Mathematical Methods of Operations Research

, Volume 54, Issue 3, pp 445–454 | Cite as

A multi-objective shortest path problem

  • Kazuyoshi Wakuta


We study a multi-objective shortest path problem. We formulate a multi-objective Markov decision process model for the problem and solve it by the policy improvement procedure. We first show by counter-examples the differences between the multi-objective shortest path problem and the single-objective one. We next introduce “locally efficient policies” and present an algorithm for finding all efficient paths from all nodes to the destination. Moreover, as an application, we consider a shortest path problem with a constraint. Last, the algorithm is illustrated by a numerical example.

Key words: shortest path problem multi-objective policy improvement procedure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kazuyoshi Wakuta
    • 1
  1. 1.Nagaoka Technical College, 888 Nishikatakai, Nagaoka, Niigata 940-8532, Japan (e-mail:

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