Abstract
In this paper a multicriterion network optimization problem is discussed. The problem formulation is given and next the min-max principle of optimality is used in order to define the optimal path in the network.
Then a method for seeking the optimal path in the network is described.
Zusammenfassung
In der Arbeit wurde das Problem der Polyoptimierung von Netzwerken dargestellt. Es wurde das Problem formuliert und weiter das Prinzip von Minimax zwecks der Bestimmung des optimalen Weges im Netzwerk ausgenutzt.
Ferner wurde die Methode des Suchens des im Sinne des Prinzips von Minimax optimalen Weges besprochen.
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Abbreviations
- \(\begin{array}{*{20}c} \Lambda \\ i \\ \end{array} \) :
-
general quantifier “for everyi”
- \(\begin{array}{*{20}c} V \\ i \\ \end{array} \) :
-
detail quantifier “there is ani”
- ∨:
-
alternative
- ∧:
-
conjunction
- ∈:
-
an element of
- ø:
-
empty set
- ⊂:
-
inclusion
- {}:
-
set
- ∪:
-
union of two sets
- Γu :
-
set of the graph nodesu a ∈U for whichu R u a
- Γ -1u :
-
set of the graph nodesu b ∈U for whichu b R u
References
Bourgoin, M. H., Heurgon, E. M. J.: Study and comparison of algorithms of the shortest path through planned experiments, in Project planning by network analysis (Lombaers, H. J. M., ed.). Amsterdam-London: North-Holland 1969.
Osyczka, A.: An algorithm of optimization for special class of networks. Computing16, 77–97 (1976).
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Osyczka, A. Multicriterion network optimization problem. Computing 25, 363–368 (1980). https://doi.org/10.1007/BF02285230
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DOI: https://doi.org/10.1007/BF02285230