Optimal paths in probabilistic networks: A case with temporary preferences

Pitu B. Mirchandani, Hossein Soroush

Research output: Contribution to journalArticle

60 Scopus citations

Abstract

The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the "traveler's" utility function for travel attributes is nonlinear, we define "optimal paths" that maximize the expected utility. We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path. In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic-a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.

Original languageEnglish (US)
Pages (from-to)365-381
Number of pages17
JournalComputers and Operations Research
Volume12
Issue number4
DOIs
StatePublished - 1985
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research

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