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1

Mo, Jiangtao, Liqun Qi, and Zengxin Wei. "A network simplex algorithm for simple manufacturing network model." Journal of Industrial & Management Optimization 1, no. 2 (2005): 251–73. http://dx.doi.org/10.3934/jimo.2005.1.251.

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2

Ahuja, Ravindra K., and James B. Orlin. "The Scaling Network Simplex Algorithm." Operations Research 40, no. 1-supplement-1 (February 1992): S5—S13. http://dx.doi.org/10.1287/opre.40.1.s5.

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3

Orlin, James B., Serge A. Plotkin, and Éva Tardos. "Polynomial dual network simplex algorithms." Mathematical Programming 60, no. 1-3 (June 1993): 255–76. http://dx.doi.org/10.1007/bf01580615.

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4

Eppstein, David. "Clustering for faster network simplex pivots." Networks 35, no. 3 (May 2000): 173–80. http://dx.doi.org/10.1002/(sici)1097-0037(200005)35:3<173::aid-net1>3.0.co;2-w.

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5

Anderson, E. J., and A. B. Philpott. "A continuous-time network simplex algorithm." Networks 19, no. 4 (July 1989): 395–425. http://dx.doi.org/10.1002/net.3230190403.

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6

Peters, Jörg. "The network simplex method on a multiprocessor." Networks 20, no. 7 (December 1990): 845–59. http://dx.doi.org/10.1002/net.3230200704.

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7

Aronson, Jay E., and B. David Chen. "A forward network simplex algorithm for solving multiperiod network flow problems." Naval Research Logistics Quarterly 33, no. 3 (August 1986): 445–67. http://dx.doi.org/10.1002/nav.3800330310.

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8

Venkateshan, Prahalad, Kamlesh Mathur, and Ronald H. Ballou. "An efficient generalized network-simplex-based algorithm for manufacturing network flows." Journal of Combinatorial Optimization 15, no. 4 (June 8, 2007): 315–41. http://dx.doi.org/10.1007/s10878-007-9080-6.

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9

Sharkey, Thomas C., and H. Edwin Romeijn. "A simplex algorithm for minimum-cost network-flow problems in infinite networks." Networks 52, no. 1 (August 2008): 14–31. http://dx.doi.org/10.1002/net.20221.

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10

Rashidi, Hassan. "A dynamic version for the Network Simplex Algorithm." Applied Soft Computing 24 (November 2014): 414–22. http://dx.doi.org/10.1016/j.asoc.2014.07.017.

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11

Armstrong, Ronald D., and Zhiying Jin. "A new strongly polynomial dual network simplex algorithm." Mathematical Programming 78, no. 2 (August 1997): 131–48. http://dx.doi.org/10.1007/bf02614366.

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12

Lee, Suk Bae, and Su Chang Auh. "Determination of the Optimal Height using the Simplex Algorithm in Network-RTK Surveying." Journal of Korean Society for Geospatial Information System 24, no. 1 (March 31, 2016): 35–41. http://dx.doi.org/10.7319/kogsis.2016.24.1.035.

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13

Morrison, David R., Jason J. Sauppe, and Sheldon H. Jacobson. "A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network." INFORMS Journal on Computing 25, no. 1 (February 2013): 2–12. http://dx.doi.org/10.1287/ijoc.1110.0485.

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14

Calvete, Herminia I. "Network simplex algorithm for the general equal flow problem." European Journal of Operational Research 150, no. 3 (November 2003): 585–600. http://dx.doi.org/10.1016/s0377-2217(02)00505-2.

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15

Shen, Wei, Yu Nie, and H. M. Zhang. "Dynamic Network Simplex Method for Designing Emergency Evacuation Plans." Transportation Research Record: Journal of the Transportation Research Board 2022, no. 1 (January 2007): 83–93. http://dx.doi.org/10.3141/2022-10.

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16

Barras, J., S. Alec, C. Pasche, P. A. Chamorel, A. J. Germond, and D. de Werra. "Network Simplex Method Applied to AC Load-Flow Calculation." IEEE Power Engineering Review PER-7, no. 2 (February 1987): 45. http://dx.doi.org/10.1109/mper.1987.5527556.

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17

Zheng, Hong. "Adaptation of Network Simplex for the Traffic Assignment Problem." Transportation Science 49, no. 3 (August 2015): 543–58. http://dx.doi.org/10.1287/trsc.2014.0574.

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18

Watanabe, Sennosuke, Hodaka Tanaka, and Yoshihide Watanabe. "NETWORK SIMPLEX ALGORITHM ASSOCIATED WITH THE MAXIMUM FLOW PROBLEM." Far East Journal of Mathematical Sciences (FJMS) 104, no. 1 (July 1, 2018): 119–32. http://dx.doi.org/10.17654/ms104010119.

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19

Goldfarb, Donald, Jianxiu Hao, and Sheng-Roan Kai. "Anti-stalling pivot rules for the network simplex algorithm." Networks 20, no. 1 (January 1990): 79–91. http://dx.doi.org/10.1002/net.3230200108.

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20

Barras, J., S. Alec, C. Pasche, P. A. Chamorel, A. J. Germond, and D. de Werra. "Network Simplex Method Applied to AC Load-Flow Calculation." IEEE Transactions on Power Systems 2, no. 1 (1987): 197–203. http://dx.doi.org/10.1109/tpwrs.1987.4335100.

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21

Ali, A. Iqbal, Ellen P. Allen, Richard S. Barr, and Jeffery L. Kennington. "Reoptimization procedures for bounded variable primal simplex network algorithms." European Journal of Operational Research 23, no. 2 (February 1986): 256–63. http://dx.doi.org/10.1016/0377-2217(86)90245-6.

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22

Arantes, José C., J. R. Birge, and K. G. Murty. "Studies of lexicography in the generalized network simplex method." Annals of Operations Research 46-47, no. 2 (September 1993): 235–48. http://dx.doi.org/10.1007/bf02023097.

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23

Manzoul, Mahmoud A., and Mamoun Suliman. "Neural network for the reliability analysis of simplex systems." Microelectronics Reliability 30, no. 4 (January 1990): 795–800. http://dx.doi.org/10.1016/0026-2714(90)90184-o.

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24

Zheng, Quan, Jun Li, Hongliang Tian, Zhizhen Wang, and Song Wang. "A 2-Layers Virtual Network Mapping Algorithm Based on Node Attribute and Network Simplex." IEEE Access 6 (2018): 77474–84. http://dx.doi.org/10.1109/access.2018.2883251.

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25

Masoood, Sarfaraz, and Nida Safdar Jan. "SIMPLEX: An Activation Function with Improved Loss Function Results in Validation." Journal of Computational and Theoretical Nanoscience 17, no. 1 (January 1, 2020): 147–53. http://dx.doi.org/10.1166/jctn.2020.8643.

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An activation function is a mathematical function used for squashing purposes in artificial neural networks, whose domain and the range are two important most features to judge its potency. Overfitting of a neural network, is an issue that has gained considerable importance. This is a consequence of a function developing some complex relationship during the training phase and then these do not show up during the testing phase due to which these relationships aren’t actually relations, but are merely a consequence of sampling noise that arises during the training phase and is absent during testing phase. This creates a significant gap in accuracy which if minimized could result in better results in terms of overall performance of an ANN (Artificial Neural Network). The activation function proposed in this work is called SIMPLEX. Over a set of experiments, it was observed, to have the least overfitting issue among the rest of the analyzed activation functions over the MNIST dataset, selected as the experimental problem.
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26

Cui, Wentian. "A NETWORK SIMPLEX METHOD FOR THE MAXIMUM BALANCED FLOW PROBLEM." Journal of the Operations Research Society of Japan 31, no. 4 (1988): 551–64. http://dx.doi.org/10.15807/jorsj.31.551.

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27

Eapen, BellRaj. "'Neural network' algorithm to predict severity in epidermolysis bullosa simplex." Indian Journal of Dermatology, Venereology and Leprology 71, no. 2 (2005): 106. http://dx.doi.org/10.4103/0378-6323.13995.

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28

Ahuja, Ravindra K., James B. Orlin, Prabha Sharma, and P. T. Sokkalingam. "A network simplex algorithm with O(n) consecutive degenerate pivots." Operations Research Letters 30, no. 3 (June 2002): 141–48. http://dx.doi.org/10.1016/s0167-6377(02)00114-1.

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29

McBride, Richard D., and John W. Mamer. "Implementing an LU Factorization for the Embedded Network Simplex Algorithm." INFORMS Journal on Computing 16, no. 2 (May 2004): 109–19. http://dx.doi.org/10.1287/ijoc.1040.0086.

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30

Crainic, Teodor Gabriel, Michel Gendreau, and Judith M. Farvolden. "A Simplex-Based Tabu Search Method for Capacitated Network Design." INFORMS Journal on Computing 12, no. 3 (August 2000): 223–36. http://dx.doi.org/10.1287/ijoc.12.3.223.12638.

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31

Ahmed, Shamsuddin. "Degenerated simplex search method to optimize neural network error function." Kybernetes 42, no. 1 (January 4, 2013): 106–24. http://dx.doi.org/10.1108/03684921311295510.

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32

Sokkalingam, P. T., Prabha Sharma, and Ravindra K. Ahuja. "A new pivot selection rule for the network simplex algorithm." Mathematical Programming 78, no. 2 (August 1997): 149–58. http://dx.doi.org/10.1007/bf02614367.

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33

Drzymała, Michał, Krzysztof Szczypiorski, and Marek Łukasz Urbański. "Network Steganography in the DNS Protocol." International Journal of Electronics and Telecommunications 62, no. 4 (December 1, 2016): 343–46. http://dx.doi.org/10.1515/eletel-2016-0047.

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Abstract This paper presents possibility of using of the DNS (Domain Name System) protocol for creating a simplex communication channel between a malware-infected computer with a compromised DNS server. The proposed channel can be used to steal data or confidential enterprise information secretly.
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34

Chen, Wei. "Application of Hybrid Genetic Algorithm in Control Network Adjustment." Applied Mechanics and Materials 353-356 (August 2013): 3434–37. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3434.

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In this paper a hybrid genetic algorithm which consists of the simplex method and the genetic algorithm is proposed for the defect of poor local search ability of genetic algorithm. The hybrid genetic algorithm has the advantages of good global convergence of the genetic algorithm and excellent local search ablility of the simplex method and can improve search speed and calculation accuracy.The hybrid algorithm is applied to the control network adjustment and experimental results demonstrates the effectiveness and superiority of the algorithm.
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35

Devriendt, Karel, and Piet Van Mieghem. "The simplex geometry of graphs." Journal of Complex Networks 7, no. 4 (January 29, 2019): 469–90. http://dx.doi.org/10.1093/comnet/cny036.

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AbstractGraphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.
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36

Aronson, Jay E., and B. David Chen. "A primary/secondary memory implementation of a forward network simplex algorithm for multiperiod network flow problems." Computers & Operations Research 16, no. 4 (January 1989): 379–91. http://dx.doi.org/10.1016/0305-0548(89)90009-9.

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37

Andreou, D., K. Paparrizos, N. Samaras, and A. Sifaleras. "Visualization software of the network exterior primal simplex algorithm for the minimum cost network flow problem." Operational Research 7, no. 3 (September 2007): 449–63. http://dx.doi.org/10.1007/bf03024857.

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38

Geranis, George, Konstantinos Paparizzos, and Angelo Sifaleras. "A dual exterior point simplex type algorithm for the minimum cost network flow problem." Yugoslav Journal of Operations Research 19, no. 1 (2009): 157–70. http://dx.doi.org/10.2298/yjor0901157g.

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A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree).
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39

Muramatsu, Masakazu. "ON NETWORK SIMPLEX METHOD USING THE PRIMAL-DUAL SYMMETRIC PIVOTING RULE." Journal of the Operations Research Society of Japan 43, no. 1 (2000): 149–61. http://dx.doi.org/10.15807/jorsj.43.149.

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40

Baloukas, Thanasis, Konstantios Paparrizos, and Angelo Sifaleras. "Teaching Note—An Animated Demonstration of the Uncapacitated Network Simplex Algorithm." INFORMS Transactions on Education 10, no. 1 (September 2009): 34–40. http://dx.doi.org/10.1287/ited.1090.0026.

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41

McBride, Richard D., and John W. Mamer. "Solving Multicommodity Flow Problems with a Primal Embedded Network Simplex Algorithm." INFORMS Journal on Computing 9, no. 2 (May 1997): 154–63. http://dx.doi.org/10.1287/ijoc.9.2.154.

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42

Arsham, H., and M. Oblak. "A comprehensive simplex-like algorithm for network optimization and perturbation analysis." Optimization 32, no. 3 (January 1995): 211–67. http://dx.doi.org/10.1080/02331939508844049.

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43

Wang, I.-Lin, and Shiou-Jie Lin. "A network simplex algorithm for solving the minimum distribution cost problem." Journal of Industrial & Management Optimization 5, no. 4 (2009): 929–50. http://dx.doi.org/10.3934/jimo.2009.5.929.

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44

Coutinho, Rafaelli de C., Lúcia M. A. Drummond, and Yuri Frota. "A distributed transportation simplex applied to a Content Distribution Network problem." RAIRO - Operations Research 48, no. 2 (March 7, 2014): 189–210. http://dx.doi.org/10.1051/ro/2014007.

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45

Ryan, Christopher Thomas, Robert L. Smith, and Marina A. Epelman. "A Simplex Method for Uncapacitated Pure-supply Infinite Network Flow Problems." SIAM Journal on Optimization 28, no. 3 (January 2018): 2022–48. http://dx.doi.org/10.1137/17m1137553.

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46

Eusébio, Augusto, José Rui Figueira, and Matthias Ehrgott. "A primal–dual simplex algorithm for bi-objective network flow problems." 4OR 7, no. 3 (September 18, 2008): 255–73. http://dx.doi.org/10.1007/s10288-008-0087-3.

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47

Paparrizos, Konstantinos, Nikolaos Samaras, and Angelo Sifaleras. "Exterior point simplex-type algorithms for linear and network optimization problems." Annals of Operations Research 229, no. 1 (January 1, 2015): 607–33. http://dx.doi.org/10.1007/s10479-014-1769-1.

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48

Çalışkan, Cenk. "A specialized network simplex algorithm for the constrained maximum flow problem." European Journal of Operational Research 210, no. 2 (April 2011): 137–47. http://dx.doi.org/10.1016/j.ejor.2010.10.018.

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49

Orlin, James B. "A polynomial time primal network simplex algorithm for minimum cost flows." Mathematical Programming 78, no. 2 (August 1997): 109–29. http://dx.doi.org/10.1007/bf02614365.

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50

Sun, Jie, and K. Tsai. "A generator and a simplex solver for network piecewise linear programs." Acta Mathematicae Applicatae Sinica 10, no. 2 (April 1994): 177–85. http://dx.doi.org/10.1007/bf02006117.

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