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Optimal paths in bi-attribute networks with fractional cost functions

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  • Soroush, H.M.

Abstract

An important routing problem is to determine an optimal path through a multi-attribute network which minimizes a cost function of path attributes. In this paper, we study an optimal path problem in a bi-attribute network where the cost function for path evaluation is fractional. The problem can be equivalently formulated as the "bi-attribute rational path problem" which is known to be NP-complete. We develop an exact approach to find an optimal simple path through the network when arc attributes are non-negative. The approach uses some path preference structures and elimination techniques to discard, from further consideration, those (partial) paths that cannot be parts of an optimal path. Our extensive computational results demonstrate that the proposed method can find optimal paths for large networks in very attractive times.

Suggested Citation

  • Soroush, H.M., 2008. "Optimal paths in bi-attribute networks with fractional cost functions," European Journal of Operational Research, Elsevier, vol. 190(3), pages 633-658, November.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:3:p:633-658
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    1. Carraway, Robert L. & Morin, Thomas L. & Moskowitz, Herbert, 1990. "Generalized dynamic programming for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 44(1), pages 95-104, January.
    2. John R. Current & Charles S. Revelle & Jared L. Cohon, 1987. "The Median Shortest Path Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in the Design of Transportation Networks," Transportation Science, INFORMS, vol. 21(3), pages 188-197, August.
    3. Current, John & Marsh, Michael, 1993. "Multiobjective transportation network design and routing problems: Taxonomy and annotation," European Journal of Operational Research, Elsevier, vol. 65(1), pages 4-19, February.
    4. R. K. Ahuja & J. L. Batra & S. K. Gupta, 1983. "Combinatorial Optimization with Rational Objective Functions: A Communication," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 314-314, May.
    5. Namorado Climaco, Joao Carlos & Queiros Vieira Martins, Ernesto, 1982. "A bicriterion shortest path algorithm," European Journal of Operational Research, Elsevier, vol. 11(4), pages 399-404, December.
    6. Hanif D. Sherali & Laora D. Brizendine & Theodore S. Glickman & Shivaram Subramanian, 1997. "Low Probability---High Consequence Considerations in Routing Hazardous Material Shipments," Transportation Science, INFORMS, vol. 31(3), pages 237-251, August.
    7. Current, John & Min, HoKey, 1986. "Multiobjective design of transportation networks: Taxonomy and annotation," European Journal of Operational Research, Elsevier, vol. 26(2), pages 187-201, August.
    8. Martins, Ernesto Queiros Vieira, 1984. "On a special class of bicriterion path problems," European Journal of Operational Research, Elsevier, vol. 17(1), pages 85-94, July.
    9. Mote, John & Murthy, Ishwar & Olson, David L., 1991. "A parametric approach to solving bicriterion shortest path problems," European Journal of Operational Research, Elsevier, vol. 53(1), pages 81-92, July.
    10. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    11. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    12. Rajan Batta & Samuel S. Chiu, 1988. "Optimal Obnoxious Paths on a Network: Transportation of Hazardous Materials," Operations Research, INFORMS, vol. 36(1), pages 84-92, February.
    13. Martins, Ernesto Queiros Vieira, 1984. "On a multicriteria shortest path problem," European Journal of Operational Research, Elsevier, vol. 16(2), pages 236-245, May.
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