Robust shortest path planning and semicontractive dynamic programming

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 inst...

Full description

Saved in:
Bibliographic Details
Published inNaval research logistics Vol. 66; no. 1; pp. 15 - 37
Main Author Bertsekas, Dimitri P.
Format Journal Article
LanguageEnglish
Published New York Wiley Subscription Services, Inc 01.02.2019
Subjects
Algorithms
Dynamic programming
Graph theory
Iterative methods
Logistics
Mathematical models
minimax formulation
Minimax technique
Minimum cost
Optimization
Policies
Predictive control
semicontractive model
Shortest path planning
Uncertainty
Online AccessGet full text

Cover

More Information
Summary: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 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.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0894-069X
1520-6750
DOI:10.1002/nav.21697