Minimum cost path problems with relays

The minimum cost path problem with relays (MCPPR) consists of finding a minimum cost path from a source to a destination, along which relay nodes are located at a certain cost, subject to a weight constraint. This paper first models the MCPPR as a particular bicriteria path problem involving an aggr...

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Vydáno v:Computers & operations research Ročník 38; číslo 1; s. 165 - 173
Hlavní autoři: Laporte, Gilbert, Pascoal, Marta M.B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 2011
Elsevier
Pergamon Press Inc
Témata:
Algorithms
Applied sciences
Bicriteria optimization
Cost engineering
Exact sciences and technology
Labeling algorithms
Mathematical analysis
Mathematical models
Mathematical programming
Minimum cost
Operational research and scientific management
Operational research. Management science
Operations research
Optimization
Relays
Shortest path algorithms
Shortest path problem
Studies
Weight function
Shortest path problem
Labeling algorithms
Bicriteria optimization
Relays
Upper bound
Costs
Weight function
Shortest path
Objective function
Time complexity
Modeling
Optimization
ISSN:0305-0548, 1873-765X, 0305-0548
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Shrnutí:The minimum cost path problem with relays (MCPPR) consists of finding a minimum cost path from a source to a destination, along which relay nodes are located at a certain cost, subject to a weight constraint. This paper first models the MCPPR as a particular bicriteria path problem involving an aggregated function of the path and relay costs, as well as a weight function. A variant of this problem which takes into account all three functions separately is then considered. Formulating the MCPPR as a part of a bicriteria path problem allows the development of labeling algorithms in which the bound on the weight of paths controls the number of node labels. The algorithm for this constrained single objective function version of the problem has a time complexity of O ( Wm + Wn log ( max { W , n } ) ) , where n is the number of nodes, m is the number of arcs and W is the weight upper bound. Computational results on random instances with up to 10 000 nodes and 100 000 arcs, are reported.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2010.04.010