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Journal articles on the topic 'Integer programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

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.

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2

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.

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3

Cornu�jols, G�rard, and William R. Pulleyblank. "Integer programming." Mathematical Programming 98, no. 1-3 (September 1, 2003): 1–2. http://dx.doi.org/10.1007/s10107-003-0417-3.

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4

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.

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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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5

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.

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6

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.

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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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7

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.

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8

Feautrier, Paul. "Parametric integer programming." RAIRO - Operations Research 22, no. 3 (1988): 243–68. http://dx.doi.org/10.1051/ro/1988220302431.

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9

Lee, Jon, and Adam N. Letchford. "Mixed integer programming." Discrete Optimization 4, no. 1 (March 2007): 1–2. http://dx.doi.org/10.1016/j.disopt.2006.10.005.

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10

Onn, Shmuel. "Robust integer programming." Operations Research Letters 42, no. 8 (December 2014): 558–60. http://dx.doi.org/10.1016/j.orl.2014.10.002.

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11

Bienstock, Daniel, and William Cook. "Computational integer programming." Mathematical Programming 81, no. 2 (April 1998): 147–48. http://dx.doi.org/10.1007/bf01581102.

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12

Schaefer, Andrew J. "Inverse integer programming." Optimization Letters 3, no. 4 (June 16, 2009): 483–89. http://dx.doi.org/10.1007/s11590-009-0131-z.

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13

Lageweg, B. J., J. K. Lenstra, A. H. G. RinnooyKan, L. Stougie, and A. H. G. Rinnooy Kan. "STOCHASTIC INTEGER PROGRAMMING BY DYNAMIC PROGRAMMING." Statistica Neerlandica 39, no. 2 (June 1985): 97–113. http://dx.doi.org/10.1111/j.1467-9574.1985.tb01131.x.

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14

Williams, H. P. "Logic applied to integer programming and integer programming applied to logic." European Journal of Operational Research 81, no. 3 (March 1995): 605–16. http://dx.doi.org/10.1016/0377-2217(93)e0359-6.

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15

Fujiwara, Hiroshi, Hokuto Watari, and Hiroaki Yamamoto. "Dynamic Programming for the Subset Sum Problem." Formalized Mathematics 28, no. 1 (April 1, 2020): 89–92. http://dx.doi.org/10.2478/forma-2020-0007.

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SummaryThe subset sum problem is a basic problem in the field of theoretical computer science, especially in the complexity theory [3]. The input is a sequence of positive integers and a target positive integer. The task is to determine if there exists a subsequence of the input sequence with sum equal to the target integer. It is known that the problem is NP-hard [2] and can be solved by dynamic programming in pseudo-polynomial time [1]. In this article we formalize the recurrence relation of the dynamic programming.

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16

De Loera, Jesús A., Raymond Hemmecke, Shmuel Onn, and Robert Weismantel. "N-fold integer programming." Discrete Optimization 5, no. 2 (May 2008): 231–41. http://dx.doi.org/10.1016/j.disopt.2006.06.006.

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17

Williams, H. P., and J. N. Hooker. "Integer programming as projection." Discrete Optimization 22 (November 2016): 291–311. http://dx.doi.org/10.1016/j.disopt.2016.08.004.

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18

Jan, Rong-Hong, and Maw-Sheng Chern. "Nonlinear integer bilevel programming." European Journal of Operational Research 72, no. 3 (February 1994): 574–87. http://dx.doi.org/10.1016/0377-2217(94)90424-3.

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19

Dua, Vivek. "Mixed integer polynomial programming." Computers & Chemical Engineering 72 (January 2015): 387–94. http://dx.doi.org/10.1016/j.compchemeng.2014.07.020.

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20

Atamtürk, Alper, and Martin W. P. Savelsbergh. "Integer-Programming Software Systems." Annals of Operations Research 140, no. 1 (November 2005): 67–124. http://dx.doi.org/10.1007/s10479-005-3968-2.

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21

Weintraub P., Andres. "Integer programming in forestry." Annals of Operations Research 149, no. 1 (December 2, 2006): 209–16. http://dx.doi.org/10.1007/s10479-006-0105-9.

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22

Firmansah, Fery, Muhammad Ridlo Yuwono, and Fika Aisyah Munif. "Application of integer linear program in optimizing convection sector production results using branch and bound method." International Journal of Applied Mathematics, Sciences, and Technology for National Defense 1, no. 1 (January 27, 2023): 13–20. http://dx.doi.org/10.58524/app.sci.def.v1i1.173.

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This study aimed to determine the application of the integer program in optimizing the production of the convection sector. Integer linear programming is a special form of linear programming in which the decision variable solutions are integers. Ayyumnah store as one part of the convection sectors with a home-scale does not have an appropriate strategy to optimize profits with limited materials owned. The method used in this study is an integer program with the branch and bound method. The result of this research is the optimal amount of production of long shirts and tunics at the Ayyumnah Store with maximum profit.

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23

Klamroth, Kathrin, Jørgen Tind, and Sibylle Zust. "Integer Programming Duality in Multiple Objective Programming." Journal of Global Optimization 29, no. 1 (May 2004): 1–18. http://dx.doi.org/10.1023/b:jogo.0000035000.06101.07.

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24

Marchand, Hugues, Alexander Martin, Robert Weismantel, and Laurence Wolsey. "Cutting planes in integer and mixed integer programming." Discrete Applied Mathematics 123, no. 1-3 (November 2002): 397–446. http://dx.doi.org/10.1016/s0166-218x(01)00348-1.

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25

Gazzah, H., and A. K. Khandani. "Optimum non-integer rate allocation using integer programming." Electronics Letters 33, no. 24 (1997): 2034. http://dx.doi.org/10.1049/el:19971417.

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26

Forrest, J. J. H., and J. A. Tomlin. "Branch and bound, integer, and non-integer programming." Annals of Operations Research 149, no. 1 (December 2, 2006): 81–87. http://dx.doi.org/10.1007/s10479-006-0112-x.

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27

Domínguez, Luis F., and Efstratios N. Pistikopoulos. "Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems." Computers & Chemical Engineering 34, no. 12 (December 2010): 2097–106. http://dx.doi.org/10.1016/j.compchemeng.2010.07.032.

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28

Maslikhah, Siti. "METODE PEMECAHAN MASALAH INTEGER PROGRAMMING." At-Taqaddum 7, no. 2 (February 6, 2017): 211. http://dx.doi.org/10.21580/at.v7i2.1203.

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<em>Decision variables in the problem solving linear programs are often in the form of fractions. In some cases there are specific desires the solution in the form of an integer (integer). Integer solution is obtained by way of rounding does not warrant being in the area of fisibel. To obtain integer solutions, among others, by the method of Cutting Plane Algorithm or Branch and Bound. The advantages of the method of Cutting Plane Algorithm is quite effectively shorten the matter, while the advantages of the method of Branch and Bound the error level is to have a little but requires quite a long calculation.</em>

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29

Earnshaw, Stephanie R., and Susan L. Dennett. "Integer/Linear Mathematical Programming Models." PharmacoEconomics 21, no. 12 (2003): 839–51. http://dx.doi.org/10.2165/00019053-200321120-00001.

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30

Lee, D.-H., H.-J. Kim, G. Choi, and P. Xirouchakis. "Disassembly scheduling: Integer programming models." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 218, no. 10 (October 2004): 1357–72. http://dx.doi.org/10.1243/0954405042323586.

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31

Gavish, Bezalel, Fred Glover, and Hasan Pirkul. "Surrogate Constraints in Integer Programming." Journal of Information and Optimization Sciences 12, no. 2 (May 1991): 219–28. http://dx.doi.org/10.1080/02522667.1991.10699064.

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32

Wilson, J. M. "Crossword Compilation Using Integer Programming." Computer Journal 32, no. 3 (March 1, 1989): 273–75. http://dx.doi.org/10.1093/comjnl/32.3.273.

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33

Feng, Zhiguo, and Ka-Fai Cedric Yiu. "Manifold relaxations for integer programming." Journal of Industrial & Management Optimization 10, no. 2 (2014): 557–66. http://dx.doi.org/10.3934/jimo.2014.10.557.

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34

Gupta, Renu, and M. C. Puri. "Bicriteria integer quadratic programming problems." Journal of Interdisciplinary Mathematics 3, no. 2-3 (June 2000): 133–48. http://dx.doi.org/10.1080/09720502.2000.10700277.

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35

Williams, H. "Integer programming and pricing revisited." IMA Journal of Management Mathematics 8, no. 3 (March 1, 1997): 203–13. http://dx.doi.org/10.1093/imaman/8.3.203.

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36

Hoşten, Serkan, and Bernd Sturmfels. "Computing the integer programming gap." Combinatorica 27, no. 3 (May 2007): 367–82. http://dx.doi.org/10.1007/s00493-007-2057-3.

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37

Hua, Hao, Ludger Hovestadt, Peng Tang, and Biao Li. "Integer programming for urban design." European Journal of Operational Research 274, no. 3 (May 2019): 1125–37. http://dx.doi.org/10.1016/j.ejor.2018.10.055.

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38

Gomory, Ralph E., and Ellis L. Johnson. "An approach to integer programming." Mathematical Programming 96, no. 2 (May 1, 2003): 181. http://dx.doi.org/10.1007/s10107-003-0382-x.

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39

Schultz, Rüdiger. "Stochastic programming with integer variables." Mathematical Programming 97, no. 1 (July 2003): 285–309. http://dx.doi.org/10.1007/s10107-003-0445-z.

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40

Röglin, Heiko, and Berthold Vöcking. "Smoothed analysis of integer programming." Mathematical Programming 110, no. 1 (January 5, 2007): 21–56. http://dx.doi.org/10.1007/s10107-006-0055-7.

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41

Zou, Jikai, Shabbir Ahmed, and Xu Andy Sun. "Stochastic dual dynamic integer programming." Mathematical Programming 175, no. 1-2 (March 2, 2018): 461–502. http://dx.doi.org/10.1007/s10107-018-1249-5.

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42

Klabjan, Diego. "Subadditive approaches in integer programming." European Journal of Operational Research 183, no. 2 (December 2007): 525–45. http://dx.doi.org/10.1016/j.ejor.2006.10.009.

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43

Sahinidis, Nikolaos V. "Mixed-integer nonlinear programming 2018." Optimization and Engineering 20, no. 2 (April 24, 2019): 301–6. http://dx.doi.org/10.1007/s11081-019-09438-1.

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44

Adams, Warren P., and Hanif D. Sherali. "Mixed-integer bilinear programming problems." Mathematical Programming 59, no. 1-3 (March 1993): 279–305. http://dx.doi.org/10.1007/bf01581249.

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45

Allahviranloo, T., Kh Shamsolkotabi, N. A. Kiani, and L. Alizadeh. "Fuzzy integer linear programming problems." International Journal of Contemporary Mathematical Sciences 2 (2007): 167–81. http://dx.doi.org/10.12988/ijcms.2007.07010.

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46

Vessal, Ahmad. "COURSE SEQUENCING USING INTEGER PROGRAMMING." Journal of Academy of Business and Economics 13, no. 4 (October 1, 2013): 97–102. http://dx.doi.org/10.18374/jabe-13-4.10.

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47

Williams, H. P. "The problem with integer programming." IMA Journal of Management Mathematics 22, no. 3 (October 5, 2010): 213–30. http://dx.doi.org/10.1093/imaman/dpq014.

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48

Lovász, László. "Integer sequences and semidefinite programming." Publicationes Mathematicae Debrecen 56, no. 3-4 (April 1, 2000): 475–79. http://dx.doi.org/10.5486/pmd.2000.2362.

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49

Labbé, Martine, Alfredo Marín, and Antonio M. Rodríguez-Chía. "Lexicographical Order in Integer Programming." Vietnam Journal of Mathematics 45, no. 3 (July 27, 2016): 459–76. http://dx.doi.org/10.1007/s10013-016-0220-0.

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50

Raghavan, Prabhakar. "Integer programming in VLSI design." Discrete Applied Mathematics 40, no. 1 (November 1992): 29–43. http://dx.doi.org/10.1016/0166-218x(92)90020-b.

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