The determination of the path with minimum-cost norm value

• Published in: Networks Vol. 41; no. 4; pp. 184 - 196
• Main Authors: Paixão, José M. P., de Queirós Vieira Martins, Ernesto, Rosa, Mário S., Santos, José Luis E.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.07.2003; John Wiley & Sons
• Subjects: Applied sciences; dominance relation; Exact sciences and technology; Flows in networks. Combinatorial problems; multiobjective shortest path; Operational research and scientific management; Operational research. Management science; ranking paths; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Valuation and optimization of characteristics. Simulation; Cost minimization; Value function; multiobjective shortest path; ranking paths; Utility function; dominance relation; Process selection; Shortest path; Problem solving; Dominance
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.10077

The multiobjective shortest path problem (MSPP) consists of finding the best nondominated path linking two specified nodes in a network where k > 1 different criteria are considered for the arc costs. Solving the MSPP implies determining all the nondominated paths; there may be many such paths, making the selection process a very hard task to accomplish. A traditional way of dealing with such a difficulty is using a utility function where the parameters are aggregated with different weights. In this work, an alternative utility function based on the norm value associated with each path is considered. Two algorithms for solving the minimum‐cost norm path problem are then proposed and some computational results are presented. © 2003 Wiley Periodicals, Inc.