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2017 | OriginalPaper | Chapter

Two FPTAS for the Constrained Shortest Path Problem Applied to Hybrid Vehicle Routing

Authors : Christian Schwan, Martin Strehler

Published in: Modeling, Simulation and Optimization of Complex Processes HPSC 2015

Publisher: Springer International Publishing

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Abstract

We consider a constrained shortest path problem with two resources. These two resources can be converted into each other in a particular manner. Our practical application is the energy optimal routing of hybrid vehicles. Due to the possibility of converting fuel into electric energy this setting adds new characteristics and new combinatorial possibilities to the common constrained shortest path problem (CSP). We formulate the resulting problem as a generalization of CSP. We show that optimal paths in this model may contain cycles and we state conditions to prevent them. The main contribution is a polynomial-time approximation scheme and a simpler approximation algorithm for computing energy-optimal paths in graphs.

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Footnotes
1
More formally, one should name such an object a walk. However, we use the term path here to indicate that we are going to compute paths eventually.
 
2
A similar idea is used for flows over time. Here, condensed time-expanded networks are use to approximate maximum flows (see [2]).
 
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Garcia, R.: Resource Constrained Shortest Paths and Extensions. Georgia Institute of Technology, Atlanta (2009)
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Ziegelmann, M.: Constrained shortest paths and related problems. Dissertation, Universität des Saarlandes, Saarbrücken, July 2001
Metadata
Title
Two FPTAS for the Constrained Shortest Path Problem Applied to Hybrid Vehicle Routing
Authors
Christian Schwan
Martin Strehler
Copyright Year
2017
Book
Modeling, Simulation and Optimization of Complex Processes HPSC 2015

Print ISBN: 978-3-319-67167-3

Electronic ISBN: 978-3-319-67168-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-67168-0_18

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