On a dual network exterior point simplex type algorithm and its computational behavior∗

George Geranis; Konstantinos Paparrizos; Angelo Sifaleras

RAIRO - Operations Research (2012)

  • Volume: 46, Issue: 3, page 211-234
  • ISSN: 0399-0559

Abstract

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The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both primal and dual feasible, i.e. it is optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual problem and at the same time infeasible for the primal problem. In this paper, we present for the first time, the mathematical proof of correctness of DNEPSA, a detailed comparative computational study of DNEPSA and DNSA on sparse and dense random problem instances, a statistical analysis of the experimental results, and finally some new results on the empirical complexity of DNEPSA. The analysis proves the superiority of DNEPSA compared to DNSA in terms of cpu time and iterations.

How to cite

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Geranis, George, Paparrizos, Konstantinos, and Sifaleras, Angelo. "On a dual network exterior point simplex type algorithm and its computational behavior∗." RAIRO - Operations Research 46.3 (2012): 211-234. <http://eudml.org/doc/222508>.

@article{Geranis2012,
abstract = {The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both primal and dual feasible, i.e. it is optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual problem and at the same time infeasible for the primal problem. In this paper, we present for the first time, the mathematical proof of correctness of DNEPSA, a detailed comparative computational study of DNEPSA and DNSA on sparse and dense random problem instances, a statistical analysis of the experimental results, and finally some new results on the empirical complexity of DNEPSA. The analysis proves the superiority of DNEPSA compared to DNSA in terms of cpu time and iterations.},
author = {Geranis, George, Paparrizos, Konstantinos, Sifaleras, Angelo},
journal = {RAIRO - Operations Research},
keywords = {Network flows; minimum cost network flow problem; dual network exterior point simplex algorithm; network flows},
language = {eng},
month = {9},
number = {3},
pages = {211-234},
publisher = {EDP Sciences},
title = {On a dual network exterior point simplex type algorithm and its computational behavior∗},
url = {http://eudml.org/doc/222508},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Geranis, George
AU - Paparrizos, Konstantinos
AU - Sifaleras, Angelo
TI - On a dual network exterior point simplex type algorithm and its computational behavior∗
JO - RAIRO - Operations Research
DA - 2012/9//
PB - EDP Sciences
VL - 46
IS - 3
SP - 211
EP - 234
AB - The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both primal and dual feasible, i.e. it is optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual problem and at the same time infeasible for the primal problem. In this paper, we present for the first time, the mathematical proof of correctness of DNEPSA, a detailed comparative computational study of DNEPSA and DNSA on sparse and dense random problem instances, a statistical analysis of the experimental results, and finally some new results on the empirical complexity of DNEPSA. The analysis proves the superiority of DNEPSA compared to DNSA in terms of cpu time and iterations.
LA - eng
KW - Network flows; minimum cost network flow problem; dual network exterior point simplex algorithm; network flows
UR - http://eudml.org/doc/222508
ER -

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