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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.
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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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... The foraging behaviors of three Sumatran stingless bee species studied in [62] inspired the development of a firstly published article on stingless bee algorithm (SBA) [63], to solve a combinatorial optimization problem from master thesis [64] based on stingless bee behaviors described in [62]. The SBA is considered to be capable of accelerating the convergence process to the optimum point than other bee inspired algorithms [63]. ...
... The foraging behaviors of three Sumatran stingless bee species studied in [62] inspired the development of a firstly published article on stingless bee algorithm (SBA) [63], to solve a combinatorial optimization problem from master thesis [64] based on stingless bee behaviors described in [62]. The SBA is considered to be capable of accelerating the convergence process to the optimum point than other bee inspired algorithms [63]. Moreover, the proposed algorithm needs to be improved for combinatorial applications and for common numerical optimization problems. ...
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... Two other methods for power system load forecasting based on ANN combined with modified shuffled frog leaping algorithm and MHBMO have been presented in the previous studies. 25,26 However, other new optimization methods such as stingless bee foraging behavior algorithm 27 can also be implemented for prediction purposes. The previous study 28 considers wind speed time series and its prediction. ...
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