CPM = (LTS, CS),
where:
LTS = (S, L,
T, S
I
, S
F
)
is a labeled transition system, and
CS
⊆
T
↛
,
,
0
,
0
is a set of configura-
tions. Configuring the configurable process model means to select a configuration
c
CS
. To get a configured model the configuration must be applied to the labeled transi-
tion system and the configurable models describe the configuration scenarios.
The controlling phase can be structured in a sequence of three consecutive stages: 1)
Data Gathering: model data, adaptation data and performance data to be gathered
throughout the customization process (model data refers to the final adapted model re-
sulting from the adaptation process; adaptation data – for the information on adaptation
process, e.g. time, order, etc.; performance data – for the information on efficiency. 2)
Data Merging: to allow comparative analyses in integrating some of the performance
data that are directly related to specific model elements. 3) Data Analysis: The data that
has been gathered and merged from different customers is being analyzed in order to
identify shortcomings and improvements of the reference model and the adaptation
mechanisms.
The second logical space is determined by the notions of agents whereas agent is an
autonomous entity, interacting within an environment to realize common goals. Being
gathered into MAS, collection of autonomous agents can sense the environment they
are part of, and act on it in order to realize a purpose.
The management process for MAS will reflect the goal(s) to be realized; such goal
then define the a certain specific state of the environment, which is desirable for the
application and can not be implemented without outside interference. An agent in the
process of communicating with the environment considers those of its parameters,
which, on the one hand, determine the state of its intentions (depending on the type of
7
agent) and on the other, can be changed, i.e. agent has the means for such an impact on
the environment in which these parameters are changed in the required way, and agent,
in defining the goals, responds only to these parameters [16-18]. The parameters of the
environment, which determine its needs, but cannot be changed by the agent indirectly
affect the behavior during goal setting. Thus, the object perceives the environment as a
finite or infinite set of its parameters:
S
= (
S
l
, ..., S
e
), each of parameters can be of interests for an agent and can be
changed. In other words, the situation perceived by the subject is always manageable:
S
(
U
)
=
(
s
1
(
U
)
, ..., s
e
(
U
)), where
U
is the agent management function.
The space of situations
{S},
which is formed by the indicated parameters
s
i
(
i =
1, ...,
e
) is introduced, and each point of this space determines some specific situation that
has developed around the agent; through such situational space
{S}
the agent perceives
the surrounding environment and various objects. However, the agent formulates its
goals not in terms of the environment
S
: it is more convenient for the agent to operate
with other properties called ‘target concepts’. Let these target concepts be described by
a vector
Z
= (
z
1
,...,
z
k
), where each target parameter
z
i
is
uniquely determined by the
situation
S
, i.e.
z
i
=
ψ
i
(
S
) (
i
= 1,...,
k
), functions ψ
i
(•) determine the relationship
between the state of the environment
I
and the target parameter
z
i
.
In vector form, this
relationship is expressed as some definite vector function
Z =
ψ
(S),
where ψ (
S
) = (ψ
1
(
S
), ..., ψ
k
(
S
)).
Consider a
k-
dimensional target space {
Z
}, which is convenient for the agent by the
fact that for each space point it can express the requirement (goal), and fulfillment of
which, according to the agent will lead to the satisfaction of one or more of its require-
ments. The agent then formulates its goal as a vector target
Z *
= (
z*
1
,...,
z*
k
), where
z*
i
is the
i
th
requirement for the state of the environment
S
, expressed using the function
ψ
i
(
S
). These requirements objectives may have a different character, but their form
should be unified. Thus, the process of formulating the objectives of the
Z
* of the agent
is related firstly with the definition of the vector function ψ(
S
) and secondly, with the
development of requirements imposed on each component of this vector. In general,
the target
Z
* is reflected in the situation space {
S
}, forming the system of target re-
quirements:
𝑆
∗
: {
𝜓
𝑖
(𝑠) = 𝑎
𝑖
(𝑖 = 1, … , 𝑠)
𝜓
𝑗
(𝑠) ≥ 𝑏
𝑗
(𝑗 = 𝑠 + 1, … , 𝑠 + 𝑝)
𝜓
𝑣
(𝑠) → 𝑚𝑖𝑛 (𝑣 = 𝑠 + 𝑝 + 1, … , 𝑠 + 𝑝 + 𝑙)
The point or area
S
* satisfying these requirements is the state of the environment
that the agent is looking for, whether the agent succeeds in achieving this state of the
environment depends on its ability to influence the environment, that is, on the type of
dependence
S = S
(
U
) and from
R
resources allocated for management:
𝑈 ∈ 𝑅
. Obvi-
ously, that these resources determine the energy, material, temporal and other manage-
ment capabilities of
U.
Now consider the interaction of the target zone
S
* and the trajectory of change of
the environment
S
(
t
) under the influence of external factors, i.e. the situation drift. If
the drift trajectory
S
(
t
) passes through the zone, the agent does not need any manage-
ment/control. It remains to him to wait when external circumstances lead to the fact that
8
S
(
t
) belongs to
S
*. The agent prefers to manage the situation, that is, it purposefully
affects the environment:
S
t
= S
(
U
,
t
) and changes it so that to achieve management ob-
jectives, i.e.
𝑆(𝑈, 𝑡) ∈ 𝑆
∗
.
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