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

Published online by Cambridge University Press:  07 September 2012

George Geranis ,
Konstantinos Paparrizos  and
Angelo Sifaleras
George Geranis
Affiliation:
Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., 54006 Thessaloniki, Greece. geranis@uom.gr; paparriz@uom.gr
Konstantinos Paparrizos
Affiliation:
Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., 54006 Thessaloniki, Greece. geranis@uom.gr; paparriz@uom.gr
Angelo Sifaleras
Affiliation:
Department of Technology Management, University of Macedonia, Loggou-Tourpali, 59200 Naoussa, Greece; sifalera@uom.gr
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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.

Keywords

Network flowsminimum cost network flow problemdual network exterior point simplex algorithm
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 3 , July 2012 , pp. 211 - 234
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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