Optimal paths in probabilistic networks: A case with temporary preferences

Pitu Mirchandani, Hossein Soroush

Research output: Contribution to journalArticle

60 Citations (Scopus)

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

Fingerprint

Optimal Path
Utility Function
Cost functions
Path
Expected Utility
Cost Function
Arc of a curve
Maximise
Attribute
travel
Optimal path
Utility function
Evaluate
Evaluation
costs
evaluation
experience
Travellers

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation

Cite this

Optimal paths in probabilistic networks : A case with temporary preferences. / Mirchandani, Pitu; Soroush, Hossein.

In: Computers and Operations Research, Vol. 12, No. 4, 1985, p. 365-381.

Research output: Contribution to journalArticle

@article{8479de0dec344b25bd6692f9792c0c2a,
title = "Optimal paths in probabilistic networks: A case with temporary preferences",
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.",
author = "Pitu Mirchandani and Hossein Soroush",
year = "1985",
doi = "10.1016/0305-0548(85)90034-6",
language = "English (US)",
volume = "12",
pages = "365--381",
journal = "Surveys in Operations Research and Management Science",
issn = "0305-0548",
publisher = "Elsevier Limited",
number = "4",

}

TY - JOUR

T1 - Optimal paths in probabilistic networks

T2 - A case with temporary preferences

AU - Mirchandani, Pitu

AU - Soroush, Hossein

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021855448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021855448&partnerID=8YFLogxK

U2 - 10.1016/0305-0548(85)90034-6

DO - 10.1016/0305-0548(85)90034-6

M3 - Article

AN - SCOPUS:0021855448

VL - 12

SP - 365

EP - 381

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 4

ER -