Multi-Agent Analysis Model of Resource Allocation Variants to

Ensure Fire Safety

Andrey Smirnov

, Renat Khabibulin

, Nikolay Topolski

and Denis Tarakanov

The State Fire Academy of EMERCOM of Russia, 129366, B. Galushkina 4, Moscow, Russia

The Ivanovo State Fire Academy of EMERCOM of Russia, 153040, Stroiteley 33, Ivanovo, Russia

Keywords: Multi-agent Systems, Multi-agent Management, Multi-level Procedure, Long-term Planning Tasks, Shannon

Entropy, Decision Support Systems.

Abstract: Algorithmization and program implementation of theoretical positions of multi-agent analysis of resource

allocation variants to ensure fire safety were conducted. The informational decision support system was

developed, within which variations of resource allocation in a multi-agent management system are offered.

The feature of the developing informational system from similar is an ability of approximations of expert’s

opinion accounting multi-level procedure of variation’s analysis in a multi-agent management system. The

multi-level procedure of variation’s analysis allows to approximate preference of the management centre

more completely and, therefore, to reduce the subjectivity of the process of making decisions on resource

allocation to ensure fire safety. The procedure includes two main stages: on the first stage component-goals

are distributed by sets; on the second stage we get the ranking according to the preference of the

management centre. Using quantitative measures of the Shannon entropy it is proved that the offered multi-

level procedure of variations analysis in multi-agent management system allows to approximate the

preference of the management centre more completely in comparison with known methods of variations of

resource allocation analysis in long-term planning tasks.

1 INTRODUCTION

An emergency on industry facilities are character by

human victims, high ecological and economic

damage (Kwanghee Lee et al., 2016), (Hyuck-myun

Kwon et al., 2016), (Nima Khakzad et al., 2016).

Using of multi-agent systems and technologies

(MAS) is offered to manage the fire safety on such

facilities because MAS are a perspective direction in

a sphere of management on active systems (Yongcan

Kao et al. 2013), (Dimos V. Dimarogonas et al.

2011), (Ferber et al., 2004). Using of MAS allows

simulating interaction in the social system of

subdivisions of organization (agents), that make an

influence on the fire risk level and resource

allocation in considering socio-economical system

(SES) (Shaun Howelletal., 2017).

There are a lot of goals that need to be reached

by SES while functioning, each of which is

implemented by a particular agent – department,

linear department or a specific agent. Agent

management in SES is realized by the management

center (figure 1). Every agent is endowed with

several properties, which help to realize interaction

with management center. Agents in the multi-agent

system, possessing their own characteristics, are not

interested in increasing the number of resources

(rational conduct). One of the properties of rational

conduct is the agent’s possibility to refer to the

management center for endowing it with number of

resources that is necessary and is enough for the

realization of the agent’s charged purpose.

A total number of the system purposes can be

divided into the purpose groups in accordance with

their content. Besides the basic purposes, there are

purposes, that are directed at the reaching the

required fire safety level expressed in the

probabilistic value, which should not exceed the

specific values of fire risks (Desheng Dash Wu et

al., 2017), (Gudin et al., 2017). In general,

understanding purposes like these can be classified

as the purposes, which are necessary for normal

functioning of such objects. At the same time, each

of these purposes for its realization, independently

on the application, suggests the necessary quantity

of resources, which is available or not available for

the system.

Smirnov, A., Khabibulin, R., Topolski, N. and Tarakanov, D.

Multi-Agent Analysis Model of Resource Allocation Variants to Ensure Fire Safety.

DOI: 10.5220/0007716403910398

In Proceedings of the 21st International Conference on Enterprise Information Systems (ICEIS 2019), pages 391-398

ISBN: 978-989-758-372-8

391

Figure 1: Structure of the multi-agent system.

MAS is applied in different spheres and subject

areas: logistics, safety, informational search, risks

management, healthcare, etc. However, despite the

increasing MAS extension, the complexity of the

process of their development remains to be

extremely high, which causes a problem of the MAS

universal design tool creation, which combines a

theoretically proved design methodology and

effective realization in the object-oriented sphere

(Alexander, R. et al., 2013).

It is necessary to be noted, that the MAS use to

ensure safety numerously was an object in the

scientific researches (Zoumpoulaki A. et al., 2010),

(Çetin Elmasa et al., 2011), (Mutovkina N. et al.,

2014), but the task of resource allocation to ensure

fire safety was not addressed within the context of

these works.

2 MULTI-AGENT

MANAGEMENT SYSTEM TO

ENSURE FIRE SAFETY

In accordance with the general agent-modeling

approaches, there is a conclusion, that there are a lot

of purposes that need to be done by the system, each

of which is implemented by a particular agent –

department, linear department or a specific agent.

Agent management is carried out by the

management center. The agent in the multi-agent

system is endowed with several properties, allowing

to describe its interaction with the management

center. Considering the agent in the resource

allocation task for industry enterprise, besides the

agent’s general properties in the multi-agent system,

it is necessary to add rational conduct in the

resources allocation, which determines the situation,

when the agent is not interested in the resource being

increased. An additional property of a system

agent’s rational conduct is a possibility to refer to

the management center for endowing it with number

of resources that is necessary and is enough for the

realization of the agent’s charged purpose.

Multi-agent approach is the importance ranking

of agent's purposes concerning the general purpose

of the management center, that is assigning the

important purpose parameters – w

and excluding

those purposes, that can’t be realized because of the

resources lack. In accordance with this approach, the

excluded purposes of the system should have the

worst estimation in compliance with ranking results,

which is the purpose of which w

→ min. For the

search of the minimum ranking coefficient purposes

in the multi-agent system it is advisable to make the

formal statement of the multi-criteria task, which

includes:

– various options of the resource allocation in the

system

xX

1,2, ,in

, n ≥ 2;

– various system purposes used for the variant

estimation

fF

1,2, ,sm

, m≥3;

– various resource allocation estimations

       

12 m

F X f X f X f X  

(1)

where: X - various resource allocation;

(Х) – are various values of the system

components with the number i on the various

options



;

F(x

)=(f

), f

),…,f

)) – variant estimation

, and then f

) – x

variant estimation according

the f

system purpose. Provided that, the

management center by its choice longs to maximize

the value of each purpose component that is f(x) →

max.

The general structure of the resource

management system is shown in figure 1 in

accordance to its formation results.

The provided structure of the agent system is

hierarchical, that is why to determine the resources

needed for the general purpose of the agent system,

which is connected with the implementation of fire

safety tasks, it is necessary to use the generalized

target function that is expressed in the additive or

multiplied form. It is known, that the model weight

coefficients characterize the level of f

influence of

purpose components on the resulting function Ф, in

the following way:

, 1

k k k

Фf







. (2)

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392

In other words, the solution of the resource

allocation task is reduced to the determination of

their quantitative shares – coefficients w

There are two main approaches for the

calculation of the weight coefficients in the multi-

agent system:

- the first approach is the comparison of two

variants of the resource allocation preference. This

approach is formalized by the relative importance

theory (Noghin V., 2014);

- the second approach supposes the component-

purposes “weighting” by the experts within the

matter of the general theory of multi-criteria

usefulness (Lootsma F., 1993).

It should be noted, that these approaches are

different on the methodological level, and in general

case, the creation of the general decision-making

system that based on these approaches consists in

the creation of two different systems.

That is why from the theoretical point of view

the actual task consists of the development of the

unified theoretical provisions for the method

realization that is based on two structurally different

approaches.

The solution on this task was carried out in the

way like this: at the first stage the relative

importance theory was implemented for the

comparison of the variants at the identical

preference, and then the comparison of the

component-purpose according to their importance

method was implemented for the received results.

In accordance with the decision-making general

task within the limits of the relative importance

theory, each couple of solution variants X

and X

induces the vector estimations F(X

)={f

); f...

); f

)} and F(X

)={f

); f... (X

); f

)}.

Applying the method of the relative importance of

quantitative functions in the multi-criteria

optimization process, let’s suppose (Noghin V.,

2014), that X

> X

, then let’s separate the

component-purposes of the multi-agent system by

the importance groups, taking into conditions:

   

i i i

S f X f X theni A   

(3)

   

j i i

S f X f X theni B   

(4)

   

s i i

S f X f X theni C   

(5)

Where S – is the difference in accordance of the i

– criterion between the variant X

estimation and the

variant X

estimation; A, B, C are the importance

groups of SES component-purpose. For all

combinations i and j from the A and B groups we

determine the relevant importance indexes







(6)



–is the direct index of the relevant importance

purpose component from group A with the number i,

above the component-purpose from group B with the

number j. Now, let’s consider the reverse situation to

, then X

, in this situation the component

purposes will be distributed the way, when the

component-purposes from the group B is more

important for the component-purposes then from the

group A, and the relevant importance index will be

determined according to the formula:







(7)

Direct and reverse indexes of the relevant

importance are connected with the expression:

ji ji





(8)

Which results from their formal determination:

ji ji

i j i j

S S S S



    



(9)

Then we will consider, that the simultaneous

implementation of the condition X

> X

, then X

< X

within the relevant importance theory (Noghin V.,

2014) results in X

~ X

For comparison by the preference “≈” of two

options in a multi-agent system on the basis of the

conditions (3)...(5) the preference matrix is formed,

the elements of which are the relative importance

direct indexes of the SES component-purposes. The

preference matrix for clarity is convenient to be

presented in tabular form in the table – table 1.

Table 1: The preference matrix of the relevant importance

indexes.

…

Sum











…

...1



























Sum



























Multi-Agent Analysis Model of Resource Allocation Variants to Ensure Fire Safety

393

In Table 1, a is determined as the component-

purposes quantity in group A and B, as the

component-purposes quantity in group B

respectively.

Then, the importance parameters calculation in

the function (1) based on preferences expressed in

the relevant importance indexes set can be realized

through the Kramer’s formulas (Vol'skii V. I., 1982):

w 

(10)

for all component-purposes from group B:

w 

(11)

where

;

i ij







i ij









and

1 1 1 1

(),

b a a b

ij ij

j i i j

b b a



   

  

 

so as

1 1 1 1

b a a b

ij ij

j i i j



   



 

the

ab

Then we finally receive the formulas for the

calculation of the function importance indexes (1)

based on the relevant importance indexes:

for all component-purposes from group A:







(12)

for all component-purposes from group B:











(13)

A unified decision-making system for resource

allocation variants to ensure fire safety is based on

the method that includes the following stages:

Stage 1. The distribution of component-purposes

of a formal model for resource allocation into two

contradictory groups A and B.

As a result, the multi-agent system component-

purposes are divided into importance groups. In the

context of this method, only groups A and B are

considered, the component-purposes that are not

included in these groups, the component-purpose

group C are excluded from further analysis. As a

result of this stage, two non-empty component-

purpose groups of components should be formed,

provided that we will consider the component-

purposes of the group A is equal to a, numbers of

these component-purposes are designated as i, then

the number of component-purposes from the group

B is equal to b with the numbers j. The conditions

(3) and (4) should be used in the components

distribution into groups while the variants couple

comparison within the relative importance theory.

Within the relevant importance theory, a person,

who makes a decision by itself, distributes the

component-purposes into the groups based on his

own understanding of their importance for decision

making.

Stage 2. The determination of the relevant

importance index set



for each combination of

component-purposes by numbers i and j.

When calculating the importance relevant



based on the relative importance theory, it is

necessary to use the formula (6) considering S

parameters, calculated by formulas (3) and (4).

Within the usefulness of theory, the relevant

importance theory coefficient should be determined

with the formula:







(14)

Where

 

exp

K pZ

and Z takes its indexes

from the round number quantity in accordance with

the described in the approach (Lootsma F., 1993).

Stage 3. The determination of the weight

importance coefficient function of the variant

ranking – resource allocation portions.

At this stage of the method, additive function

coefficients for each component – purpose with the

number i from group A and the component-purpose

with the number j from group B are determined

through the formula (14).

An important practical aspect of the developed

method of resource allocation is the possibility of

decision-making expert to get results with the

formalization of the previous experience. In this

connection it is worth mentioning, that the

developed agent component functions relevant

importance indexes account is varied from the

existing higher level of expert estimations

approximations, which are determined by a large

quantity of agent component-purposes allocation

variants into the importance groups A and B. The

existing method of the component-purposes

allocation into the importance groups, based on the

preference X

> X

determines the situation when A

group includes the component-purposes with the

coefficients W

for all i ϵA and j ϵ B. The

proposed method is based on the preference X

≈ X

and is free from this restriction.

Let’s look at the application of the developed

procedure on illustrated example.

If fire safety was consumed R1 amount of

resource and it was distributed between training of

personnel 0,3R

and automated informational system

of fire and explosion safety (further – AISFES) 0,7R1.

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394

Next year the budget increased 1.7 times, but the

development of a safety system provides for the

need to develop automated system of management

primary rescue operations that costs R1.

Based on the specifics of object’s fire safety

measures realization of total conditions can be

assigned R2=1,7R1, at the same time, the resources

for the training system cannot be reduced, that is

0,3R1.

1,7R1-0,3R1=1,4R1 is necessary to distribute

between AISFES and automated system of primary

rescue operations management.

Phase 1. The distribution of component

objectives by importance.

Determine the importance coefficient between

AISFES and training of personnel system.

If component objectives connected with

implementation costs of AISFES with number 1,

that is f1, then а=1. The remaining target component

that determines the cost of personnel’s training f2

will be assigned to the B group, that is b=1. The new

automated system of primary rescue operations

management will be assigned to A group, that is f3

belongs to A and (а=2)

Phase 2. Calculation of relative importance.

Source share of resources will be

0,7





, likewise

0,3





By formula (11) we determine the value of last

year relative importance index and it is

12 1

0,7ab



   

As the cost of personnel’s training should be

0,3R1 then this year it will be spent 0,176R2. the

value is obtained by the formula:

0,3 0,3

0,176

1,7



   

Let’s determine the value of the relative

importance sum in this year based on the condition

obtained using the formula (12):

 

12 32

2 2 1 0,176 1,69







     

Considering than last year

0,7





, than

relative importance index for the new system will be

1,69 0,7 0,94



  

So, the result of this phase realization are two

relative importance index

0,7





and

0,94





Phase 3. Determining a share of resources.

Determine the importance coefficients.

So, target components with numbers 1 and 3 are in

the A group, then by formula (11):

0,7

0,35 0,35





   



;

0,94

0,47 0,47





   



For target component with number 2 from B group

by formula (12):

   

12 32

2 0,7 0,94

0,18





   

  



Answer: optimal resource allocation in this task

will be fire and explosion safety automated system –

0,35R2; training of personnel system – 0,18R2;

automated system of primary rescue operations

management – 0,47R2.

Thus, the way of optimal resource allocation

variants to ensure fire safety based on the developed

method is presented.

The application of the theory of relative

importance in a formalized description of the

resource allocation experience and it’s applications

in making a decision in the current period of.

Let’s use the concept and quantitative criterion

of Shannon entropy (Shannon C. E., 1948) for the

quantified estimation of the approximation of expert

opinion degree with the use of these two methods.

We designate the existing expert opinion

approximation method on the preference based on X

> X

in Q, then the proposed method based on the

preference of relation X

≈ X

. Shannon entropy for a

deterministic case depends on the quantity of state

allocation of component-purposes groups, which is

N and is determined by the formula S=logN. N state

quantity depends on the agent quantity in the system

m for the existing method Q, the allocations quantity

linearly depends on m and is equal to N

=m-1.

For the developed method P, the allocation

quantity is determined by the complex combinatorial

dependencies that are obtained by the numerical

analysis of distribution component-purposes for

agent quantity, which are measured in the first-order

decimal system. For the convenience of perception

of numerical analysis of results it’s advisable to

consider the combinatorial dependencies * and * *

(even and odd):

if n is odd, then:

 

m j j















(15)

if n is even, then:

   

2 ! ! ! !

m K K m j j











    





(16)

where

Multi-Agent Analysis Model of Resource Allocation Variants to Ensure Fire Safety

395















(17)

The component-purposes allocation by variant

evaluation results into the groups A and B in the

binary system with m=2, ..., 9 are shown in Figure 2.

The corresponding Shannon entropy indexes are

shown in Figure 3.

Analyzing the obtained data, we can draw the

following conclusions:

 for the known method Q, the Shannon entropy

linearly increases while the increase of agents in the

MAS.

 for the proposed method P, this dependence is

not linear and in all cases except (m=2), it exceeds

the indexes of Q method.

Therefore, method P is more beneficial in

comparison with method Q in all cases.

Thus, based on the developed method, the

optimal resources allocation for the safety tasks was

suggested. The relative importance application in

formal description of the resources allocation

experience and its application in decision-making in

the current period of the safety system development

and operation are shown.

Figure 2: Component-purposes variants allocation quantity

depending on their quantity in MAS.

Figure 3: Shannon entropy estimation for the component-

purposes allocation in the MAS.

3 DECISION-MAKING

SUPPORT SYSTEM

DEVELOPMENT

The decision-making support system (DSS) for

resources allocation variants for ensuring the fire

safety tasks of protection objects was suggested on

the basis of developed method. The general structure

of the system is shown as the scheme at the picture

4. The DSS allows carrying out ranking of resource

allocation variant in the multi-agent system, as well

as realization of the algorithms of multi-criteria

analysis based on the optimal management concept

in the agent system.

Figure 4: Decision support system functional scheme.

The following blocks can be specified in this

scheme:

 Data entry block (researched object data entry);

 Double variants comparison block. Double

variants comparison and results are drawn in this

block.

 Importance coefficients determination for the

agent groups A and B. According to double

comparison results, the alternatives allocation into

groups A and B is carried out. Relative’s indexes of

importance are determined for these groups.

 Variants ranking relatively of the expert’s

opinion block. Parallel with the previous actions in

the system, the variants ranking relatively of the

expert’s opinion is carried out. The quantitative

estimations variants of resources allocation are

calculated. The received moisture indexes for groups

A and B are used in the vector estimation

calculation.

100

120

140

160

2 4 6 8

N - allocation variants

m - component-purposes quantity

0.0

0.5

1.0

1.5

2.0

2.5

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396

 Importance criteria weighing block. The

importance criteria weighting coefficient (Kij)

calculations are carried out.

 Importance coefficients array formation block.

The importance indexes array is based on the

conducted calculations. The received results are

shown in the diagram. Allocation variants are ranked

from more preferable to less preferable.

4 CONCLUSIONS AND FUTURE

WORK

With the help of MAS, the task of resources

allocation variants to ensure fare safety on industry

enterprises was solved.

The distinctive feature of the developing model

from similar is an ability of creation of multi-level

procedure of options analysis in MAS, which is

determined by the possibility of the importance

indexes calculation for the agents and the relevant

coefficient-purposes. The DSS, where the algorithms

are formed in the way, that the MAS resources

allocation variants on the first stage are distributed

by multiplicities and then ranked in accordance with

the management system preference, was developed.

Multi-level procedure of variants’ analysis in MAS

allows approximating the preferences of

management center more complete.

Further research is focused on the development

of the evaluation of MAS application’s efficiency

criteria.

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