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This article can be cited as E. Joelianto and B. Prakoso, Stingless Bee Foraging Behaviour Algorithm for

Optimisation, International Journal of Artificial Intelligence, vol. 15, no. 1, pp. 1-20, 2017.

Copyright©2017 by CESER Publications

Stingless Bee Foraging Behaviour Algorithm for

Optimisation

Endra Joelianto1 and Bowo Prakoso2

1Instrumentation and Control Research Group, Faculty of Industrial Technology,

Bandung Institute of Technology, Bandung 40132, Indonesia;

Email: ejoel@tf.itb.ac.id

2Instrumentation and Control Master Program, Faculty of Industrial Technology,

Bandung Institute of Technology, Bandung 40132, Indonesia;

Email: prakosonic@gmail.com

ABSTRACT

Foraging behaviour of stingless bee has specific characteristics and it is of interest to be

adapted as an optimisation algorithm. Foraging behaviour of stingless bee either as an

individual worker or as a colony is different from the foraging behaviour of other group of

bees. This paper considers an optimisation algorithm based on specific characters of

stingless bee. The developed stingless bee algorithm is then tested for solving an

optimisation problem of a wireless network routing with residual energy cognizance.

Elapsed time of the computation of the stingless bee algorithm is examined by varying

node number using 5 nodes, 10 nodes, 15 nodes, 20 nodes, and 25 nodes. The larger

number of nodes means there are more candidate of solutions. The reduction mechanism

and the early termination mechanism used in the stingless bee algorithm are the important

parts of the developed stingless bee algorithm. The two mechanisms distinguish the

algorithm from other bee colony based algorithms.

Keywords: Stingless bee algorithm, foraging behaviour, optimisation, reduction mechanism,

early-termination mechanism, energy cognizance routing.

Mathematics Subject Classification: 68T99, 92B20

Computing Classification System: I.2

1. INTRODUCTION

Stingless bees (Meliponini) belong to a tribe of Apidae family among others different tribes i.e. honey

bees (Apini), bumble bees (Bombini) and orchid bees (Euglossini), the taxonomi is shown in figure 1.

Stingless bees have an interesting pattern of foraging behaviour to be adopted into an optimisation

algorithm as part of the swarm intelligence, in which, the foraging behaviour of honey bees (Apini)

has received considerable attention and has been adopted into Artificial Bee Colony algorithm

(Karaboga, 2005) and some other algorithms (Nakrani and Tovey, 2003), (Teodorovic and Dell’Orco,

2005), (Yang, 2005). Foraging behaviour of honey bees has inspired a population based search

algorithm to find the optimal solution which was firstly proposed by D. Karaboga in 2005 (Karaboga,

2005). The algorithm exploits the food foraging behaviour of honey bee swarms. Karaboga and his

team have investigated the artificial bee colony (ABC) algorithm and its applications to real problems.

Karaboga and Basturk have studied the performance of the ABC algorithm on either unconstrained

(Basturk and Karaboga, 2006), (Karaboga and Basturk, 2007a), (Karaboga and Basturk, 2008) or

constrained numerical optimisation problems (Karaboga and Basturk, 2007b).

Figure 1. The taxonomi tree of meliponini in Apidae family.

The ABC algorithm has also been implemented in neural network training in (Karaboga and Akay,

2007), (Karaboga et al., 2007). In (Hadidi et al., 2010), it was considered an Artificial Bee Colony

(ABC) algorithm based approach for structural optimisation. In 2011, Zhang et al. implemented the

ABC algorithm for various applications, such that optimal multi-level thresholding (Zhang and Wu,

2011a), MR brain image classification (Zhang et al., 2011a), cluster analysis (Zhang et al., 2011b),

face pose estimation (Zhang and Wu, 2011b), and 2D protein folding (Zhang and Wu, 2012). The

application of honey bee algorithm in smart lights by using feedback control has been considered in

(Alfonso et al., 2016). The honey bee algorithm proposed in (Karaboga, 2005) is an algorithm which

has received considerable attention since the first publication. Another honey bee algorithm has been

developed by (Nakrani and Tovey, 2003). More inspired algorithms by the behaviour of honey bee

have been studied in (Ozturk et al., 2010), (Chitra and Subbaraj, 2010). .

An Australian research (Heard, 1994) described comparison between honey bee species and a

specie of stingless bees. The research showed that stingless bees visit less flower for exploitation

than honey bees in the same interval time. Variation communications made by stingless bees are

more diverse with more types of information transmitted (Nieh, 2004). The stingless bee does not only

performing the waggle dance in the nest but also using chemical communication by spreading special

odour in the feeder, around the feeder or some places on the path to the feeder. The uniqueness of

stingless bee colony is its fastidious selection in feeder exploration. It inspires to develop an algorithm

which fastidious in candidates selection. Moreover, it can reduce the candidates before further

execution and eliminates some candidates before the final calculation in selection process.

Stingless bees use and communicate with more information than honey bees. Research on three

Sumatran stingless bees (in Sumatra Island, Indonesia) has shown that an individual of stingless bees

which flies to exploite floral resources will also perform exploration eventhough the floral resources

have not been fully consumed (Inoue et al., 1985). In contrast, honey bees will perform continuous

exploitation until the floral resources is emptied (Von Frisch, 1967). Information of floral resources

given by stingless bees includes direction, height and amount of nectar compared to honey bees that

only give direction and amount (Nieh, 2004).

The paper proposes an optimisation algorithm based on the stingless bee foraging behaviour by

adopting the unique characteristics studied in (Heard, 1994), (Nieh, 2004), (Inoue et al., 1985), (Von

Frisch, 1967), (Roselino and Hencir, 2012), (Kakutani et al., 1993), (Jarau et al., 2004), (Reichle et al.,

2013), (Jacobus and Judith, 2004), (Peter et al., 2010), (Jarau, 2009), (Sanchez et al., 2008). This

work is motivated by the experimental result in (Kakutani et al., 1993) in which the stingless bees

foraged well than the honey bees that foraged inefficiently. The paper considers the development of a

stingless bee algorithm (SBA) by using less number of visited flowers in an interval time characteristic.

The behaviours of stingless bees are used for reduction of states of solution candidates. The main

different with the well known honey bee algorithm and various variants of the original algorithm is in

the alteration of the reduction part. The proposed algorithm is then tested for solving an optimisation

problem in a wireless sensor network routing to find the best route either by setting the value of the

residual energy at each node or without pre-defined routes by searching and calculating any possible

routes randomly.

2. STINGLESS BEE ALGORITHM

The bee optimisation algorithms have been developed by mimicking the behaviour of colonies in

exploring and exploiting floral resources. In wild habitat, there are similarities between honey bees

and stingless bees. Foraging behaviour of bees can be divided into two types, i.e. colony and

individual behaviours (Heard, 1994), (Nieh, 2004). There are similarities and also differences on

behavioural patterns among tribes in Apidae family. Several entomology studies have made

comparison between the two types of bees that are stingless bees (Meliponini) and honey bees (Apini)

(Heard, 1994), (Nieh, 2004). The foraging behaviour of stingless bees, i.e, the colony behaviour and

individual behaviours are as follow.

2.1. Colony Behaviour

In foraging activity, as very social colonies, the honey bees, stingless bees and the bumble bees

distribute tasks among the colony members (Sanchez et al., 2008). However, only some colony

members are going out in the same time while the majority members are in the nest. The colony

members that stay in the nest (onlookers/unemployed/un-experienced workers) are waiting the

foragers bringing information of floral resources. In addition, several foragers who explore and find the

floral resources then recruit colony members in order to exploit found floral resources. Some

members fly out of the nest as the explorer to find feeder, but some members stay in the nest to

observe any information brought by the explorers that fly back into the nest.

Bees communicate each other by using visual and chemical communications. Waggle dance as a

visual communication presents the profitability and location information of the feeder. The waggle

dance of honey bees foraging behaviour is adopted by D. Karaboga (Karaboga, 2005) as an

important part of Artificial Bee Colony (ABC) algorithm. Stingless bees also perform waggle dance as

a visual communication to recruit observer bees. However, the waggle dance on stingless bee is more

varied and contains more information compared to the waggle dance of honey bees. It presents

complete information of related feeders (Jarau, 2009).

In addition to waggle dance, stingless bees also communicate with the chemical signal. It provides

odour guidance which presents profitability and direction information of floral resources to be

recognised by other members of colony (Roselino and Hencir, 2012), (Sanchez et al., 2008).

Stingless bees have varied odour to broadcast different information (Roselino and Hencir, 2012),

(Kakutani et al., 1993). Beside the odour produced by the body of bees, stingless bee also observe

the floral odour of food. Then, the observer bees can switch to be the explorer for searching the food

source based on their recognition to the odour of the food which brought to the nest by explorer bees

in advance (Jarau et al., 2004). It has been shown in (Roselino and Hencir, 2012) that stingless bees

will put repellent odour to the certain resources that are considered as not eligible or even fake

resources. Hence, the others explorers will not explore the marked location. In this case, stingless

bees have developed an efficient exploration mechanism.

2.2. Individual Behaviour

The individual workers of stingless bees are able to make decision during foraging activity. It has been

observed that the foragers perform exploitation of resources and can switch to do exploration in their

flight although the current food sources have not been exhausted (Von Frisch, 1967). In contrast to

the behaviour of honey bees which still continue to visit the same food sources even until the next day

after the food source have been exhausted (Heard, 1994), (Von Frisch, 1967). A single explorer of

stingless bees can mark one or more feeder using odour as repellent signal in order to avoid other

members visiting those locations. This shows that stingless bee foragers perform pre selection in their

exploration. Moreover, individual explorers are also able to create full or partial trail by spreading

odour that linking the feeder location and the nest (Roselino and Hencir, 2012).

2.3. Algorithm Based on Foraging Behaviour of Stingless Bee

An algorithm based on foraging behaviour of stingless bees is considered by adapting the information

communication exchange during foraging. Before describing the algorithm, the following definition is

required.

Definition:

• Permanently ineligible candidate:

A candidate which does not fulfil the threshold to be chosen permanently.

• Temporary unfit candidate:

A candidate which only unfits in a specific condition, but in principle it fulfils the threshold

to be an acceptable solution.

The algorithm proposed in this paper is based on foraging behavioural patterns of stingless bees. The

structure of the algorithm is described in the flowchart shown in figure 2.

Figure 2. The Stingless Bee Algorithm Flowchart with relation to common bee colony

algorithms

START

Initialisation

Do exploration for new

candidate solutions without

repellent odour

Permanent ineligible

candidates

Reduction by

marking with

repellent odour

Feeder recognition

Temporary unfit?

Calculate cost in the feeder

area

Selection based on cost

information in the nest area

All

neighbours

information

gathered?

Update and record the best

solution

Satisfy termination

criteria

Final best solution

FINISH

Explore any

neighbours

without repellent

odour

Yes

Yes

No

No

No

No

Yes

Yes

: used in SBA (new

procedure added)

: used in common

bee colony

algorithm, still used

in SBA

With the stingless bee algorithm (SBA) procedure, available observed edges (or candidate solutions)

can be reduced in a significant number. Therefore, this makes a good impact on computation. The

key process for presenting the final best result in SBA is the reduction of unfit candidate solutions with

repellent odour. The explorer bees can perform selective decision to the colony in order to avoid

inefficient foraging visit to the ineligible location. The explorers mark several feeder locations with

repellent signal. These show that the individual forager can eliminate ineligible feeders in order to

avoid the other foragers visit the ineligible feeders. The information is not necessarily to be sent to the

nest for the response of the colony.

The algorithm described in the flowchart in figure 2 adopts the foraging behaviour of the stingless

bees which have more information communication variaties. In principle, the algorithm is influenced by

the honey bee algorithm developed in (Karaboga, 2005). The stingless bee algorithm is developed by

performing the reduction of candidates by means of eliminating the permanent ineligible candidates.

Hence, it does not need to be involved in further selection process. For real time applications, it is a

very useful mechanism in order to reduce the computational load and to increase the searching speed.

In addition to the reduction mechanism, it is also considered an early termination mechanism. In the

early termination of stingless bee algorithm, the looping process does not need to be run until the end

of calculation. The algorithm will terminate the current process to the next process earlier without

finishing the process in a loop. It is useful when the candidates of solutions that have been found are

recognised as temporary unfit. The temporary unfit candidates do not need to be calculated in further

process. In contrast with permanent ineligible candidates which are permanently unacceptable, since

the temporary unfit is temporary unaccepted, it may be accepted in the next loop.

In the considered SBA algorithm, there are two mechanisms have been added, i.e. candidate

reduction and early termination mechanisms compared to the ABC algorithm. The two mechanisms in

the SBA algorithm make up two stages with the ABC algorithm. In recent years, algorithms with multi

strategies have been developed with various combinations of heuristic and/or classical methods. The

algorithms have been successfully implemented in solving, for example, nonlinear functions,

combinatorial optimisation problems, high-dimensional and large-scale regression datasets, and have

achieved the high performance of the results. To illustrate, El Sehiemy et al., 2013 has considered a

multi-objective fuzzy-based procedure for solving reactive power management in practicable

environment. The procedure comprises both economical and technical aspects of reactive power

supports. Osaba et al., 2013 has proposed a parallel genetic algorithm for solving combinatorial

optimisation problems. In the algorithm, a communication between subpopulations called migration

has shown to increase the performance of the algorithm. Precup et al., 2013 has developed a reduced

parametric sensitivity method using Gravitational Search Algorithms (GSAs) to minimise the objective

functions of classified optimisation problems which increases the search accuracy. Gacto et al., 2014

has considered a two-stage method to yield proper fuzzy modelling in high-dimensional regression

problems by means of an approximate Takagi–Sugeno–Kang fuzzy system. The stages consist of an

inductive rule based learning process with an evolutionary data base learning, and a post-processing

process acting as a rule selection and a scatter-based tuning of the membership functions of the

determined solutions which include an efficient Kalman filter to find out the coefficients of the

consequent polynomial function in the rules of the fuzzy system. The mechanisms in the both stages

produce a fast convergence in optimisation problems of high-dimensional and large-scale regression

datasets with enhanced accuracy.

3. PROBLEM FORMULATION AND IMPLEMENTATION OF ALGORITHM

3.1. Problem Formulation

Given an ad-hoc network which has N nodes, where each node has the same transmission range of

coverage denoted by

λ

. Nodes are scattered at the position };;;;{ 321 N

kkkkk L

=

, where 1

k,2

k ,

L,N

k represent the coordinates ),( yx location of the node. Each node is assumed to have a

residual energy which is expressed in the set };;;;{ 321 N

eeeee L

=

.

The optimisation goal is to minimise a cost function, C, which defines the required energy from the

source node to the destination node. The optimisation problem is then formulated mathematically as

follows.

Minimise C (1)

where

t

tt DC e

1

+=

α

(2)

∑

∈

=

Nji ijij

dD ),( A (3)

⎩

⎨

⎧≤−<

=,else

kkif ij

ij 0

0,1

λ

A (4)

In equation (2), t

e denotes the value of residual energy at the node in t position, while the cost of

distance from the current node to the next node in t position is denoted by t

D. For the node i to

node

j

, ij

dis the distance between of these nodes and ij

D will be calculated if and only if the

distance ij

d fulfils the range transmission criteria i.e.

λ

≤

ij

d which is marked on ij

A. Hence, the

cost of distance on a full path transmission is given by D as shown in equation (3),

α

is a multiplier

factor to make the cost value of the distance to be much smaller than the energy cost as the main

issue in this paper is based on energy cognition.

A

is a matrix that shows the link availabilities refer

to the coverage transmission of each sensor node. ij

A will be 0 (zero) if it does not meet the

provisions.

3.2. Implementation of the procedure of stingless bee algorithm

The combinatorial solution is expressed by

p

which contains some partial solutions t

p, is a set of

nodes that form a full path from the source node to the destination node. The t

p is defined by the

following equation

⎡⎤

1)( ftlbublbpt

⇔

−+=

φ

(5)

and

1=⇔= tpspt (6)

In this case psis a source node, lb is the node with the lowest index while ub is the node with the

highest index.

φ

in equation (5) is a random value between 0 and 1. A source node is given with the

lowest index, while the destination node is given with the highest index in the range, whereas the

other nodes are indexed randomly. All indexes are integer, hence the ceiling bracket (

⎡⎤

•) is used in

order to keep the equation provides integer value, such as the integer value of node's index in its

range.

Explorers of stingless bees are trying to obtain information about any detected food sources and will

decide whether it will be marked with a repellent odour or will be communicated about its cost to the

observer in the nest. In this case, the criteria for repellent odour is the solution if the path does not

meet the initial constraint, means represented with 0

=

ij

A (equation (4)) and the additional constraint

(equation (7))

2

λ

≤= ijij dD (7)

⎩

⎨

⎧

=2

,1

,0

λ

f

ij

dif

else

ij

R , ijij kkd −= (8)

Equation (7) will reduce the number of edges. As a result, a number of solution paths that has one or

more unmarked edges by the repellent odour 1

=

ij

R will be eliminated. In other words, the full path

solution contains repellent odour in one edge or more , 1≥

path

R, will be ignored.

∑

∈

=

Nji ijpath RR , (9)

The next stage is to calculate the C value with the function in equation (2). In this step, the only path

that is free from repellent odour (in the previous stage) will be proceeded in the selection stage.

The information of C value is then shared to the observer bees that are waiting in the nest. Next, on

the exploitation phase, the worker bees in flight are also looking for the neighbour food sources.

Equation (10) represents the neighbour exploration:

⎡⎤

pspqlbublbq ttti

≠

≠

⇔

−+= )(

φ

(10)

The observer bees in the nest are comparing the cost of neighbour solutions to previous solution. The

solution with less cost is then selected as a new solution.

The early termination mechanism performs termination of the process in a loop when a temporary

unfit feeder is found. Hence, it is not necessary to continue the process untill the final calculation, but

it will jump to the next iteration immediately. In this case, the temporary unfit feeder is a candidate

which has the residual energy below the average of residual energy,

γ

in one neighbourhood nodes.

⎩

⎨

⎧

=≥

γ

)(,1

,0

t

qif

else

fit E

(11)

A node may unfit in one group of neighbourhood but it may be fit in other groups, so it is called a

temporary unfit.

4. SIMULATION RESULTS

The simulation was performed by using MATLAB in order to test the performance of the proposed

stingless bee algorithm in generating solutions. The results are shown in the figure 3, there are 25

nodes with 158 edges, and one node can have up to 21 neighbour nodes (node 22).

Figure 3. Available link on the network based on coverage transmission of each node

The simulation begins by setting the value of the residual energy at each node by 15 Joules. In this

condition, the algorithm performed to get the optimal route from node 18 to node 25, as shown in

figure 4.

Figure 4. Simulation for optimal routing transmission of node 18 to node 25

In the first simulation, the result is presented in figure 4. The optimal route from node 18 to node 25 is

known through the node 22. To test the algorithm in obtaining the optimal route, the next case, a

scenario is run by changing the value of residual energy at node 22 of 15 Joules to 14 Joules. In this

scenario the route was changed, as shown in figure 5.

Figure 5. Second simulation for optimal route of node 18 to node 25

From the simulation results, it was obtained the route from node 18 to node 25.It can be seen that the

algorithm can determine the optimal route by selecting the path through the node which has higher

residual energy. The route 18-22-25 was originally the optimal route, when the value of the residual

energy at node 22 is reduced then the algorithm will search for a new solution. The new solution is

found as neighbours of the previous solution, i.e. 18-23-25 .

In the next simulation scenario, the selected nodes are located quite far from the sink node so that the

simulation can be made with the two nodes on the residual energy value decreased significantly. In

this scenario, node 1 is chosen as a source node and node 25 as a destination node. Each node is

given by the residual energy of 15 Joules. The simulation result of this scenario is shown in the figure

6.

Figure 6. Simulation of 1st scenario for optimal route of node 1 to node 25

In the simulation results (figure 6), it is found the optimal route from node 1 to the node 25 through the

path 1-4-5-21-25. In this scenario the entire value of each component of the energy matrix e is 15

Joules.

To test the algorithm, a second simulation on the route from the source node 1 to the sink node 25 is

performed. The second scenario is run by changing the value of the residual energy at node 4 and

node 21 of 15 Joules to 7 and 5 Joules respectively. The purpose of this simulation scenario is to

determine whether the algorithm can find a new route solution if the old route runs into a lower

residual energy level. Simulation result in this scenario presents the route changes, as shown in figure

7.

Figure 7. Simulation of 2nd scenario for optimal route of node 1 to node 25

For these scenarios, the numbers of node is 25 nodes. It is observed the reduction of candidate

solutions by the algorithm as shown in table 1. The reduction of candidate solutions is represented by

the reduction of the number of observed edges. The early termination and the reduction mechanism

of the stingless bee algorithm lead to the reduced elapse time of execution to produce the optimal

solution.

Table 1: Performance of the algorithm in simulation

Value

Parameters Initial value stingless bee

algorithm

(with

reduction)

Number of observed nodes 25 25

Number of observed edges 158 50

The maximum number of

neighbour nodes 21 6

The minimum number of

neighbour nodes 8 3

The algorithm is then tested by changing the number of nodes into several scenarios (5 nodes, 10

nodes, 15 nodes, 20 nodes and 25 nodes). From this test, it is known the elapsed time of the

algorithm which gives the required time of the searching process. The results are shown in table 2

and figure 8.

Table 2: Simulation results of elapsed time

Nodes

Run

5 nodes 10 nodes 15 nodes 20 nodes 25 nodes

1st 0.924243 s 1.246057 s 1.930346 s 2.082516 s 2.660983 s

2nd 0.934927 s 1.231707 s 1.811621 s 2.0712 s 2.649989 s

3rd 0.800293 s 1.207068 s 1.803981 s 2.030206 s 2.559149 s

4th 0.778148 s 1.192857 s 1.730544 s 2.004045 s 2.444357 s

5th 0.768285 s 1.18623 s 1.720151 s 1.967595 s 2.330155 s

Average 0.841179 s 1.212784 s 1.799329 s 2.031112 s 2.528927 s

Figure 8. The elapsed time of computation performance of stingless bee algorithm

Figure 9. The multiples of average of elapsed times to the increment of nodes

In table 2 and figure 8, the searching process of the stingless bee algorithm becomes slower as the

number of the nodes grows to be larger. However, the increasing of elapsed times is not linear as the

linear increased of related numbers of node as shown in figure 9.

The next test was performed to find the best route from node 1 to 6. In the first test, all possible routes

were defined (in MATLAB program) i.e :

rout1 = [1 2 3 4 5 6];

rout2 = [1 2 4 3 5 6];

rout3 = [1 2 4 5 3 6];

rout4 = [1 2 5 4 3 6];

rout5 = [1 2 5 3 4 6];

rout6 = [1 2 3 5 4 6];

rout7 = [1 3 2 4 5 6];

rout8 = [1 3 4 2 5 6];

rout9 = [1 3 2 5 4 6];

rout10 = [1 3 4 5 2 6];

rout11 = [1 3 5 4 2 6];

rout12 = [1 3 5 2 4 6];

rout13 = [1 4 2 3 5 6];

rout14 = [1 4 3 2 5 6];

rout15 = [1 4 3 5 2 6];

rout16 = [1 4 2 5 3 6];

rout17 = [1 4 5 3 2 6];

rout18 = [1 4 5 2 3 6];

rout19 = [1 5 4 3 2 6];

rout20 = [1 5 4 2 3 6];

rout21 = [1 5 3 4 2 6];

rout22 = [1 5 3 2 4 6];

rout23 = [1 5 2 3 4 6];

rout24 = [1 5 2 4 3 6];

rout25 = [1 2 3 4 6];

rout26 = [1 2 3 5 6];

rout27 = [1 2 4 3 6];

rout28 = [1 2 5 3 6];

rout29 = [1 2 4 5 6];

rout30 = [1 2 5 4 6];

rout31 = [1 3 2 4 6];

rout32 = [1 3 2 5 6];

rout33 = [1 3 4 2 6];

rout34 = [1 3 5 2 6];

rout35 = [1 3 4 5 6];

rout36 = [1 3 5 4 6];

rout37 = [1 4 3 2 6];

rout38 = [1 4 2 3 6];

rout39 = [1 4 3 5 6];

rout40 = [1 4 5 3 6];

rout41 = [1 4 5 2 6];

rout42 = [1 4 2 5 6];

rout43 = [1 5 3 2 6];

rout44 = [1 5 2 3 6];

rout45 = [1 5 4 2 6];

rout46 = [1 5 2 4 6];

rout47 = [1 5 3 4 6];

rout48 = [1 5 4 3 6];

rout49 = [1 2 3 6];

rout50 = [1 2 4 6];

rout51 = [1 2 5 6];

rout52 = [1 3 2 6];

rout53 = [1 3 4 6];

rout54 = [1 3 5 6];

rout55 = [1 4 2 6];

rout56 = [1 4 3 6];

rout57 = [1 4 5 6];

rout58 = [1 5 2 6];

rout59 = [1 5 3 6];

rout60 = [1 5 4 6];

rout61 = [1 2 6];

rout62 = [1 3 6];

rout63 = [1 4 6];

rout64 = [1 5 6];

rout65 = [1 6];

The algorithm was then performed based on those fixed 65 routes. The second test was carried out

without defined routes, it was fully random. The best route was found by searching and calculating

any possible routes randomly.

Both Fixed and Random produce same route (1-3-2-4-6) in 10 tests, but the SBA yields different

performances between them. With fixed parameters of routes are defined, the SBA finds the best

route faster than randomly as shown in figure 10. The average of elapsed times for the fixed

parameters is 0.20 seconds which is three times faster than 0.69 seconds of the random. However,

the SBA with fixed route parameters needs more efforts such as higher capacity of memory and

manual update for pre-defined all combination route in the plant than the random routes. More nodes

added require more efforts. The SBA with random parameters causes the algorithm more flexible

especially in dealing with huge number of nodes.

Figure 10. The elapsed time in 10 tests

Fixed Random

Figure 11. Simulation results

5. CONCLUSION

An algorithm based on foraging behaviour of stingless bee was developed in this paper. The main

idea of the proposed algorithm was the inclusion of reduction mechanism and early termination

mechanism. The reduction mechanism mimics the stingless bee foraging behaviour by marking

ineligible feeders and the early termination mechanism mimics the stingless bee behaviour leaving the

feeder during exploitation process to explore new fit feeders. The proposed stingless bee algorithm

successfully found the optimal route rapidly in any environmental changes i.e. the changes of residual

energy value distributed in the network. Only two foraging behaviours of stingless bee were adopted

in the proposed algorithm. In fact, there are still many foraging behaviours of stingless bee that can be

explored for future development in order to improve the algorithm. Future work is aimed to exploit the

other foraging behaviours in order to produce an optimal algorithm.

ACKNOWLEDGMENT

This work was supported in part by the Directorate of Higher Education, Ministry of National Education

and Culture, Indonesia under the Decentralised Research Grant, Bandung Institute of Technology,

Bandung, Indonesia 2012. The authors would like to thank the anonymous reviewers for their helpful

comments and suggestions which have helped to significantly improve the presentation of the paper.

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