On the simplex algorithm initializing This paper discusses the importance of a starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on the Netlib test problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

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  1. Ploskas, Nikolaos; Sahinidis, Nikolaos V.; Samaras, Nikolaos: A triangulation and fill-reducing initialization procedure for the simplex algorithm (2021)
  2. Martín Martín, Raúl; García-Camacha Gutiérrez, Irene; Torsney, Bernard: Efficient algorithms for constructing (D)- and (I)-optimal exact designs for linear and non-linear models in mixture experiments (2019)
  3. Zhen, Lu; Yu, Shucheng; Wang, Shuaian; Sun, Zhuo: Scheduling quay cranes and yard trucks for unloading operations in container ports (2019)
  4. Hoeher, P. A.: OFDM data detection and channel estimation (2017)
  5. Gao, Pei-wang: Improvement and its computer implementation of an artificial-free simplex-type algorithm by Arsham (2015)
  6. Ma, Yanqin; Zhang, Lili; Pan, Pingqi: Criss-cross algorithm based on the most-obtuse-angle rule and deficient basis (2015)
  7. Nabli, Hédi; Chahdoura, Sonia: Algebraic simplex initialization combined with the nonfeasible basis method (2015)
  8. Rudolph, Helmut: Some applications of the semi-infinite simplex algorithm (2015)
  9. Saito, G.; Corley, H. W.; Rosenberger, Jay M.; Sung, Tai-Kuan; Noroziroshan, Alireza: Constraint optimal selection techniques (COSTs) for nonnegative linear programming problems (2015)
  10. Boonperm, Aua-aree; Sinapiromsaran, Krung: Artificial-free simplex algorithm based on the non-acute constraint relaxation (2014)
  11. Du, Xiuli; Cui, Dong; Hou, Benwei: An initial population improvement strategy of empirical genetic-simplex algorithm (2014)
  12. Stojković, Nebojša V.; Stanimirović, Predrag S.; Petković, Marko D.; Milojković, Danka S.: On the simplex algorithm initializing (2012)
  13. Al-Najjar, Camelia; Malakooti, Behnam: Hybrid-LP: finding advanced starting points for simplex, and pivoting LP methods (2011)
  14. Li, Wei; Li, Haohao: On simplex method with most-obtuse-angle rule and cosine rule (2011)
  15. Malakooti, Behnam; Al-Najjar, Camelia: The complex interior-boundary method for linear and nonlinear programming with linear constraints (2010)
  16. Nabli, Hédi: An overview on the simplex algorithm (2009)
  17. Yeh, Wei-Chang; Corley, H. W.: A simple direct cosine simplex algorithm (2009)
  18. Arsham, H.: A computationally stable solution algorithm for linear programs (2007)
  19. Arsham, Hossein: A hybrid gradient and feasible direction pivotal solution algorithm for general linear programs (2007)
  20. Hu, Jian-Feng: A note on “An improved initial basis for the simplex algorithm” (2007)

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