi.org/10.1145/513918.513923.
Khoat, Than Quang. "On the bounded integer programming." In 2008 IEEE International Conference on Research, Innovation and Vision for the Future in Computing and Communication Technologies. IEEE, 2008. http://dx.doi.org/10.1109/rivf.2008.4586328.
Zarate, David Cheng, Pierre Le Bodic, Tim Dwyer, Graeme Gange, and Peter Stuckey. "Optimal Sankey Diagrams Via Integer Programming." In 2018 IEEE Pacific Visualization Symposium (PacificVis). IEEE, 2018. http://dx.doi.org/10.1109/pacificvis.2018.00025.
Li, Yuying, Lixiang Li, Qiaoyan Wen, and Yixian Yang. "Integer Programming via Chaotic Ant Swarm." In Third International Conference on Natural Computation (ICNC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icnc.2007.444.
Bixby, Robert E. Linear Programming Tools for Integer Programming. Fort Belvoir, VA: Defense Technical Information Center, October 1989. http://dx.doi.org/10.21236/ada219013.
Bixby, Robert. Linear-Programming Tools in Integer Programming: The Traveling Salesman. Fort Belvoir, VA: Defense Technical Information Center, October 1992. http://dx.doi.org/10.21236/ada261398.
Terlaky, Tamas. Mixed-Integer Conic Linear Programming: Challenges and Perspectives. Fort Belvoir, VA: Defense Technical Information Center, October 2013. http://dx.doi.org/10.21236/ada590477.
Prokopyev, Oleg A. New Theory and Methods in Stochastic Mixed Integer Programming. Fort Belvoir, VA: Defense Technical Information Center, July 2014. http://dx.doi.org/10.21236/ada610045.
Nemhauser, George L. Application of Mixed-Integer Programming to Selected Military Problems. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada276197.
Saltzman, Robert M. A Heuristic Ceiling Point Algorithm for General Integer Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, November 1988. http://dx.doi.org/10.21236/ada202285.
Saltzman, Robert M., and Frederick S. Hillier. An Exact Ceiling Point Algorithm for General Integer Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, November 1988. http://dx.doi.org/10.21236/ada202286.
Bixby, Robert E., E. A. Boyd, and Ronni R. Indovina. A Test Set of Real-World Mixed Integer Programming Problems. Fort Belvoir, VA: Defense Technical Information Center, January 1992. http://dx.doi.org/10.21236/ada455431.
Saltzman, Robert M., and Frederick S. Hillier. The Role of Ceiling Points in General Integer Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, August 1988. http://dx.doi.org/10.21236/ada199744.
Bays, Matthew J., and Thomas A. Wettergren. Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, January 2016. http://dx.doi.org/10.21236/ad1005254.
