=Paper=
{{Paper
|id=Vol-2899/paper013
|storemode=property
|title=Designing an algorithm for supporting information generation process optimization
|pdfUrl=https://ceur-ws.org/Vol-2899/paper013.pdf
|volume=Vol-2899
|authors=Tatyana E. Smolentseva,Andrey V. Svishchev,Nataliya V. Katakhova
}}
==Designing an algorithm for supporting information generation process optimization==
https://ceur-ws.org/Vol-2899/paper013.pdf
Designing an algorithm for supporting information generation
process optimization
Tatyana E. Smolentseva 1, Andrey V. Svishchev 2 and Nataliya V. Katakhova 3
1
Federal State Budgetary Educational Institution of Higher Education "MIREA - Russian Technological
University", Moscow, Russia
2
Federal State Budgetary Educational Institution of Higher Education "MIREA - Russian Technological
University", Moscow, Russia
3
Federal State Budgetary Educational Institution of Higher Education "MIREA - Russian Technological
University", Moscow, Russia
Abstract
The paper considers the structural elements for an automated information reference decision
support system (AIRDSS) in hierarchical multilevel complex organizational systems
(HMLCOS). The task to ensure the functioning of the AIRDSS has been formulated. To solve
it the main steps have been designated, which comprise the calculation of the importance
coefficients for the supporting information (SI) elements and ordering of options based on a
decision-maker’s preference followed by the choice of the utility prospective one. On the basis
of the steps considered, the authors propose the algorithm to form the optimal structure of the
AIRDSS procedural component’ elements for obtaining SI; the algorithm has a number of
advantages: calculation simplicity for various experiments, a relatively simple formalization
of expert knowledge into numerical values of importance.
Keywords
an automated information reference decision support system, supporting information, a
decision-maker, coefficient of importance, control actions
1. Introduction
The main task that ensures the functioning of the automated information reference system for
decision-making support (AIRDSS) is the procedural component’s elements optimal structure
generation to obtain supporting information (SI).
The solution to this problem is carried out in two steps:
calculation of the importance coefficients ωn for the SI Ion elements;1
solving the problem of optimizing the SI contentю
For any situation and solution, the utility function is determined [1, 2] by using the theory of rational
decisions, which evaluates the utility and the value of Ei in the situation Sj from the standpoint of the
l-th feature. Then based on the rationality postulates it is necessary to order the options according to the
decision-maker’s preference followed by the choice of the utility prospective one. [3]
There are no universal methods for the formation of options while analyzing the problem area of
hierarchical multilevel complex organizational systems (HMLCOS), except for some models for
management decision-making (MD) problems, which determine the necessary and sufficient conditions
for determining all solution options.
III International Workshop on Modeling, Information Processing and Computing (MIP: Computing-2021), May 28, 2021, Krasnoyarsk,
Russia
EMAIL: e-mail: smoltan@bk.ru (Tatyana Smolentseva); svishev7@mail.ru (Andrey Svishchev); Katakhova@mirea.ru (Nataliya Katakhova)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
85
2. Discussion
The process of calculating the importance coefficients of the SI elements can be represented in the
form of the algorithm in Figure 1:
Figure 1: Algorithm for calculating coefficient of importance
For any situation S j ( j 1, n) and decision Ei (i 1, m) the utility function is determined [4, 5]
using the theory of rational decisions l ( S j , Ei ), l 1, L which evaluates the utility and the value
of the decision Ei in the situation Sj from the standpoint of the l-th feature. Then based on the postulates
of rationality it is necessary to order the options according to the decision-maker’s preference (DM)
followed by the choice of the utility prospective one. [6]
Optimization of the solutions obtained is carried out on the basis of certain preferences according to
the criterion K (or criteria) selection from the best solution point of view determined by the following
expression:
max E ( Ei ) E0 ,
i
( i 1, m ), (1)
where Eo is an optimal (solution) decision; Ei – i-th decision variant; (Ei) – the value of the preference
(utility) function on the i-th option.
For each i - th solution option, a number of preference functions l (Ei) are formed, and the best
option will be the one that meets all the criteria:
1 ( Ei ) max, 2 ( Ei ) max, ,
(2)
l ( Ei ) max, , L ( Ei ) max.
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Therefore, from (1) and (2), a set of possible solutions is formed, E (E1, E2 , , Em ) in which
there are the solutions with the remained problematic situations. The optimal solution for making
management decisions (MD) is written in the form:
, (3)
where: S - problematic situation, C - goals, G - constraints, E - solution options, - preferences, K -
criteria, E0 - optimal solution [7].
3. Materials and methods
The process of the SI formation is presented in the diagram (Figure 2:)
Figure 2: SI formation scheme
Step 1. To calculate the scores of importance, one can apply a number of mathematical methods,
which usually relate to a specific subject area, that is why a special method must be developed for the
adoption of each control action. In our case it seems desirable to apply universal methods. One of the
universal methods is the method of T. Saaty [8,9].
One of the main difficulties in using models for the control actions formation is the utilization of
judgments identified by numerical values through a certain scale. These methods must meet many
criteria, such as to reflect appropriately the subject’s feelings in his judgments; the presence of
judgments uncertainty should not affect the required numerical value; a large difference in judgments
should reflect a significant difference on the numerical scale.
The developed model should provide close values with small deviations in the numerical
representation of judgments. Comparison of two complex objects describing judgments is not so easy
to carry out based on the numbers of feelings and experience about how much the influence of one of
the objects affects the achievement of an assigned goal in comparison with the other one The very idea
of defining numbers seems to be artificial, since it is exercised arbitrarily.
As more static data is gained, the original scale that was determined for pairwise comparisons can
be adjusted and generalized. In order to form the result of the comparison of two objects in the form of
objective numbers, it is necessary to conduct a more detailed analysis of these objects functioning and,
in particular, how their parameters will affect the achievement of the main goal.
The source for formalizing the essence of judgments is a survey of the studied subject area experts.
These judgments will determine the relative importance of one object functioning in comparison with
another one in terms of the possibility of each of them to achieve its goals. Usually, when forming
numerical preferences, an expert is asked the following questions: which of the two investigated objects,
in his opinion, is more important; it is necessary to determine the difference on a given scale that is of
greater importance. [10]
The influence of one object on another is taken into account only for those parameters that directly
affect the objects functioning, and allows you to achieve the assigned goals. Consideration of the
influence of indirect impacts on the objects can be carried out through the ratio of the input - output
type between the objects.
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This approach is used, for example, in the distribution of energy resources between interdependent
industries, taking into account their priorities. The development of the scale of the importance of objects
will be carried out with the definition of the ranks of importance (Figure 3:).
Figure 3: Relative preference scale
Let us define a set (w1, ..., wn) of true values of importance for each n-th object; on the basis of the
formed scale it is possible to obtain comparative assessments of importance. Each element of the wij
matrix of pairwise comparisons A forms an expert assessment of the ratio in the form of the expression
wij=wi/wj.
While obtaining wijwik=wik and, in particular, wii=1 wji=1/wij, one can form a matrix. We should
remember that when forming a matrix, the values obtained depend on the results of the expert judgments
that are definitely difficult to formalize.
To improve the consistency of the matrix, we can recommend that the experts tried to set the value
1/wij to wji, as the result of comparison the i-th object with the j-th one. In particular, it is preferable to
define wii = 1.
With this approach, assuming that one object has importance w times when compared to another,
the expert will determine the importance of the second object as 1 / w of the importance of the first one.
It is clear that when forming the matrix A, it has rank one, i.e.if the values of one of its lines are known,
all its elements can be calculated (wij = w1j / w1i).For the matrix A, we assume that w1i ≠ 0 for all i.
The particular case of the matrix consistency is easier to analyze, but the task will be to determine
the rational ways of adopting MD regardless of the insolvency. If all judgments are determined by one
or a group of experts (for example, if the knowledge of each expert is insufficient to answer all the
questions). [11]
The main problem in this case is a large number of questions asked to an expert; in this case it is
necessary to form 0.5n (n-1) judgments regarding each of the defined goals when calculating reciprocal
values. We assume that the required set (w1, ..., wn) must satisfy the equation Aw = lmax, where lmax is
the A’s largest eigenvalue.
If the matrix A is non-negative and irreducible, this equation will be unique (to within a constant
factor) and will have a non-negative solution w.
If the experts formed comparative judgments and determined the first row or column, other pairwise
comparisons can be used for more accurate determination of the importance of objects, since with small
deviations from the consistency, stability can be increased.
If each expert from the group forms an independent comparative pair of objects, then it becomes
possible to carry out multidimensional tests. Consequently, the method proposed requires to form a
matrix with a list of all objects. Then, a certain goal is determined and, on the basis of all available
information about the relative importance of one object in comparison with others in achieving a certain
goal, the matrix elements are sequentially formed. For each goal, the process is repeated and several
matrices are formed. Further, a pairwise comparison of these goals is also carried out according to their
contribution to the achievement of the global goal.
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The method proposed has the following advantages:
1. It provides a relatively elementary formalization of expert knowledge (used to form A) into
numerical values of importance.
2. This method is distinguished by the simplicity of calculations and, for various experiments carried
out, has shown good results; for example, small changes in A lead to slight result changes.
Step 2. The problem under consideration is a linear programming problem with nonnegative
coefficients in the objective function and constraints. Such problems can be solved, for example, using
the Lauler-Bell method [16].
The algorithm for the AIRDSS procedural component elements’ optimal structure generation to
obtain SI is shown in Figure 4:
Figure 4: Algorithm for the AIRDSS structure to obtain SI
The considered algorithm for the SI generation process optimization is the basis of the process for
organizational systems’ (OS) multilayer hierarchy structuring, presented in the form of a set of
programs: "Generation", "Approximation” and "Recursion". Building a multilayer OS hierarchy by
hand is rather cumbersome. Therefore, to automate this process at the first stage, the "Generation"
program has been developed.
The "Generation" program is designed to solve the following tasks:
Determination of the graph’s vertices, reflecting the structural relationship between the goals
of the system function;
Determination of the graph’s arcs reflecting the relationship between the vertices of the OS
graph;
Definition of the OS goals;
Definition of OS tasks;
Determination of the relative volume of the work performed.
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It is possible to save a graphic image of the developed multilayer OS hierarchy in the bmp format.
The structure of the program is shown in Figure 5:.
The initial data for the program when working in the mode of editing the network model of the
organization's activity are:
Expert assessments of the graph’s arcs for the multilayer OS hierarchy.
Expert assessments of the tasks of the OS multilayer hierarchy.
Structure of the OS multilayer hierarchy.
Figure 5: The structure of the set of programs for the multilayer hierarchy generation
Upon completion of the OS multilayer hierarchy generation process and processing of the expert
survey data, the preliminary model for the OS multilayer hierarchy is entered into the database. The
developed preliminary model for the OS multilayer hierarchy can be written into a * .bmp file. Screen
forms of an example of working with the program are shown in Figure 6:, Figure 7:, Figure 8:.
Figure 6: Entering OS multilayer hierarchy vertices
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Figure 7: Editing OS multilayer hierarchy
Figure 8: Editing the structure for OS multilayer hierarchy preliminary model
4. Conclusions
The algorithm presented is a corrected version of the algorithm for solving the linear programming
problem by the Lauler-Bell method [3]. Its correctness is due to the above given property of the
functionals GtX, t = 0,1, ..., s. If the solution of the X problem (3) is determined, then the time for
obtaining the SI is specified by the following expression:
6 i i
N
T0 x x n aOn i
qi VOn , t On , (4)
n 1 i 1
and the total duration of the step for adopting the MD from (4) is described by (5):
6 i i
N
V
T x B t B xn aOn qi VOni , tOn TLPR . (5)
VB n 1 i 1
Based on the algorithm obtained, the set of programs for a multilayer hierarchy generation is to be
intended to:
determine the goals of the organizational system,
analyze the multilayer hierarchical structure,
form the planning parameters system and analyze the OS functioning, - determine the standard
values and coefficients of the relative importance parameters,
specify the integral criteria for the evaluation of the OS functioning.
5. References
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processes in complex systems, Scientific bulletin of Belgorod State University. Series: Economics.
Informatics 13(210) (2015)104–108.
[3] B. N. Ivanov, Discrete Math. Algorithms and programs, Moscow, Laboratory of fundamental
knowledge, p. 288, 2000.
91
[4] K. V. Baldin et al., Investments. System analysis and management, M. Dashkov and Ko, p. 288,
2018.
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