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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Formation of the Structure of Multilayer Polyagent Functionals</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Serhii Holub</string-name>
          <email>s.holub@chdtu.edu.ua</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Svitlana Kunytska</string-name>
        </contrib>
      </contrib-group>
      <abstract>
        <p>The processes of intellectual monitoring in emergencies are studied. The intelligent monitoring system is an environment for creating and using intelligent agents to provide knowledge of decision-making processes. In emergencies, objects acquire new properties quickly, and the informativeness of the results of previous observations decreases. To increase the power of data mining tools, monitoring agents are combined into agent functionalities with a multi-tier structure. The paper presents the results of research on the processes of formation of multiechelon polyagent functionals. The efficiency of construction of a multi-echelon polyagent functional in solving the problem of predicting the incidence of the population of Ukraine on Covid-19 in conditions of low informativeness of the results of observations has been experimentally confirmed.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Intelligent monitoring</kwd>
        <kwd>emergencies</kwd>
        <kwd>polyagent functional</kwd>
        <kwd>echelon</kwd>
        <kwd>prognosis</kwd>
        <kwd>Covid-19</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>In the context of crisis monitoring, reducing
the informativeness of the observations results is
one of the problems that reduces the efficiency of
the process of extracting knowledge from data
sets. In emergencies, the monitored objects move
to another state and acquire new properties. These
properties are not fully reflected in the arrays of
the results of previous observations. The period of
time for new observations is much longer than the
time during which it is necessary to provide the
results of monitoring to the decision maker.</p>
      <p>
        This problem is overcome by information
technology of intelligent monitoring through the
use of a multi-agent approach to the creation of
monitoring information systems (MIS). A
separate agent is built to perform monitoring
tasks. When the informativeness of the input data
arrays (IDA) is reduced, superagent formations
are built - agents functionals. The concept of
"functional" is interpreted here as "function of
functions". Agent functionality (AF) is a
structural element of the monitoring information
system [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>
        The technology of building polyagent
functionalities (PAF) involves the creation of
agents with structural tasks and combining them
into a system based on a matching IDA. Matching
IDAs for structural agents are formed on the basis
of the same array of observation results [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>This paper presents the results of research on
the process of forming a many echelon structure
of the polyagent functional of the monitoring
information system. The technology of
construction of PAF is presented on an example
of improvement of process of performance of the
monitoring task on forecasting of number of
diseases of the population of Ukraine on
Covid19.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Multi-agent systems</title>
      <p>
        There are several approaches to creating
many-agent systems. The problem-oriented
approach is based on the assertion that several
agents can achieve a goal that is beyond the power
of one agent [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. This approach involves
“developing mechanisms and methods that ensure
agents interact at the human level (or better) and
understand the processes of interaction of
intelligent computing entities. Simplifying, the
result should be an algorithm that will tell who
how and with whom to interact (at any time) [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        The object-oriented approach assumes that
MAS is a combination of autonomous intelligent
agents, each of which performs its task and each
interacts with other agents of this MAS [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ].
      </p>
      <p>The problem-oriented approach to the creation
of MAS is used by information technology of
intelligent monitoring (ITIM) in the process of its
implementation in the form of MIS to perform the
task of predicting the incidence of the population
of Ukraine on Covid-19.</p>
      <p>
        In case it is not possible to build an agent to
perform a new monitoring task due to insufficient
informativeness of the array of results of previous
observations, the agent functional is built. A
system approach is used to build the agent
functionality. Agent functionality is built as a
system. The functional emergence is formed due
to the effective combination of agents and a more
complete reflection of the properties of the object
in the model knowledge bases of the monitoring
information system. This effect is manifested by
improved signal characteristics at the MIS output
and increased adequacy of interpretation of
monitoring results. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>
        An attempt to build an agent with a monitoring
task to predict the number of diseases in Ukraine
with a horizon of 7 days with this forecast task
was unsuccessful. The array of observation results
obtained from an open source [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] was not
informative enough. This array was formed by
limited data on the incidence of Covid-19 abroad,
and the simulated trait is presented in the form of
an average incidence rate in Ukraine. It was not
possible to obtain additional data on the incidence
of the population in some regions, which contain
different mechanisms of emergency formation.
The error in predicting the incidence of the
population of Ukraine at the 7th step of the
forecast horizon was 16.90% with an average
value of 7 steps - 11.01% [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>MIS did not have built agents that would
perform tasks based on different information
sources in other subject areas, so the construction
of multi-agent functionality was impossible. To
fulfill the monitoring task, the IIA built the PAF.</p>
      <p>
        The construction of a single-echelon PAF
allowed to obtain the forecasting result with an
error of 13.99% on the horizon of 7 days and to
improve the average forecasting error to 6.15%
[
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. The use of feedback in the construction of the
PAF structure allowed to reduce the forecasting
error on the horizon of 7 days to a value of 7.49%,
while the average value of the forecasting error
was 3.09% [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Problem</title>
      <p>statement
description
and
tasks</p>
      <p>
        To reliably assess the influence of factors, the
signs of which are included in the array of
observations, it is necessary to build a model with
a minimum value of forecasting error. Therefore,
studies of the process of constructing a PAF to
enhance the emergence of an agent combination
were performed. The task of building a PAF is to
create a method that would provide knowledge
about the patterns of pandemic development in
Ukraine in the future from previously observed
results. The forecasting problem formulated in [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]
has a solved:
      </p>
      <p>An array of X results of population morbidity
monitoring during 2020 is given:</p>
      <p>X = {xij}, i=1,n; j=1,m , (1)
where n is the number of signs that reflect the
incidence of the population, m is the number of
observation points (recorded number of diseases
in countries with a discreteness of 1 day).</p>
      <p>The number of observation points is
determined by the duration of the historical period
of time during which the values of morbidity were
recorded:</p>
      <p>T = {t, t-1, t-2, t-m}, (2)
where t is the observation time; m is the
number of observation points.</p>
      <p>The monitoring information system builds a
set of agents with structural tasks:</p>
      <p>Y = {Yx1, Yx2, Yx3, …, Yxn}, (3)
where n is the number of agents that perform
structural tasks.</p>
      <p>It is necessary to build a polyagent functional
for predicting the incidence of Covid-19
population of Ukraine with a forecasting horizon
of 7 steps, for which the deviation of the
forecasting results from the actual values becomes
minimal:</p>
      <p>Zx1= f(T, X, Y, t+7), (4)
where Zx1 – signal at the output of the agent
functional with the monitoring task of forecasting
the number of diseases of the population of
Ukraine; t+7 – forecast horizon (7 steps).</p>
    </sec>
    <sec id="sec-4">
      <title>4. Hypotheses</title>
      <p>output signals of the agents included in the
structure of the lower echelons of the functional.</p>
      <p>
        Execution of new monitoring tasks on the basis
of previous results of supervision is provided by
construction of agent functionalities with
multilevel hierarchical structure. The upper
echelons of the functional are formed from agents
that are not included in the structure of the lower
echelons. Increasing the informativeness of the
signals at the output of these agents is achieved by
increasing the number of features in the agent IDA
due to the signals from the output of lower
echelon agents. The hierarchical structure of
multi-echelon agent functionals is built by the
method of ascending synthesis of elements [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>
        The IDA for the structural tasks of the higher
echelon agents is formed from the features
obtained as a result of observations and from the
Table 1
Signs of the initial description of diseases on COVID-19 [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>Indicators
Observation time; morbidity in Ukraine; morbidity in France; morbidity in
Belarus; morbidity in Georgia; morbidity in Germany; morbidity in Israel;
morbidity in Italy; morbidity in Moldova; morbidity in Slovakia; morbidity in
Slovenia; morbidity in Russia; morbidity in Portugal; morbidity in Poland;
morbidity in Romania; morbidity in Spain; morbidity in Turkey; morbidity in
Egypt; morbidity in Greece; morbidity in the United States; morbidity in China;
incidence in England</p>
    </sec>
    <sec id="sec-5">
      <title>5. The results of experiments and their discussion</title>
      <p>
        To perform the monitoring task of forecasting
the number of diseases of the population of
Ukraine on Covid-19 on the horizon of 7 days, an
array of signs was formed, obtained as a result of
observations of morbidity of the population of
other countries during 2020 with a step of 1 day.
The results of observations were obtained from an
open source [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. The list of features that formed
the initial description of the monitored object is
given in Table 1.
      </p>
      <p>Comments</p>
      <p>results of
The
daily
observations
obtained during
2020</p>
      <p>After that, the method of forming the structure
of a multi-echelon polyagent functional
ascending construction of layers was applied.
Agents who did not complete their task on the
lower layer of the PAF began to perform this task
on the upper layer. All agents that performed the
task formed the structure of the layer. The signals
at the output of these agents were used as
additional features in the input array of higher
echelon.</p>
      <p>Table 2 presents the characteristics of the
output signals of agents that performed structural
tasks in the construction of PAF layers. The
characteristics of the agents that performed the
structural task and entered the structure of the
corresponding echelon in table 2 are highlighted
in bold.</p>
      <p>Thus, after the construction of the polyagent
functional, the error in predicting the incidence of
the population of Ukraine decreased by 72.96%
compared to the results of forecasting this
indicator by the agent who performed this task.</p>
      <p>The input array for the upper echelon was
formed from the signals at the output of the agents
that entered the structure of the lower echelons.</p>
      <p>If the error in predicting the signal at the output
of the agent is less than the limit value of 12%, the
structural task is considered completed, the agent
acquires the state "Used" and is included in the
structure of the corresponding echelon. Structural
tasks that were not performed by the lower
echelon PAF agents are assigned by the MIS to be
performed by the upper echelon. According to
Table 2, 9 structural tasks for morbidity
forecasting in the respective countries were
performed at the first echelon. The structure of the
first echelon of PAF includes 9 agents. For
execution on the second echelon MIS transferred
7 structural tasks. Of these, 3 tasks were
completed.</p>
      <p>And, accordingly, the structure of the second
echelon was formed by 3 agents. The prediction
errors in the signals at the output of all agents were
less than the characteristics of the signals that had
agents with the same tasks in the previous
echelon. Therefore, unfulfilled tasks are
transferred for execution to the highest echelon.</p>
      <p>Of the 5 tasks of the third echelon, the agents
did not complete any. Agents 4 and 19 at the
output had prediction errors greater than those
they had in the previous echelon.</p>
      <p>Prediction of morbidity in Ukraine
on the 7th day
Prediction of morbidity in France
on the 7th day
Prediction of morbidity in Belarus
on the 7th day
Prediction of morbidity in Georgia
on the 7th day
Prediction of morbidity in
Germany on the 7th day
Prediction of morbidity in Israel on
the 7th day
Prediction of morbidity in Italy on
the 7th day
Prediction of morbidity in
Moldova on the 7th day
Prediction of morbidity in
Slovakia on the 7th day
Prediction of morbidity in
Slovenia on the 7th day
Prediction of morbidity in Russia
on the 7th day
Prediction of morbidity in Poland
on the 7th day
Prediction of morbidity in Portugal
on the 7th day
Prediction of morbidity in
Romania on the 7th day
Prediction of morbidity in Spain
on the 7th day
Prediction of morbidity in Turkey
on the 7th day
Prediction of morbidity in Egypt
on the 7th day
Prediction of morbidity in Greece
on the 7th day
Prediction of morbidity in the
United States on the 7th day
Prediction of morbidity in China
on the 7th day
Prediction of morbidity in England
on the 7th day
Prediction of morbidity in Canada
on the 7th day
1
11,01%
4,43%
13,81%
5,50%
69,94%
3,56%
7,66%
101,38%
197,22%
14,18%
1,94%
26,86%
2,94%
8,80%
4,70%
91,68%
48,90%</p>
      <p>In the fourth echelon, structural monitoring
agents managed to complete the task of predicting
morbidity in Slovenia. The construction of the
fifth echelon of the PAF has made it possible to
carry out morbidity forecasting tasks in England
and Canada.</p>
      <p>The output signal of the 6-tier polyagent
functional performed the task of predicting the
number of diseases in the population of Ukraine
on the 7th day after the last observation. The
forecasting error on the horizon of 7 steps became
4.57% with the average value of 7 steps - 2.6%.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions</title>
      <p>The construction of multilevel polyagent
functionalities allows overcoming the problem of
performing monitoring tasks in the conditions of
insufficient informativeness of the arrays
observation results. Using the results of previous
research on the construction of echelons the agent
functional and feedback in their structure, a
method for forming a multi-echelon structure of
polyagent functional is proposed.</p>
      <p>The experimental test of the method was
carried out in the process of solving the task of
forecasting in the conditions of insufficient
informativeness of historical data.</p>
      <p>The results of the solving problem are
predicting the incidence of the population of
Ukraine on Covid-19 in conditions of low
informativeness. Due to the construction of a
multi-tier polyagent functional, the prediction
error is reduced by 72.96%.</p>
    </sec>
    <sec id="sec-7">
      <title>7. References</title>
    </sec>
  </body>
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