icacsis2011-ai.pdf

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AbstractThis paper presents model of social

interaction in multi-agent simulation on the basis

of the model of personality traits. The goal of this

study is to investigate behavioral movement in

architectural design simulation. Personality traits

used in this model influence behavioral movementsof the agents toward group formation. We modeled

force of attraction and force of repulsion as key

drivers for such purpose. The force of attraction

and the force of repulsion depend on the level of

Extraversion trait to represent the dynamic

characteristic of personal distance. The model of

intension for group formation is by means of social

interaction level which depends on Agreeableness

trait. Experiments showed implementation of these

models in multi agent simulation using basic

detection method on movement and direction. As

result, the personality traits-driven model can

provide heterogeneity and flexibility for socialinteraction that demonstrate human behavioral

movements.

I. INTRODUCTIONhe model of social interaction used in this study

refers to the correspondence of personality traits

with the probability to form a group formation. A

group formation means that at least two agents are

become approaching each other and stand together at

close range of distance at a given time.

Previous study of personality model [1], [2], [3]

noted that personality traits which are related forsocial interaction is Agreeableness and Extraversion.

Agreeableness relates to the adjective attributes such

as kindness, affectionate and helpful whereas

Extraversion relates to energetic, talkative and

assertive kind of traits.

Model of the basic social interaction particularly on

how individual (agent) can form a group and

performing group behavior had become object study

of pedestrian dynamics [4], [5], [6], [7]. The social

Manuscript received September 9, 2011.

1 Aswin Indraprastha is with Building Technology Research

Group, Architectural Computation Lab. ITB, Indonesia (email:[email protected], [email protected])

force model is among few models that can describe

social interaction and social behavior among agents in

term of Newtonian forces of attraction and repulsion.

Another concept of the model of social interaction

comes from the study of its dynamic features [4], [5]

followed by study to synthesize internal dynamicsvariables [8] with less elaboration on the personality

traits that could affect behavioral movements.

This research aims at the development of

personality traitsdriven social interaction where the

behavioral movement for establishing a group

formation depends on the personality type of the

agents. Output of this work will make benefit for the

study of behavioral-based simulation in architectural

design where each personality trait has preference

over particular architectural design elements.

II. MODEL OF SOCIAL INTERACTIONA. Personality Traits Model

Our model determined social interaction by the

level of Extraversion trait and Agreeableness trait. The

Extraversion trait level determine likeness of agent to

attract or to repel other agent and the Agreeableness

trait level determine the possibility of agent to be

attracted by other agent to conduct social interaction.

These traits are determined from multiple numerical

inputs according to each personality facets and then

each trait is categorized into three levels of traits: low,

medium and high, respectively. On each category, wedefined its behavioral characteristic level of force of

attraction, force of repulsion and social interaction.

These forces model are developed as an improvement

from previous study [10] to suit with the situation and

specific variables of simulation.

1) The Force of Attraction (FoA)Mathematical model to describe attraction force is

based on the distance over two agents by using

Probability Distribution Function. The computation

used real time distance data during simulation. This

model can be formulated as (1):

Computational Model of Social Interaction in Multi-

agent Simulation based on Personality Traits

Aswin Indraprastha

School of Architecture, Planning and Policy Development

Institut Teknologi Bandung, Indonesia

T
mailto:[email protected]:[email protected]:[email protected]


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Where y=force of attraction; x=distance between

agents; a and b=simulation chosen constant according

to Extraversion level.

The value of a and b is determined according to theExtraversion level as depicted in diagram below(Fig.1):

Fig. 1. Force of attraction of the three categories of Extraversion

types. The extrovert type has highest level of attraction and it lastsin longest distance than others.

The above constants are conformed the category of

personal distances from Proxemic theory [9]. By this

category, social interaction is likely occurred in the

range of social distance (between 1.22 m to 3.66m) as

depicted in figure below (Fig. 2):

Fig. 2. Category of personal distances by Hall (1960)

2) The Force of Repulsion (FoR)In modeling repulsion force, we used Moderate

level of Extraversion as a base line for determining a

personal distance where agent repulses other agents.

The maximum value of this force is 1.0 and by

reaching 0.5, agent is repulsing other agents.

The model to describe this force is using

exponential decay function as presented (2):

Where f= force of repulsion; d=distance betweenagents; c is the constant for the limit of personal

distance categories. For Moderate-Extraversion type

personality, the constant c=2.13, for Extrovert and

Introvert types, the constant c=0.46 and 7.62,

respectively.

The Extrovert type has minimum repulsion distance

as he tends to attract other agent. On the other way,

the Introvert type has the maximum repulsion distance

as he tends not to be disturbed by other agent.

The overall model for each of Extraversion

category is by changing the constant as described

below (Fig. 3).Figure 3 indicates that Moderate Extraversion type

has the level of force of repulsion= 0.5 at the distance

of 1m-1.2m. The same level reached at the 0.65m and

1.75m for Extrovert and Introvert types respectively.

Fig. 3. Force of repulsion of the three categories of Extraversion

types.

3) Level of Social InteractionThe social interaction level is determined by two

factors: first, the interaction level which is determined

by level of Extraversion using this formula (3):

Where i and j =agent, I = interaction level, E=

Extraversion level .The formula above indicates dependency of

interaction level by the Extraversion level of each

agent. At the first encounter, social interaction level

depends on the level of Extraversion trait of each

agent.Second, the social interaction level is likely changes

by the influence of Agreeableness level and an

uncertainty factor that occurred after the first

encounter. This can be modeled by using exponential

decay function that relates interaction level,

Agreeableness level, and randomized value that

represents its uncertainty (4).

Where A= Interaction level (I), B=

Agreeableness level (), x= random value(

).

Our model determined the social interaction is

occurred if the current state of interaction level is

greater than 0.5.

4) Uncertainty model with random valueThe idea to use randomize value is to represent and

to model uncertainty or unpredictable of behaviortowards forming a social interaction.

Even though an agent is considered as an Altruist(high level of Agreeableness), there is no guaranteethat he intends to make interaction with others. In our

model, Agreeableness level could increase the chanceof the establishment of social interaction.

Assuming random value is a normal distribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 3.6

Attraction

force

Distance

Moderate

Extrovert

Introvert

a=2.89;b=2.40

a=1.0;b=1.45

a=0.225;b=0.762

0

0.2

0.4

0.6

0.8

1

1.2

0 0.30.60.91.21.51.82.12.42.7 3 3.33.6

Repulsion

force

Distance

Moderate

Extrovert

Introvert

c=7.62

c=2.13

c=0.46


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then the relationship between Agreeableness level and

Interaction level is as presented in Figure 4.

Fig. 4. Influence of Agreeableness level and random value to the

interaction level

As depicted in Figure 4, there are some pointsnoted:

On any random value (0,1 ), highAgreeableness level (Altruist) alwaysobtain highest interaction level with loweststandard deviation (around 0.17). Thelowest interaction level is achieved when

random value>0.8

On any random level, in the range of loweragreeableness level, the result has widespectrum (with highest standard deviation,

around 0.32). The way to get interactionabove 0.5 is when random value between

0-0.5Using standard deviation on each range of

Agreeableness level, we developed three categories of

interaction level to filter out the probability of group

formation based on Agreeableness level with the

consideration of random value as follows:

for Altruist=0.48. It increases possibility ofgroup formation by 80%;

for Moderate=(0.48+0.22)=0.69; for Egoist=(0.48+0.32)=0.80;

Using this threshold value, the Altruist type hasmost probability to create a group and in other way,the Egoist type has less probability to create a group.

In Our experiments, this model fairly representsbehavior of Altruist type that has 90% possibility to

create a group formation than others two types of

Agreeableness. The moderate type has 50%

possibility, which appropriately make sense and the

last, the Egoist type has near zero possibility to create

group form after ten experiments.

B. Group FormationA group formation is a model to represent socialinteraction of agent with different personality types.

As stated in previous section, the driving force for

social interaction is Extraversion level andAgreeableness level. Extraversion level falls into three

categories: Extrovert, Moderate and Introvert.Agreeableness level falls into three categories:Altruist, Moderate and Egoist.

On the basis of these categories, we modeled thegroup category based on Extraversion level.

TABLE.1.GROUP CATEGORY BASED ON EXTRAVERSION LEVEL

E is extrovert or

tolerant

E is introvert

E is extrovert

or tolerant

Group type-1 Group type-2

E is introvert Group type-2 No group

Group category as determined in Table 1 suggests

that agent who feels comfortable with certain type of

other agent possibly forms a group for a certain time

delay. This group formation also may occurred if they

attract each other.

1) Group type-1This group formed by the members of extrovert or

tolerant agents. The characteristic of group type-1 is

where in range of the force of attraction, they

approach each other to where group will be formed.

This characteristic can be illustrated in Table 2 below:

TABLE.2.GROUP TYPE-1

(t=0) (t=t1) (t=t+t1)All tree agent has

E

introvert

Suppose agenti andagent j are extrovert

or combination of

extrovert and tolerantthen they will

approach each other

to form first group

Suppose agentk iseither extrovert

or tolerant, then

he will approachfirst group if the

group is within

the distance ofhis attraction

force

2) Group type-2This group formed between any members of

extrovert or tolerant with introvert agents. The

characteristic of group type-2 is the member from

higher level of Extraversion approaches the introvert

agents as illustrated in Table 3 below:

TABLE.3.GROUP TYPE-2

(t=0) (t=t1) (t=t+t1)Only agentk is

introvert

Suppose agenti and

agent j are extrovert

or combination with

tolerant then they

will approach eachother

agentk is introvert,

then he stays and

approached by

other agents

0

0.2

0.4

0.6

0.8

1

1.2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 1

Interactionlevel

Agreeableness

Rand=0.2

Rand=0.4

Rand=0.8

Rand=0.6

AltruistModerateEgoist

Altruist

0.17

Moderate

0.22Egoist

0.32

Base=0.48

Agent i

Agentj

Agent k

Agent i

Agentj

Agent k

Agent i

Agentj

Agent k

Agent i

Agentj

Agent k

Agent i

Agentj

Ag

Agentj

Agent i

Agent k


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III. MODEL IMPLEMENTATIONA. The Detection Procedure

Assume that maximum distance for social interactionis 3.60m and horizontal viewing angle is 100 0. Theneach agent is going to detect position of any otheragent at any time, whether it is in the area of his

viewing field.If so, then program begins for social interaction

procedures. We denoted that this visibility area of theagent is a mean for triggering social interaction.

For such purpose, the model of viewing area relieson the followings factors:

1. Frontal outward distance: 3.60m as a constantwhere social contact is occurred.2. Viewing angle: 1000 as average human horizontal

viewing angle.

Illustration of viewing area used by this concept is

as follows (Figure 5):

Fig. 5. Horizontal viewing area

The visibility area model is an isosceles triangle

where greatest angle is at the point of viewer=1000

as

displayed in Figure 5. Since the frontal distance and

origin angle is constant which is 3.60 and 100 0

respectively, we can determine the other two

maximum points (Figure 6):

Fig. 6. Determination of maximum coordinates of an isoscelestriangle.

The procedure to determine maximum coordinates

is as follows:1. Define current position of agent i (xi,yi)

2. Define current unit vector direction of agent i(xi,yi)

3. Define frontal distance d=3.64. Determine 5. Determine point of frontal view (xid,yid) by:

6. Determine orthogonal vectoridir=idirby:

7. Determine two maximum coordinatesimax1(ximax1, yimax1) and imax2(ximax2, yimax2) by:

B. Detection of movement and directionThe social interaction only occurs if agents are

facing each others. By this logic, if an agent sees other

agent in his viewing area, he must detect other agent is

moving towards him and not the other way.

In our model, the agent detects this condition by

comparing distance on a time stamp. This concept is

illustrated in Figure 7.

If the agent detects other agent, he set the time t=t0and gets the distance to other agent, d=d0. On the

t1=t0+1, he gets the distance d1=d. Ifd1>d0 then it is

assumed that he and/or other agent are moving

towards each other

Fig. 7. Distance different on a specific time-stamp

C. Point-in-Polygon AlgorithmFollowing above procedure, we develop technique to

determine whether a point lies in the interior or on the

line of the viewing area. There are various methods to

compute this condition as the viewing area model is a

polygon that is two dimensional, simple (there is no

intersection segment) and a convex one.

For a simple and practical purpose, we choose a

method of intersected route [11]. This method is

illustrated by diagram below (Figure 8).Given O is current agent iposition, J is agent j

( , )pos i i

i x y

diri

( , )d id id

i x y

h

d

m ax 1 m ax 1 m ax 1( , )

i ii x y

Y

X X

Y

1'dir

i

m ax 2 m ax 2 ma x 2( , )

i ii x y

2'dir

i

Agent ix-

z-

Agent k

x+

z-

Agent ix-

z-

Agent k

x+

z-

1 0tandis ce at t t

2 0tan tdis ce at t t

2 1tan tandis ce dis ce


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position, A and B are maximum point of agent i

viewing area. The method considers polygon OAB as

a path that traverses from O to point A and to point B

and finally back to point A. Point J is in the interior of

polygon OAB if and only if it is always on the same

side of all the line segments that making up the path.

Fig. 8. Point-in-Polygon

The procedure of the method is as follows:1. Define: O(xo,yo), A(xA,yA), B (xB, yB), and J

(xJ,yJ)2. Determine J where:

J1=(yj-y0)(xa-x0)-(xj-x0)(ya-y0)J2=(yj-ya)(xb-xa)-(xj-xa)(yb-ya)J3=(yj-yb)(x0-xb)-(xj-xb)(y0-yb)

3. J(xj,yj) is inside OAB if: {J1 andJ2 andJ3}>04. J(xj,yj) is on and outside OAB if : {J1 orJ2 or

J3} 0

D. Distance interpolationIn multi agent simulation, the total influence ofinfluence (FoA and FoR) received by current agent by

having other agents personality is by mean ofinterpolation of their distance.

This means the determination of force of attraction

and force of repulsion are not solely rely on thenearest agent but considering influence of distanceand direction from others as well.

If there are three agents: i, j, k, and the distances

between them are ij, ik, jk , then the distances

towards agent i are ij and ik. The procedure for

distance interpolation considering these distances and

direction of other agent as follows:

1. If other agents are either moving towardagent i or moving outward, then the

interpolated distance is in favor of the nearestone (in this case, agentj):

d1=(0.5(0.75ij+0.25ik))2. If only one agent is moving toward agent i,

then the interpolated distance has greatervalue by the nearest one (in this case, agentj): d2=(0.5(0.90ij+0.10ik))

Figure 9 below illustrates the distance interpolation

criteria:

(a) (b)

(c) (d)

Fig. 9. Criteria for distances interpolations

a) all agents moving toward each othersd(t)


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On each personality trait, we generate random

sequence of these goals so each personality trait has

different routes to visit all goals.

On an example, we presented the group simulationas a result from personality-traits driven behavioralmovements using these personality types (Table 4):

One of the examples is presented here as follows(Table 5):

TABLE.4. PERSONALITY TYPES OF AGENTS FOR EXPERIMENT

Extraversion

level

Agreeableness

level

Agent i 0.89 (Extrovert) 0.94 (Altruist)

Agent j 0.44 (Moderate) 0.86 (Altruist)

Agent k 0.79 (Extrovert) 0.21 (Egoist)

The snapshots of the experiment shows dynamicforces applied (Figure 10):

(a) (b) (c)Fig. 10. Snapshots of the experiment; the dots represent goals

In Figure 10, all snapshots show radius of the forceof attraction (outer circle) and the force of repulsion(inner circle). These radiuses are depending on thepersonality type of the agent and the distance towards

other agent at any given time. On this situation,

Extrovert agent has greatest FoA radius and lowestFoR radius.

Following the experiments, we presented the groupformation simulation as a result from personality-traitsdriven behavioral movements using differentpersonality traits levels (Table 5):

TABLE.5.PERSONALITY TYPES OF AGENT FOR EXPERIMENT OF

GROUP FORMATION

Extraversionlevel

Agreeablenesslevel

Agent i 0.82 0.17Agent j 0.81 0.86

Agent k 0.76 0.21

The snapshots of simulation are presented asfollows (Figure 11.):

(a) (b) (c)

(d) (e) (f)Fig. 11. Snapshots of the experiment of group formation; grey

circles on area represents traces of group formations.

From experiments as demonstrated above, we can

see that if we embedded procedures for socialinteraction into each agent, it is increasing probability

for group formation.It makes sense to note that if two or more group

node intersects with each other (imagef in Figure 10),

that particular area is regarded as area with higher

probability for social interaction than the others and

could be considered as public area.

V. DISCUSSIONThrough series of experiments, the proposed model isable to represent variability of social interaction in

virtual simulation. The sociability levels beingmodeled are based on category of personality traits.We suggested that based on this model, the moreelaborated method which extent each personality traitfeatures can be achieved.

We proposed model of the force of attraction andthe force of repulsion as basic features to distinguishExtraversion trait levels with respect to the category of

social distances. This provides solution to address

aspects of heterogeneity and dynamic situation insocial interaction simulation, particularly in relationwith architectral design elements.

In practical level, behavioral-based simulation in

architectural design can facilitate quantitative analysis

of the relationship between personalities and design

qualities.

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