Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms

Zbigniew Tarapata

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 2, page 269-287
  • ISSN: 1641-876X

Abstract

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The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.

How to cite

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Tarapata, Zbigniew. "Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms." International Journal of Applied Mathematics and Computer Science 17.2 (2007): 269-287. <http://eudml.org/doc/207836>.

@article{Tarapata2007,
abstract = {The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.},
author = {Tarapata, Zbigniew},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {stochastic shortest path; routing problem; algorithm complexity; multiobjective shortest path; approximation algorithm; terrain-based modeling},
language = {eng},
number = {2},
pages = {269-287},
title = {Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms},
url = {http://eudml.org/doc/207836},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Tarapata, Zbigniew
TI - Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 2
SP - 269
EP - 287
AB - The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.
LA - eng
KW - stochastic shortest path; routing problem; algorithm complexity; multiobjective shortest path; approximation algorithm; terrain-based modeling
UR - http://eudml.org/doc/207836
ER -

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