A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set

Teodros Getachew; Michael M. Kostreva

RAIRO - Operations Research (2010)

  • Volume: 36, Issue: 3, page 175-190
  • ISSN: 0399-0559

Abstract

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In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real" valued decisions. A computational application to time-dependent fuzzy dynamic programming is presented.

How to cite

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Getachew, Teodros, and Kostreva, Michael M.. "A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set." RAIRO - Operations Research 36.3 (2010): 175-190. <http://eudml.org/doc/105269>.

@article{Getachew2010,
abstract = { In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real" valued decisions. A computational application to time-dependent fuzzy dynamic programming is presented. },
author = {Getachew, Teodros, Kostreva, Michael M.},
journal = {RAIRO - Operations Research},
keywords = {Multi-criteria optimization; time-variant networks dimension reduction.; multi-criteria optimization; time-variant networks; dimension reduction},
language = {eng},
month = {3},
number = {3},
pages = {175-190},
publisher = {EDP Sciences},
title = {A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set},
url = {http://eudml.org/doc/105269},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Getachew, Teodros
AU - Kostreva, Michael M.
TI - A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 3
SP - 175
EP - 190
AB - In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real" valued decisions. A computational application to time-dependent fuzzy dynamic programming is presented.
LA - eng
KW - Multi-criteria optimization; time-variant networks dimension reduction.; multi-criteria optimization; time-variant networks; dimension reduction
UR - http://eudml.org/doc/105269
ER -

References

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  1. R.E. Bellman, On a Routing Problem. Quarterly Appl. Math. 16 (1958) 87-90.  Zbl0081.14403
  2. R.E. Bellman and L.A. Zadeh, Decision-Making in a Fuzzy Environment. Management Sci.17 (1970) B-141-B-164.  Zbl0224.90032
  3. T.A. Brown and R.E. Strauch, Dynamic Programming in Multiplicative Lattices. J. Math. Anal. Appl.12 (1965) 364-370.  Zbl0132.40303
  4. K.L. Cooke and E. Halsey, The Shortest Route through a Network with Time-Dependent Internodal Transit Times. J. Math. Anal. Appl.14 (1966) 493-498.  Zbl0173.47601
  5. H.W. Corley and I.D. Moon, Shortest Paths in Networks with Vector Weights. J. Opt. Theory Appl.46 (1985) 79-86.  Zbl0542.90099
  6. H.G. Daellenbach and C.A. DeKluyver, Note on Multiple Objective Dynamic Programming. J. Oper. Res. Soc.31 (1980) 591-594.  Zbl0434.90086
  7. E.W. Djikstra, A Note on Two Problems in Connection with Graphs. Numer. Math.1 (1959) 269-271.  
  8. S.E. Dreyfus, An Appraisal of Some Shortest Path Algorithms. Oper. Res.17 (1969) 395-412.  Zbl0172.44202
  9. S.E. ElMaghraby, The Concept of ``State'' in Discrete Dynamic Programming. J. Math. Anal. Appl.29 (1970) 523-557.  Zbl0191.49201
  10. T. Getachew, M. Kostreva and L. Lancaster, A Generalization of Dynamic Programming for Pareto Optimization in Dynamic Network. RAIRO: Oper. Res.34 (2000) 27-47.  Zbl0963.90055
  11. J. Halpern, Shortest Route with Time-Dependent Length of Edges and Limited Delay Possibilities in Nodes. Z. Oper. Res.21 (1977) 117-124.  Zbl0366.90116
  12. M.I. Henig, The Principle of Optimality in Dynamic Programming with Returns in Partially Ordered Sets. Math. Oper. Res.10 (1985) 462-470.  Zbl0582.90104
  13. D.E. Kaufmann and R.L. Smith, Minimum Travel Time Paths in Dynamic Networks with Application to Intelligent Vehicle-Highway Systems. University of Michigan, Transportation Research Institute, Ann Arbor, Michigan, USA, IVHS Technical Report 90-11 (1990).  
  14. M.M. Kostreva and M.M. Wiecek, Time Dependency in Multiple Objective Dynamic Programming. J Math. Anal. Appl.173 (1993) 289-308.  Zbl0805.90113
  15. A. Orda and R. Rom, Shortest-Path an Minimum-Delay Algorithms in Networks with Time-Dependent Edge-Length. J. Assoc. Comp. Mach.37 (1990) 607-625.  Zbl0699.68074
  16. J. Kacprzyk and A.O. Esogbue, Fuzzy Dynamic Programming: Main Developments and Applications. Fuzyy Sets Sys.81 (1996) 31-45.  Zbl0879.90185
  17. M.L. Hussein and M.A. Abo-Sinna, A Fuzzy Dynamic Approach to the Multicriterion Resource Allocation Problem. Fuzzy Sets Sys.69 (1995) 115-124.  

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