A Bee Colony Optimization Algorithm Biology Essay

Arrested development testing is the confirmation procedure of modified package in the care stage. Due to budget and clip restraints regression test suite size and its choice is a critical issue. A Bee Colony Optimization ( BCO ) algorithm for the arrested development trial suite prioritization has been developed and is presented in this paper. The behaviour of two types of bees ; scout bees and forager bees have been used to prioritise the trial suite. The proposed algorithm has been explained utilizing illustrations on entire mistake sensing in clip constrained environment and entire codification coverage. Average Percentage of Fault Detection ( APFD ) metric has been used to demo the effectivity of algorithm proposed.

After development and release, package undergo reasoning backward care stage of 10 to fifteen old ages. Alterations in package may be due to alter in client ‘s demands or alteration in technology/platform. These grounds lead to the release of legion versions/editions of the bing package. Development clip and budget of a package permits for its thorough testing but same is non the instance for arrested development testing. Besides in instance of the version/edition ‘s trial merely modified and affected parts are to be tested to leave assurance in the modified package. So effectual and intelligent reordering/prioritization of the existent package ‘s trial suite has to be done to do singular nest eggs of clip and budget, in the testing of the modified package ‘s version.

Several efforts have been made in happening techniques/algorithms for the arrested development trial suite prioritization. Many algorithms such as Greedy algorithms, non-evolutionary algorithms, evolutionary algorithms, seeking algorithms etc have been used. Searching Algorithms are algorithms in which we search the needed piece of information ( based some standards which is the solution to our job ) in the available sample infinite. So seeking algorithms will be really utile and helpful in seeking the trial instances for arrested development trial suite. One system which is based on seeking algorithm is the Bee Colony System which have been studied and mapped to happen the ordination of the modified package trial suite.

Automated package proving has long been an country of concern for large package development companies. In mechanization testing development and executing of trial instances can be done unattended. Besides, comparing of existent consequences to expected consequences and logging position can be determined. It is the mechanization of the manual testing procedure. It improves truth ; increases trial coverage, saves clip and money and helps developers and examiners to develop trial instances rapidly and expeditiously. This algorithm automates the trial suite prioritization procedure as per the bee settlement optimisation standards.

Organization of the paper is as follow. Related work is presented in subdivision 3, BCO method has been explained in subdivision 4. Section 5 presents the formalistic BCO algorithm for arrested development trial suite prioritization, in subdivision 5.1 the account of the algorithm is given, 5.2 nowadayss the prioritization of trial instances based on entire mistake coverage with illustrations, 5.3 nowadayss the prioritization of trial instances based on entire codification coverage with an illustration showing the working of the BCO algorithm. Section 6 gives the comparision of assorted prioritization attacks to BCO. And eventually in the succeeding subdivisions menaces to cogency, decision and futute work are presented.

3. Related Work

Bee Colony Optimization is an emerging field for research workers. It has been applied to countries like “ Optimization Algorithms ” [ 18 ] , ” Traveling Salesman Problem ” [ 20 ] , ” Job Shop Scheduling job ” [ 22 ] , ” Combinatorial Techniques like Generation of pair-wise trial sets ” [ 23 ] , ” Solving Sudoku Puzzles “ [ 27 ] , ” Routing Algorithm ” [ 29 ] .

4. BEE COLONY OPTIMIZATION ( Natural Phenomenon of Bee Colony )

Bee Colony Optimization is the name given to the settlement formed by the common apprehension of the natural bees in the nutrient scrounging procedure. In malice all the animals on this Earth follow one or the other mechanism/process to happen nutrient that suite them and these mechanism are found in insects like emmets, bees or cockroaches.

Honey bee comb build-up and direction is a authoritative illustration of teamwork, experience, co-ordination and synchronism. The manner the honey bees find, build and maintain their comb and hive is singular. These are the factors which have given rise to involvement of research workers to happen solutions to their jobs.

In a natural honey bee hive there are a assortment of bees with specific function ( s ) to execute. There are three types of bees:

Queen Bee ( one )

She is responsible to put eggs which are used to construct new settlements.

Male Drone Bees ( many )

These are responsible for copulating with the queen bee.

Worker Bees ( 1000s )

These bees perform all the care and direction occupations in the hive. There are two types of worker bees, viz. scout bees and forager bees, which perform the lookout behaviour and forager behaviour severally, which are jointly responsible for the working of the honey bee settlements.

1. The Scout Behavior

In the lookout behaviour there are following stairss:

The lookout bees start from the hive in hunt of nutrient beginning randomly.

They keep on this geographic expedition procedure until they are out of energy/tired and return back to the hive.

When they return back to the hive, they portion their experience and cognition with the forager bees by executing the mechanism called “ shake dance ” .

It is the agencies by which the bees communicate. It is used to convey the parametric quantities like nutrients Source Quality, distance of nutrient beginning from hive, Location of nutrient beginning w.r.t. Sun, to steer the way to the available forager bees.

These stairss of the lookout bees constitute the first measure of the BCO procedure called the “ Path Construction ” .

2. The Forager Behavior

In the Forager behaviour, the forger bees do the followers:

The Forager bees observe and learn the stairss done by the lookout bees while waggling so as to ease their journey.

Then these forager bees go to the nutrient beginnings as guided by the lookout bees to work them

These forms the 2nd measure of the BCO procedure called the “ Path Restructuring ” .

5. PROPOSED ALGORITHM

Artificial bee settlement system has been modeled in [ 1 ] . This paper presents a new optimisation algorithm that maps the nutrient scrounging behaviour of natural bees as a process to prioritise arrested development test suite ‘s trial instances. This algorithm takes the trial instances as nutrient beginnings, the figure of mistakes detected upon executing clip of each trial instance as the nutrient beginning quality and figure of trial instances as the figure of lookout bee plus figure of forager bees which makes the initial population.

Following is the basic flow of the BCO Algorithm:

Figure1. Basic flow of BCO Algorithm

Following is the list of notations that are being used in the proposed algorithm

Nbee: Entire figure of bees ( Initial Population )

NSB: Number of lookout bees

NFB: Number of forager bee

Ei: Energy at ith loop

FSQi: ith Food Source Quality

SBi: ith Socut Bee

Federal bureau of investigation: ith Forager Bee

PSBi: Way of SBi

PFBi: Way of FBi

ET: Execution clip of trial instance

FC: Number of Faults covered

In the executing of the algorithm two tabular arraies will be formed.

PSB Table

Way of Scout Bee tabular array, as seen in table 2, 5, 8 contains all the waies visited ( explored ) by the SB. It is used for the way building stage of SB. This tabular array will move as input for the way restructuring stage which is done by FB.

PFB Table

Way of Forager Bee tabular array, as seen in table 3, 6, 9 contains all the waies selected ( exploited ) by the FB. An history of the entire ET of each way is besides kept in this tabular array. This tabular array helps in concluding way choice.

Following are the proposed algorithm ‘s chief stairss

1 ) Low-level formattings

Nbee = NSB + NFS

NSB = NFB = figure of trial instances in the trial suite under trial.

E0 = 100 % .

2 ) Premises

The nutrient beginnings have been identified.

The distance between hive to nutrient beginning, nutrient beginning to nutrient beginning, nutrient beginning to hive is unity.

Any nutrient beginning is visited merely one time.

Each SBi will get down the random hunt from ith nutrient beginning.

Each FBi will work merely SBi way.

E0 ( Initial energy degree of of SB and FB ) is 100 % .

Energy decrease rate is set up such that merely 50 % of the trial suite gets executed.

FSQi==

Stoping standards

Entire figure of mistakes covered

Ei = 0 ; Ei =1- i*energy decrease rate

3 ) Algorithm

Start

Repeat NSB times ( Path building )

{

Repeat until halting standards is met

Each SBi starts researching from ith nutrient beginning and signifiers PSBi ( table 1 ) .

}

( 2 ) Repeat NFB times ( Path Structuring )

Each FBi starts working PSBi to organize PFBi ( table 2 )

( 3 ) Final Path Selection

Choose way PFBi with minimal ET

Stop

Explanation of the BCO algorithm

1. Way building

This is the first measure in the executing of the algorithm. This measure is executed by the lookout bees, NSB times, in order to research all the nutrient beginnings ( Test Case ) available. The SBi starts its geographic expedition procedure from the ith nutrient beginning ( Test Case ) . After this they explore the Test Cases indiscriminately until any one of the halting standard is met. Each way PSBi constructed by the SBi is entered into the PSB tabular array.

2. Way Restructuring

In the following measure the forager bees exploit the PSBs. This measure uses the PSB tabular array as input. Each FBi starts working the PSBi to organize the PFBi. Here each FBi chooses the trial instance ( nutrient beginning ) with best FSQi value. The wining trial instances are chosen such that which detects mistakes those are non detected by the bing trial instances. The status makes certain that merely those trial instances are executed which are effectual in mistake sensing and entire mistake coverage ( halting standards ) . Besides the summing up of the ET of all the trial instances present in a peculiar PFBi is done to acquire that way ‘s entire ET. All these entries are maintained in PFB tabular array.

3. Path Choice

This is the concluding measure of the algorithm done by the FBi. From the PFB tabular array select the PFBi with minimal Entire ET.

5.1 Prioritization of trial instances based on entire mistake coverage

In this technique the trial instances are prioritized in such a mode so as to accomplish entire mistake coverage within minimal executing clip. To guarantee that all the mistakes are covered by the trial instances selected in the prioritized ordination we use mutation testing.A In this we intentionally alter a plan ‘s codification, so re-run a suite of valid trials against the mutated program.A A good trial will observe the alteration ( mistake ) in the plan and fail consequently. Therefore, the proposed algorithm ‘s effectivity is measured utilizing mutant proving. This is illustrated by two illustrations in which mutations are created.

5.1.1 Example 1 ( Based on Entire Fault Detection )

The job taken is “ college plan for admittance in classs ” . The job specification is available at website hypertext transfer protocol: //www.planet-source-code.com.

In this illustration a trial suite has been developed which consisted of 35 trial instances. For simplified account of the working of the algorithm, a trial suite with 9 trial instances is considered in it, covering a sum of 5 mistakes.

The arrested development trial suite contains 9 trial instances with default telling { T1, T2, T3, T4, T5, T6, T7, T8, T9 } , the mistakes covered ( FC ) by each trial instance, the executing clip ( ET ) required by each trial instance in happening mistakes and nutrient beginning quality ( FSQ ) are as shown in Table 1. Equal precedence is given to the figure of mistakes covered and minimal executing clip in choosing trial instances.

Table 1: Trial instances with the mistakes covered, executing clip and Food Source Quality.

Test Case

F1

F2

F3

F4

F5

FC

ET

FSQi

T1

Ten

Ten

Ten

Ten

4

11.5

.34

T2

Ten

Ten

2

11.5

.17

T3

Ten

Ten

Ten

3

12.33

.24

T4

Ten

Ten

Ten

3

10.66

.28

T5

Ten

1

15

.06

T6

Ten

Ten

Ten

3

8.33

.36

T7

Ten

1

15

.06

T8

Ten

Ten

Ten

3

10

.30

T9

Ten

1

11

.09

Measure 1. Scout Bee Performs Path Construction and creates PSB TABLE 2

Table 2: Way Constructed by lookout bee. ( Path of lookout bee tabular array ) .

SBi

PSBi

SB1

T1

T6

T7

T4

SB2

T2

T1

T9

T4

SB3

T3

T1

T6

T8

SB4

T4

T3

T5

T7

T2

SB5

T5

T1

T4

SB6

T6

T3

T5

T7

T2

T4

SB7

T7

T6

T3

T9

T1

T8

SB8

T8

T1

SB9

T9

T5

T7

T8

T3

Measure 2. Forger Bee Performs Path Restructuring and creates PFB TABLE 3

Table 3: Way restructured by Forager bee. ( Path of forager bee tabular array ) .

Federal bureau of investigation

PFBi

Entire ET

FB1

T6

T1

T4

30.49

FB2

T1

T4

22.16

FB3

T6

T1

T8

29.83

FB4

T4

T3

T2

34.49

FB5

T1

T4

22.16

FB6

T6

T4

T2

30.49

FB7

T6

T1

T8

29.83

FB8

T1

T8

21.5

FB9

T8

T3

22.33

Measure 3. Forger Bee Performs Final Path choice

Hence PFB8 with trial instances T1 T8 forms the prioritized trial suite for the given job.

5.1.2 Example 2 ( Based on Entire Fault Detection )

Another job specification for “ Hotel Reservation ” which militias the suites in hotel and maintains the record. The complete job specification is available at the website hypertext transfer protocol: //www.planet-source-code.com.

In this illustration a trial suite has been developed which consisted of 40 trial instances. For simplified account of the working of the algorithm, a trial suite with 5 trial instances is considered in it, covering a sum of 5 mistakes.

The arrested development trial suite contains 5 trial instances with default telling { T1, T2, T3, T4, T5 } , the mistakes covered ( FC ) by each trial instance, the executing clip ( ET ) required by each trial instance in happening mistakes and nutrient beginning quality ( FSQ ) are as shown in Table 4. Equal precedence is given to the figure of mistakes covered and minimal executing clip in choosing trial instances.

Table 4: Trial instances with the mistakes covered, executing clip and Food Source Quality.

Test Case

F1

F2

F3

F4

F5

FC

ET

FSQi

T1

ten

ten

ten

3

12.2

.2459

T2

ten

1

10

.10

T3

ten

ten

ten

3

10.67

.28

T4

ten

1

7

.14

T5

ten

ten

ten

ten

4

9.97

.40

Measure 1. Scout Bee Performs Path Construction and creates PSB TABLE 5

Table 5: Way Constructed by lookout bee. ( Path of lookout bee tabular array ) .

SBi

PSBi

SB1

T1

T2

T3

T4

SB2

T2

T3

T5

SB3

T3

T1

T2

T5

SB4

T4

T3

T2

T5

SB5

T5

T3

Measure 2. Forger Bee Performs Path Restructuring and creates PFB TABLE 6

Table 6: Way restructured by Forager bee. ( Path of forager bee tabular array ) .

Federal bureau of investigation

PFBi

Entire ET

FB1

T3

T1

22.87

FB2

T5

T3

20.64

FB3

T5

T3

20.64

FB4

T5

T3

20.64

FB5

T5

T3

20.64

Measure 3. Forger Bee Performs Final Path choice

Hence PFB2 with trial instances T5 T3 forms the prioritized trial suite for the given job.

5.2 Prioritization based on Entire Code Coverage

Prioritization based on structural proving allows prioritize/reorder the trial instances based on the internal workings of the codification. Structural testing is besides called way proving since trial instances are chosen that cause waies to be taken from different parts ( construction ) of the plan. There are certain degrees of coverage in way proving viz. statement coverage, subdivision coverage, status coverage and way coverage. Each degree of coverage indicates the degree of proving. As we move towards the higher degree, more hard and complete the proving procedure becomes. The purpose of way testing is to achieve the highest degree of coverage that is condition coverage.

The logical flow of a plan can be analysed utilizing graphical representation known as the flow graph. Flow graph coevals is the first measure of way testing. Then the determination to determination ( DD ) way graph is generated from the flow graph. It is used to happen independent waies. In DD way graph all the consecutive nodes are clubbed into a individual node go forthing behind the determination nodes. An independent way is any way through the DD way graph that introduces at least one new statement node or status node. Therefore, we need to put to death all the independent waies at least one time during the procedure of way testing.

5.2.1. Example 1 ( based on Entire Code Coverage )

The illustration taken for codification coverage is the trigon job which takes the three sides ( a positive whole number in the scope of 0 to 100 ) of the trigon as input and gives the end product as scalene, isosceles, equilateral, non a trigon and invalid inputs harmonizing to the input. [ 3 ] .The trial instances are generated harmonizing to robust value proving. The trial instances, end products, statements, conditions and independent waies covered are shown in the tabular array 7.

Table 7: Trial instances with inputs and end products

Trial CASE NO.

Ten

Yttrium

Omega

EXPECTED OUTPUT

INDEPENDENT PATH

Condition COVERED

NODES COVERED

STATEMENT COVERED

1

50

50

0

INVALID INPUT

abfgnpqr

3

8

21

2

50

50

1

ISO

abcdeghjkmqr

5

12

23

3

50

50

2

ISO

abcdeghjkmqr

5

12

23

4

50

50

50

EQUI

abcdeghimqr

4

11

22

5

50

50

99

ISO

abcdeghjkmqr

5

12

23

6

50

50

100

NT A TRI

abcdegnoqr

4

10

21

7

50

50

101

INVALID INPT

abcegnpqr

4

9

20

8

50

0

50

INVALID INPT

abfgnpqr

3

8

21

9

40

20

30

SCALENE

abcdeghjlmqr

5

12

24

10

50

1

50

ISO

abcdeghjkmqr

5

12

23

11

50

2

50

ISO

abcdeghjkmqr

5

12

23

12

50

99

50

ISO

abcdeghjkmqr

5

12

23

13

50

100

50

NT A TRI

abfgnoqr

3

8

20

14

50

101

50

INVALID INPT

abcegnpqr

4

9

21

15

0

50

50

INVALID INPT

abfgnpqr

3

8

21

16

1

50

50

ISO

abcdeghjkmqr

5

12

23

17

20

40

30

SCALENE

abcdeghjlmqr

5

12

24

18

80

50

80

EQUI

abcdeghimqr

4

11

22

19

100

50

50

NT A TRI

abcdegnoqr

4

9

21

20

101

50

50

INVALID INPT

abcegnpqr

4

9

21

Measure 1. Scout Bee Performs Path Construction and creates PSB TABLE 8

Table 8: Way Constructed by lookout bee. ( Path of lookout bee tabular array ) .

SBi

PSBi

SB1

T1

T3

T19

T17

T18

T13

T14

SB2

T2

T15

T4

T6

T7

T9

T13

T18

T16

SB3

T3

T1

T13

T9

T20

T19

T18

T12

SB4

T4

T13

T17

T20

T19

T18

T2

T15

T8

SB5

T5

T6

T7

T8

T10

T12

T18

T20

13

T16

SB6

T6

T19

T1

T8

T15

T2

T3

T5

T10

T12

SB7

T7

T1

T8

T16

T20

T18

T13

T9

T2

SB8

T8

T2

T4

T6

T7

T9

T13

SB9

T9

T17

T1

T8

T15

T10

T11

T12

T16

T19

SB10

T10

T20

T1

T5

T15

T13

T16

T17

T18

T2

SB11

T11

T1

T2

T3

T6

T8

T9

T10

T7

T13

SB12

T12

T1

T12

T4

T19

T7

T17

T18

T13

SB13

T13

T9

T7

T6

T18

T5

T8

SB14

T14

T1

T2

T8

T6

T8

T9

T10

T7

T13

SB15

T15

T20

T13

T3

T5

T7

T11

T17

T18

T9

SB16

T16

T15

T14

T19

T18

T13

T17

T20

SB17

T17

T6

T13

T18

T20

T2

T1

SB18

T18

T1

T2

T3

T4

T18

T6

T19

T13

T17

SB19

T19

T16

T9

T1

T18

T13

T20

SB20

T20

T2

T3

T5

T13

T19

T18

T16

T1

T3

Measure 2. Forger Bee Performs Path Restructuring and creates PFB TABLE 9

Table 9: Way restructured by Forager bee. ( Path of forager bee tabular array ) .

Federal bureau of investigation

PFBi

FB1

T3

T17

T18

T19

T14

T1

T13

FB2

T2

T9

T4

T6

T7

T15

T13

FB3

T3

T9

T20

T19

T18

T1

T13

FB4

T2

T17

T18

T19

T20

T15

T13

FB5

FB6

FB7

FB8

T2

T9

T4

T6

T7

T8

T13

FB9

FB10

FB11

FB12

FB13

T9

T5

T18

T6

T7

T13

T8

FB14

FB15

FB16

FB17

T17

T2

T18

T20

T6

T13

T1

FB18

FB19

T9

T16

T19

T18

T20

T1

T13

FB20

Measure 3. Forger Bee Performs Final Path choice

Hence following are the concluding prioritization

FB1 T3 T17 T18 T19 T14 T1 T13

FB2 T2 T9 T4 T6 T7 T15 T13

FB3 T3 T9 T20 T19 T18 T1 T13

FB4 T2 T17 T18 T19 T20 T15 T13

FB8 T2 T9 T4 T6 T7 T8 T13

FB13 T9 T5 T18 T6 T7 T13 T8

FB17 T17 T2 T18 T20 T6 T13 T1

FB19 T9 T16 T19 T18 T20 T1 T13

We are acquiring so many waies because there is no ET in this illustration. Otherwise the way with mini ET could hold been chosen.

6. COMPARISION

The illustrations mentioned in subdivisions 5.1 and 5.2 are compared with regard to the following ordination: No order, Reverse order, Random order, Optimal order of the trial instances. The ordinations with regard to these attacks for illustration 1 and 2 are listed in Table 10 and 11 severally. These attacks are compared by ciphering Average Percentage of Faults Detected ( APFD ) [ 4 ] which is given by APFD =

Where, T – The trial suite under rating

m – The figure of mistakes contained in the plan under trial Phosphorus

n – The entire figure of trial instances and

TFi – The place of the first trial in T that exposes mistake I.

The consequences are shown in fig. 2 to fig. 11. It shows that the APFD values for the prioritization achieved utilizing BCO are comparable to that obtained with the optimal ordination.

Table 10. Order of trial instances for assorted prioritization attacks for illustration 1.

No Order

Rearward Order

Random Order

Optimum Order

BCO

Order

T1

T9

T3

T8

T1

T2

T8

T7

T6

T8

T3

T7

T1

T5

T6

T4

T6

T5

T4

T3

T5

T5

T4

T1

T5

T6

T4

T2

T7

T2

T7

T3

T6

T3

T4

T8

T2

T9

T2

T9

T9

T1

T8

T9

T7

Fig. 2 APFD chart for original ordination of trial instances of illustration 1. Fig. 3.APFD chart for random ordination of trial instances of illustration 1.

Fig. 4.APFD for contrary ordination of trial instances of illustration 1. Fig. 5.APFD chart for optimum ordination of trial instances of illustration 1.

Fig. 6.APFD chart for telling utilizing BCO Prioritization order of trial instances of illustration 1.

Table 11.Order of trial instances for assorted prioritization attacks for illustration 2.

No Order

Random Order

Rearward Order

Optimum Order

BCO

Order

T1

T2

T5

T5

T3

T2

T1

T4

T3

T5

T3

T5

T3

T4

T2

T4

T3

T2

T1

T1

T5

T4

T1

T2

T4

Fig. 7 APFD chart for original ordination of trial instances of illustration 2 Fig. 8 APFD chart for random order of illustration 2

Fig. 9 APFD chart for optimum order of illustration 2 Fig. 10 APFD chart for contrary of illustration 2

Fig. 11 APFD chart for BCO of illustration 2

7. Menace TO VALIDITY

The unreal BCO algorithm which has been presented here has certain short approachs which are as follows:

In the natural BCO the figure of lookout bees is 5-10 % of forager bees which are assumed to be equal in the algorithm proposed here.

The construct of shake dance was non required so has non been incorporated in the algorithm which is used s a agency of communicating in the natural BCO.

The energy decrease rate has been chosen such that merely 50 % of the trial suite gets executed which leaves the staying trial suite unexplored. Since it executes upto 50 % of the trial suite, manual executing of little trial suites is possible. As the size of trial suite increases the manual executing of the trial suite becomes hard and cumbersome.

8. Decision and FUTURE WORK

An unreal bee settlement optimisation algorithm for the arrested development trial suite prioritization has been developed. This algorithm makes effectual use the way building ( geographic expedition ) and way structuring ( development ) phenomenon of lookout bees and forager bees for the prioritization of the trial suite of the modified codification. The effectivity of this algorithm has good been demonstrated utilizing APFD values which are comparable to the optimum ordination values.

First, all the defects mentioned above will be overcome. Due to the manual executing of the algorithm, it has been applied to prove suites with less figure of trial instances. But it has besides been observed that this algorithm ‘s consequences are comparable to optimum telling consequences. So to use it in existent situation/ larger plans, there is a demand to automatize this algorithm. Therefore an mechanization tool for the complete use of the algorithm is being developed.

9. REFRENCES

[ 1 ] Hussein Owaied, Saif Saab: Modeling Artificial Bees Colony System.IC-AI: pp.443-446 ( 2008 ) .

[ 2 ] Dorigo, M. ; Maniezzo, V. ; Colorni, A. ( 1991 ) : The Ant System: An Autocatalytic Optimizing Process, Technical Report TR91-016, Politecnico di Milano.

[ 3 ] Aggarwal, K.K. ; Singh, Y. : A book on package technology.

[ 4 ] Kristen R.Walcott, Gregory M.Kapfhammer, Mary Lou Soffa, Robert S. Roos ” Time-aware trial suite prioritization ” .

[ 29 ] Rahmatizadeh, Sh. , H. Shah-Hosseini and H. Torkaman, 2009. The ant-bee routing algorithm: A new agent based nature-inspired routing algorithm. J. Applied Sci,983- 987.

[ 20 ] li-pei wong, Malcolm yoke hean low, chin shortly chong, ” A bee settlement optimisation algorithm for going salesman job ” , Second Asia International Conference on Modelling & A ; Simulation.

[ 22 ] Chin Soon Chong, Appa Iyer Sivakumar, Malcolm Yoke Hean Low, Kheng Leng Gay, “ A bee settlement optimisation algorithm to occupation store scheduling ” , Winter Simulation Conference.

[ 18 ] Saif Mahmood Saab, Dr. Nidhal Kamel Taha El-Omari, Dr. Hussein H. Owaied, ” Developing Optimization Algorithm Using Artificial Bee Colony System. ”

[ 23 ] James D. McCaffrey, ” Generation of pairwise trial sets utilizing a fake bee settlement algorithm ” 10th IEEE international conference, 2009.

[ 27 ] Jaysonne A. Pacurib, Glaiza Mae M. Seno, John Paul T. Yusiong, “ Solving Sudoku Puzzles Using Improved Artificial Bee Colony Algorithm, ” Innovative Computing, “ Information and Control, International Conference on, pp. 885-888, 2009 Fourth International Conference on Innovative Computing, Information and Control, 2009.

[ 19 ] Dervis Karaboga, Bahriye Basturk, ” A powerful and efficient algorithm for numerica map optimisation: unreal bee settlement ( ABC ) algorithm ” , J Glob Optim ( 2007 )