Robust shortest path planning and semicontractive dynamic programming

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6 Scopus citations

Abstract

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit-evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra-like algorithm for problems with nonnegative arc lengths.

Original languageEnglish (US)
Pages (from-to)15-37
Number of pages23
JournalNaval Research Logistics
Volume66
Issue number1
DOIs
StatePublished - Feb 1 2019
Externally publishedYes

Keywords

  • dynamic programming
  • minimax formulation
  • semicontractive model
  • shortest path planning

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

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