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Journal articles on the topic 'Nonlinear Knapsack Problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Hochbaum, Dorit S. "A nonlinear Knapsack problem." Operations Research Letters 17, no. 3 (April 1995): 103–10. http://dx.doi.org/10.1016/0167-6377(95)00009-9.

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2

ZHANG, BIN, and BO CHEN. "HEURISTIC AND EXACT SOLUTION METHOD FOR CONVEX NONLINEAR KNAPSACK PROBLEM." Asia-Pacific Journal of Operational Research 29, no. 05 (October 2012): 1250031. http://dx.doi.org/10.1142/s0217595912500315.

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In this paper, we consider a class of convex nonlinear knapsack problems in which all decision variables are integer and the objective and knapsack functions are nonlinear. This generalized problem is characterized by positive marginal cost (PMC) and increasing marginal loss-cost ratio (IMLCR). By analyzing the structural properties of the problem, we develop an efficient heuristic and propose search and branching rules to improve the branch and bound method for solving exact solution. Numerical study is done for showing the effectiveness of the proposed heuristic and the modified branch and bound method.

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3

Bretthauer, Kurt M., and Bala Shetty. "The nonlinear knapsack problem – algorithms and applications." European Journal of Operational Research 138, no. 3 (May 2002): 459–72. http://dx.doi.org/10.1016/s0377-2217(01)00179-5.

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4

Klastorin, T. D. "On a discrete nonlinear and nonseparable knapsack problem." Operations Research Letters 9, no. 4 (July 1990): 233–37. http://dx.doi.org/10.1016/0167-6377(90)90067-f.

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5

D’Ambrosio, Claudia, and Silvano Martello. "Heuristic algorithms for the general nonlinear separable knapsack problem." Computers & Operations Research 38, no. 2 (February 2011): 505–13. http://dx.doi.org/10.1016/j.cor.2010.07.010.

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6

Luss, Hanan. "A nonlinear minimax allocation problem with multiple knapsack constraints." Operations Research Letters 10, no. 4 (June 1991): 183–87. http://dx.doi.org/10.1016/0167-6377(91)90057-v.

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7

Ping, Yuan, Baocang Wang, Shengli Tian, Jingxian Zhou, and Hui Ma. "PKCHD: Towards A Probabilistic Knapsack Public-Key Cryptosystem with High Density." Information 10, no. 2 (February 21, 2019): 75. http://dx.doi.org/10.3390/info10020075.

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By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit attacker has to solve at least two hard number-theoretic problems, namely integer factorization and simultaneous Diophantine approximation problems. In PKCHD, the encryption function is nonlinear about the message vector. Under the re-linearization attack model, PKCHD obtains a high density and is secure against the low-density subset sum attacks, and the success probability for an attacker to recover the message vector with a single call to a lattice oracle is negligible. The infeasibilities of other attacks on the proposed PKCHD are also investigated. Meanwhile, it can use the hardest knapsack vector as the public key if its density evaluates the hardness of a knapsack instance. Furthermore, PKCHD only performs quadratic bit operations which confirms the efficiency of encrypting a message and deciphering a given cipher-text.

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8

Korutcheva, E., M. Opper, and B. Lopez. "Statistical mechanics of the knapsack problem." Journal of Physics A: Mathematical and General 27, no. 18 (September 21, 1994): L645—L650. http://dx.doi.org/10.1088/0305-4470/27/18/001.

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9

Hou, Wenjun, and Marek Perkowski. "Quantum-based algorithm and circuit design for bounded Knapsack optimization problem." Quantum Information and Computation 20, no. 9&10 (August 2020): 766–86. http://dx.doi.org/10.26421/qic20.9-10-4.

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The Knapsack Problem is a prominent problem that is used in resource allocation and cryptography. This paper presents an oracle and a circuit design that verifies solutions to the decision problem form of the Bounded Knapsack Problem. This oracle can be used by Grover Search to solve the optimization problem form of the Bounded Knapsack Problem. This algorithm leverages the quadratic speed-up offered by Grover Search to achieve a quantum algorithm for the Knapsack Problem that shows improvement with regard to classical algorithms. The quantum circuits were designed using the Microsoft Q# Programming Language and verified on its local quantum simulator. The paper also provides analyses of the complexity and gate cost of the proposed oracle. The work in this paper is the first such proposed method for the Knapsack Optimization Problem.

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10

Fontanari, J. F. "A statistical analysis of the knapsack problem." Journal of Physics A: Mathematical and General 28, no. 17 (September 7, 1995): 4751–59. http://dx.doi.org/10.1088/0305-4470/28/17/011.

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11

Goos, P., U. Syafitri, B. Sartono, and A. R. Vazquez. "A nonlinear multidimensional knapsack problem in the optimal design of mixture experiments." European Journal of Operational Research 281, no. 1 (February 2020): 201–21. http://dx.doi.org/10.1016/j.ejor.2019.08.020.

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12

Inoue, Jun-ichi. "Statistical mechanics of the multi-constraint continuous knapsack problem." Journal of Physics A: Mathematical and General 30, no. 4 (February 21, 1997): 1047–58. http://dx.doi.org/10.1088/0305-4470/30/4/008.

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13

Granmo, Ole-Christoffer, and B. John Oommen. "Learning automata-based solutions to the optimal web polling problem modelled as a nonlinear fractional knapsack problem." Engineering Applications of Artificial Intelligence 24, no. 7 (October 2011): 1238–51. http://dx.doi.org/10.1016/j.engappai.2011.05.018.

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14

Wang, Wei, Ting Yu, Tian Jiao Pu, Ai Zhong Tian, and Ji Keng Lin. "The Optimal Controlled Partitioning Strategy for Power System Based on Master-Slave Problem." Applied Mechanics and Materials 385-386 (August 2013): 999–1006. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.999.

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Controlled partitioning strategy is one of the effective measures taken for the situation when system out-of-step occurs. The complete splitting model, mostly solved by approximate decomposition algorithms, is a large-scale nonlinear mixed integer programming problem. A new alternate optimization method based on master-slave problem to search for optimal splitting strategy is proposed hereby. The complete model was converted into master-slave problems based on CGKP (Connected Graph Constrained Knapsack Problem). The coupling between master problem and slave problem is achieved through load adjustment. A better splitting strategy can be obtained through the alternating iteration between the master problem and the salve problem. The results of the examples show that the method can obtain better splitting strategy with less shed load than other approximate algorithms, which verifies the feasibility and effectiveness of the new approach presented.

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15

Zare, M. Hosein, Oleg A. Prokopyev, and Denis Sauré. "On Bilevel Optimization with Inexact Follower." Decision Analysis 17, no. 1 (March 2020): 74–95. http://dx.doi.org/10.1287/deca.2019.0392.

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Traditionally, in the bilevel optimization framework, a leader chooses her actions by solving an upper-level problem, assuming that a follower chooses an optimal reaction by solving a lower-level problem. However, in many settings, the lower-level problems might be nontrivial, thus requiring the use of tailored algorithms for their solution. More importantly, in practice, such problems might be inexactly solved by heuristics and approximation algorithms. Motivated by this consideration, we study a broad class of bilevel optimization problems where the follower might not optimally react to the leader’s actions. In particular, we present a modeling framework in which the leader considers that the follower might use one of a number of known algorithms to solve the lower-level problem, either approximately or heuristically. Thus, the leader can hedge against the follower’s use of suboptimal solutions. We provide algorithmic implementations of the framework for a class of nonlinear bilevel knapsack problem (BKP), and we illustrate the potential impact of incorporating this realistic feature through numerical experiments in the context of defender-attacker problems.

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16

Granmo, Ole-Christoffer, B. John Oommen, Svein Arild Myrer, and Morten Goodwin Olsen. "Learning Automata-Based Solutions to the Nonlinear Fractional Knapsack Problem With Applications to Optimal Resource Allocation." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 37, no. 1 (February 2007): 166–75. http://dx.doi.org/10.1109/tsmcb.2006.879012.

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17

Yanıkoğlu, İhsan. "Robust reformulations of ambiguous chance constraints with discrete probability distributions." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 9, no. 2 (July 31, 2019): 236–52. http://dx.doi.org/10.11121/ijocta.01.2019.00611.

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This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation.

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18

Granmo, Ole-Christoffer, and B. John Oommen. "Optimal sampling for estimation with constrained resources using a learning automaton-based solution for the nonlinear fractional knapsack problem." Applied Intelligence 33, no. 1 (April 24, 2010): 3–20. http://dx.doi.org/10.1007/s10489-010-0228-1.

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19

Sharkey, Thomas C., H. Edwin Romeijn, and Joseph Geunes. "A class of nonlinear nonseparable continuous knapsack and multiple-choice knapsack problems." Mathematical Programming 126, no. 1 (March 5, 2009): 69–96. http://dx.doi.org/10.1007/s10107-009-0274-9.

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20

Körner, Frank. "A hybrid method for solving nonlinear knapsack problems." European Journal of Operational Research 38, no. 2 (January 1989): 238–41. http://dx.doi.org/10.1016/0377-2217(89)90109-4.

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21

Zhang, Bin, Zhe Lin, and Yu Wang. "A Class of Continuous Separable Nonlinear Multidimensional Knapsack Problems." American Journal of Operations Research 08, no. 04 (2018): 266–80. http://dx.doi.org/10.4236/ajor.2018.84015.

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22

Elhedhli, Samir. "Exact solution of a class of nonlinear knapsack problems." Operations Research Letters 33, no. 6 (November 2005): 615–24. http://dx.doi.org/10.1016/j.orl.2005.01.004.

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23

Chen, Juan, Xiao-ling Sun, and Hui-juan Guo. "An efficient algorithm for multi-dimensional nonlinear knapsack problems." Journal of Shanghai University (English Edition) 10, no. 5 (October 2006): 393–98. http://dx.doi.org/10.1007/s11741-006-0079-5.

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24

Kong, Shan-shan, and Xiao-ling Sun. "Surrogate dual method for multi-dimensional nonlinear knapsack problems." Journal of Shanghai University (English Edition) 11, no. 4 (August 2007): 340–43. http://dx.doi.org/10.1007/s11741-007-0404-1.

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25

Li, D., X. L. Sun, J. Wang, and K. I. M. McKinnon. "Convergent Lagrangian and domain cut method for nonlinear knapsack problems." Computational Optimization and Applications 42, no. 1 (October 31, 2007): 67–104. http://dx.doi.org/10.1007/s10589-007-9113-1.

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26

Sniedovich, Moshe, and Shamsedin Vazirinejad. "A Solution Strategy for a Class of Nonlinear Knapsack Problems." American Journal of Mathematical and Management Sciences 10, no. 1-2 (January 1990): 51–71. http://dx.doi.org/10.1080/01966324.1990.10737276.

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27

Smith, J. MacGregor, and Nikhil Chikhale. "Buffer allocation for a class of nonlinear stochastic knapsack problems." Annals of Operations Research 58, no. 5 (September 1995): 323–60. http://dx.doi.org/10.1007/bf02038860.

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28

Melman, A., and G. Rabinowitz. "An Efficient Method for a Class of Continuous Nonlinear Knapsack Problems." SIAM Review 42, no. 3 (January 2000): 440–48. http://dx.doi.org/10.1137/s0036144598330177.

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29

Beheshti, Behdad, Osman Y. Özaltın, M. Hosein Zare, and Oleg A. Prokopyev. "Exact solution approach for a class of nonlinear bilevel knapsack problems." Journal of Global Optimization 61, no. 2 (May 3, 2014): 291–310. http://dx.doi.org/10.1007/s10898-014-0189-8.

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30

Kim, Gitae, and Chih-Hang Wu. "A pegging algorithm for separable continuous nonlinear knapsack problems with box constraints." Engineering Optimization 44, no. 10 (October 2012): 1245–59. http://dx.doi.org/10.1080/0305215x.2011.646263.

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31

Zhang, Bin, and Zhongsheng Hua. "A unified method for a class of convex separable nonlinear knapsack problems." European Journal of Operational Research 191, no. 1 (November 2008): 1–6. http://dx.doi.org/10.1016/j.ejor.2007.07.005.

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32

Ohtagaki, H., Y. Nakagawa, A. Iwasaki, and H. Narihisa. "Smart greedy procedure for solving a nOnlinear knapsack class of reliability optimization problems." Mathematical and Computer Modelling 22, no. 10-12 (November 1995): 261–72. http://dx.doi.org/10.1016/0895-7177(95)00203-e.

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33

Ghassemi-Tari, Farhad, and Eshagh Jahangiri. "Development of a hybrid dynamic programming approach for solving discrete nonlinear knapsack problems." Applied Mathematics and Computation 188, no. 1 (May 2007): 1023–30. http://dx.doi.org/10.1016/j.amc.2006.10.067.

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34

Ohtagaki, H., A. Iwasaki, Y. Nakagawa, and H. Narihisa. "Smart greedy procedure for solving a multidimensional nonlinear knapsack class of reliability optimization problems." Mathematical and Computer Modelling 31, no. 10-12 (May 2000): 283–88. http://dx.doi.org/10.1016/s0895-7177(00)00097-2.

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35

Riha, W. O., and J. Walker. "An efficient algorithm for the Lagrangean dual of nonlinear knapsack problems with additional nested constraints." Journal of Computational and Applied Mathematics 78, no. 1 (February 1997): 9–18. http://dx.doi.org/10.1016/s0377-0427(96)00101-x.

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36

Crama, Yves, and Joseph B. Mazzola. "Valid inequalities and facets for a hypergraph model of the nonlinear knapsack and the FMS part selection problems." Annals of Operations Research 58, no. 2 (March 1995): 99–128. http://dx.doi.org/10.1007/bf02032163.

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37

Visagie, SE. "On the efficient solvability of a simple class of nonlinear knapsack problems." ORiON 24, no. 1 (June 1, 2008). http://dx.doi.org/10.5784/24-1-56.

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