Skip to main content
Log in

An algorithm of optimization for a special class of networks

Ein Algorithmus für die Optimierung einer speziellen Klasse von Netzwerken

  • Published:
Computing Aims and scope Submit manuscript

Abstract

In this paper the author presents an algorithm of optimization for a special class of networks not having the Markov property. A definition of the class of networks under consideration and a formulation of the optimization problem are given. A conception of the algorithm is discussed and next the general and detailed flow diagrams of the algorithm are offered. The realization of the algorithm is illustrated with a simple example showing the process of execution of the tasks included in the algorithm. Some possibilities of applying the algorithm in allocation problems and nonlinear integer programming are presented.

The computer program in FORTRAN IV for the execution of the algorithm is enclosed.

Zusammenfassung

In dieser Arbeit wird ein Optimierungsalgorithmus für nichtmarkowsche Netze dargestellt. Es wird die Definition des betrachteten Netzes gegeben und ein Optimierungsproblem formuliert. Es werden das allgemeine Konzept und dann das Ablaufschema des Algorithmus dargestellt. Die Realisierung des Algorithmus wird an einem einfachen Beispiel erklärt. Es werden auch die Möglichkeiten der Anwendung des Verfahrens für Allokationsprobleme und für nichtlineare Programmierung erwähnt.

Das Programm ist in FORTRAN IV geschrieben. Es ermöglicht die Realisierung des Verfahrens auf einer EDV-Anlage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

\(\mathop \wedge \limits_x\) :

universal quantifier “for eachx

\(\mathop \vee \limits_x\) :

existential quantifier “there is suchx

¬:

negation

⋏:

conjunction

u∈U :

u belongs toU

\(\{ U_1 ,...U_w ,...U_{w_x } \}\) :

the set consisting of the elements\(U_1 ,...U_w ,...U_{w_x }\)

Γ u :

the set of the graph nodesu a ∈U for whichu \(\vec R\) u a

\(\Gamma _u^{ - 1}\) :

the set of the graph nodesu b ∈U for whichu b \(\vec R\) u

∪:

union of set

∩:

intersection of set

⊘:

the empty set

References

  1. Beckmann, M. J.: Dynamic Programming of Some Integer and Nonlinear Programming Problems, in: Integer and Nonlinear Programming. Amsterdam-London: North-Holland Publ. Co. 1970.

    Google Scholar 

  2. Bellman, R.: Applied Dynamic Programming. New Jersey: Princeton University Press 1962.

    Google Scholar 

  3. Dantzig, G. B.: On the Shortest Route Through a Network. Math. Sci.6, 187–190 (1960).

    Google Scholar 

  4. Floyd, R. W.: Algorithm 97: Shortest Path. Communication of ACM5, 345 (1962).

    Google Scholar 

  5. Hu, T. C.: Revised Matrix Algorithms for Shortest Paths in a Network. I. SIAM15, 207 to 218 (1967).

    Google Scholar 

  6. Kaufman, A.: Graphs, dynamic programming and finite games. (English translation.) New York-London: 1967.

  7. Osyczka, A.: Statical Optimization of the Machine Tool Gear Boxes. D. Sc. Thesis, Politechnika Krakowska, 1973.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Osyczka, A. An algorithm of optimization for a special class of networks. Computing 16, 77–97 (1976). https://doi.org/10.1007/BF02241982

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02241982

Keywords

Navigation