MARITIME ACTIVITY AS A PROCESSING IN HIERARCHICAL
ENVIRONMENT

Tiit Riismaa
Institute of Cybernetics at Tallinn University of Technology
Akadeemia tee 21, Tallinn 12618, Estonia
Phone: +372 6204192 Fax: +372 6204151
tiitr@ioc.ee

KEYWORDS
Hierarchical processing systems, optimization of
hierarchies, discrete structures, adjacent matrixes,
continuous structures, density functions, discrete-convex
programming.

ABSTRACT
Discrete and continuous approaches of representation
and optimization of the structure of hierarchical
processing system are presented and compared. For
discrete statement the feasible set of hierarchies is a set
of oriented trees. Connections between neighboring
levels are presented by adjacency matrixes. For discrete
approach the graph theory description of feasible set of
hierarchies based on the product of adjacency matrixes is
given. For continuous statement a feasible set of
hierarchies is an ordered set of sizes of levels.
Connections between the adjacent levels are described
by density function of distribution. This density function
describes how the size of each level is distributed
between the sizes of next level. It is shown that the given
choice of variable parameters and the statement of the
optimization problem as a double minimum problem
enable to construct methods for finding a global
optimum of total loss function and select the
corresponding structure. For continuous statements the
conditions of optimality for horizontal homogeneous
hierarchies and homogeneous hierarchies are given.