Shariba Islam Tusiy 11.01.04.137

Nasif Shawkat 11.01.04.041

Md. Arman Ahmed 11.01.04.031

Biswajit Panday 11.01.04.033

Abstract

The purpose of this thesis is to compare about two well-known Meta-

heuristics algorithm (ABC & ICS) which is related to nature.

Artificial Bee Colony (ABC) algorithm is based on swarm intelligence

that how they maintain their life in a colony.

Cuckoo Search is based on the manner of cuckoo species in

combination with the Levy flight behavior of some birds and fruit flies.

Introduction

Artificial bee colony (ABC) is optimization algorithm introduced by D.

Karaboga.

The algorithm describes the intelligent provision behavior of honey

bee swarms.

In ABC, honey bees are classified into three groups namely employed

bees, onlooker bees and scout bees.

It is found that the ABC algorithm prefers exploration at the cost of the

exploitation.

Introduction (Cont.)

Cuckoo search (CS) is an optimization algorithm developed by Xin-she-Yang and

Suash Deb in 2009-2010.

It was inspired by the obligate brood parasitism of some cuckoo species by

laying their eggs in the nests of other host birds.

Cuckoos have an aggressive reproduction strategy.

Cuckoo has an amazing timing of laying their eggs.

On Which we have Focused

In this great world we have a lot of topic to share & to

research with. Now a days the topics are going hard to

get a change to find new findings from the old ones. Still

we have tried our best to find some unknowns from the

known world. Our main topic where we focused on is

Meta-heuristics. Meta-heuristic algorithms, which are

inspired by nature coming out and they become

progressively comprehensive.

Cuckoo Search

Behavior Of Cuckoos

Cuckoo species ware chosen not only for their charming sounds they

can make, because for their invasive reproduction strategy.

Some female cuckoo like Guira and Ani can copy the patterns and colors

of a few chosen host species. .

there must be a timing factor of lay their eggs .

Parasitic cuckoos used to choose a nest where the host birds just lay its own

eggs.

Improved Cuckoo Search

The key difference between the ICS and CS is in the way of adjusting pa and

α.

To improve the performance of the CS algorithm and eliminate the drawbacks

lies with fixed values of pa and α, the ICS algorithm uses variables pa and α.

The values of pa and are dynamically changed with the number of

generation

Levy Flights

In nature, animals search for food in a random or quasi random manner.

the foraging path of an animal is effectively a random walk because the next

move is based on both the current location/state.

The chosen direction implicitly depends on a probability, which can be

modeled mathematically.

A Lévy flight is a random walk in which the step-lengths are distributed

according to a heavy-tailed probability distribution.

Pseudo Code

Begin

Objective function f(x), x = (x1, ..., xd)T ;

Initial a population of n host nests xi (i = 1, 2, ..., n);

while (t <MaxGeneration) or (stop criterion)

Get a cuckoo (say i) randomly by Lévyflights;

Evaluate its quality/fitness Fi;

Choose a nest among n (say j) randomly;

if (Fi > Fj)

Replace j by the new solution;

end

A fraction (pa) of worse nests are abandon and

new once are built.

Keep the best solutions (or nests with quality solutions);

Rank the solutions and find the current best;

end while

Post-process results and visualization;

End

Artificial Bee Colony

Nature/Behavior Of Bees

In ABC, honey bees are classified into three groups namely employed

bees, onlooker bees and scout bees.

The employed bees are the bee which searches the food source and

gather the information about the quality of the food source.

Onlooker bees stay in the hive and search the food sources on the basis of

the information gathered by the employed bees.

The scout bee, searches new food sources randomly in places of the

abandoned foods sources

Pseudo Code - 1

Initialize the parameters;

while Termination criteria is not satisfied do

Step 1: Employed bee phase for generating new food sources

Step 2: Onlooker bees phase for updating the food sources

depending on their nectar amounts;

Step 3: Scout bee phase for discovering the new food sources

in place of abandoned food sources;

step 4: Memorize the best food source found so far;

End while

Output the best solution found so far.

Equations Used In ABC

1. xij = xminj + rand[0, 1](xmaxj − xminj )

2. vij = xij + φij (xij − xkj )

Pseudo Code – 2

Input: solution x i , probi and j ∈ (1, D);

for j ∈ { 1 to D } do

if U (0, 1) > probi then

v i j = x i j + φ i j (x i j – x k j ) + ψ i j ( x best j – x i j ) ;

else

v i j = x i j ;

end if

end for

Comparison Analysis

Comparison Analysis

Function Dim ABC ICS

F1

5 + -

10 - +

15 + -

25 - +

F2

5 = =

10 + -

15 = =

25 + -

F3

5 + -

10 - +

15 - +

25 - +

Comparison Analysis

Function Dim ABC ICS

F4

5 - +

10 - +

15 - +

25 - +

F5

5 - +

10 - +

15 - +

25 - +

F6

5 - +

10 + -

15 + -

25 + -

Total 8 14

Comparison Summery

we calculate our result we find that the ABC gives good

result for lower dimension. when the dimension

increases it gives poor result then ICS. That means ICS

gives the better result in high Dimension.

Graph Analysis

Graph Analysis

Fig: 3D surface plots (2 view) of Rosenbrock function that best for ICS.

Rosenbrock Function that gives the best result for ICS

Fig: 3D surface plots (2 view) of Ackley function that best for ICS.

Graph Analysis Ackley Function that gives the best result for ICS

Fig: 3D surface plots (2 view)of Rastrigin function that best for ICS.

Graph Analysis Rastrigin Function that gives the best result for ICS

Graph Analysis

Fig: 3D surface plot of Schwefel function that best for ABC.

Fig: 3D surface plots (2 view)of Griewank function that 2nd best for ABC.

Graph Analysis Griewank Function that gives the best result for ABC

Fig: 2D plot of ICS vs ABC algorithm.

Graph Analysis Comparison Graph for ABC Vs ICS

Fig: 3D plot of Rosenbrock Function Of ICS algorithm.

Graph Analysis Comparison Graph For ICS Between Rosenbrock Function

Findings

In ABC algorithm we find the fitness and globalmins to compare with ICS

algorithm.

We try to make balance of the degrees of exploration and

exploitation for both of the algorithms.

We mainly find the differences between these two algorithm and we did

it basis on the mean value and on the basis of time.

we calculate our result we find that the ABC gives good result for lower

dimension. when the dimension increases it gives poor result then ICS.

That means ICS gives the better result in high Dimension.

After calculating various aspects,we can also say that ICS is better

than ABC

Future Plan

Till now we have worked on the difference between ABC

and ICS. And between this ICS gives the better result.

In future, we want to improve ICS and ABC more than now

and we will work hardly to fulfill these.

We will try to find more effective results with different

dimentions.

We will also focus on the algorithm to improve.

Future Plan

In ICS,we have already checked between Cuckoos minimum position

& Cuckoos New Position.

We have already changed the equation of minimum & new Positions

of CS(Cuckoo Search).

At the time of comparison we have found that gives better result

than ICS for same parameters.

And hope that we will succeed to fulfill these achievement

Conclusion

Here we have covered the comparative study between swarm

intelligence base and Levy flight behavior base algorithms

the Artificial Bee Colony (ABC) algorithm and the Improved

Cuckoo Search (ICS) algorithm. ABC uses swarm intelligence

to find the global optimum value of the continuous

optimization problems. And ICS uses Levy flight behavior to

find the global optimum value of the continuous optimization

problems.

References

References

[1] D. Karaboga, "An Idea Based On Honey Bee Swarm For Numerical Optimization," Technical

Report TR06,Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.

[2] X. S. Yang, "Nature-Inspired Metaheuristic Algorithms," LuniverPress,UK, 2008.

[3] M. Gendreau, "Handbook of Metaheuristics," in An introduction to tabu search, Kluwer

Academic Publishers,2003, p. 37–54.

[4] X. Yang and S. Deb, "Engineering Optimisation by Cuckoo Search," in Int. J. Mathematical

Modelling and Numerical Optimisation, 2010, p. 330–343.

[5] I. J. Fister, X. Yang, D. Fister and I. Fister, "Cuckoo search: A brief literature review,"

Cuckoo Search and Firefly Algorithm: Theory and Applications, Studies in Computational

Intelligence, vol. 516, pp. 49-62, 2014.

References

[6] X.-S. Yang, "Bat algorithm: literature review and applications," Int. J. Bio-Inspired

Computation, vol. 5, p. 141–149, 2013.

[7] I. J. Fister, D. Fister and X.-S. Yang, "A hybrid bat algorithm," in Elek-trotehniski vestnik, press, 2013.

[8] X.-S. Yang, "Flower pollination algorithm for global optimiza-tion," Unconventional putationand Natural Computation 2012,Lecture Notes in Computer Science, vol. 7445, pp. 240-249, 2012.

[9] X.-S. Yang and s. H. Xing, "Firefly Algorithm: Recent Advances and Applications," Int. J. S

[10] X.-S. Yang, "Firefly algorithms for multimodal optimization," Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, vol. 5792, pp. 169-178, 2009.warm Intelligence, vol. 1, p. 36–50, 2013.

References

[11] D. Karaboga, "An Idea Based on Honey Bee Swarm for Numerical Optimization.TechnicalReport-TR06," in Erciyes University, Computer Engineering Department, 2005.

[12] M. Kiran and A. Babalik, "Improved Artificial Bee Colony Algorithm for Continuous Optimization Problems," Journal of Computer and Communications, vol. 2, pp. 108-116, 2014.

[13] A. Farzindar and V. (. Keselj, Canadian AI 2010, LNAI 6085, 2010.

[14] H. P. Corporation, "Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem," International Journal of Combinatorics, 2011.

[15] M. S. Innocente and J. Sienz, "Particle Swarm Optimization with Inertia Weight and Constriction FactorCivil and Computational Engineering Centre," ASTUTE project, Digital Technium Building, College of Engineering, Swansea University, Singleton Park, SA2 8PP, United Kingdom.

References

[16] O. BUFFET, L. CUCU, L. IDOUMGHAR and R. SCHOTT, "Tabu Search Type Algorithms for the Multiprocessor Scheduling Problem".

[17] X.-S. Yang, From the book Nature-inspired Metaheuristic Algorithms.

[18] X.-S. Yang, Optimization Problem, Department of Engineering,University of Cambridge, Trumpinton Street, Cambridge CB2 1PZ, UK.

[19] M. Gendreau, "An introduction to tabu search," in Handbook of Metaheuristics, Kluwer Academic Publishers, 2003, p. 37–54.

[20] E. Valian, S. Mohanna and S. Tavakoli, "Improved Cuckoo Search Algorithm for Global Optimization," University of Sistan and Baluchestan, Dec. 2011.

References

[21] X.-S. Yang, Cuckoo Search via L´evy Flights, Department of Engineering,University of Cambridge, Trumpinton Street, Cambridge CB2 1PZ, UK.

[22] B. Kumar and D. Kumar, A review on Artificial Bee Colony algorithm, Dept. of Computer Science & Engineering, Guru Jambheswar University, Hisar, Haryana, India.

[23] D. Karaboga and C. Ozturk, "A novel clustering approach: Artificial Bee Colony (ABC) algorithm," Kayseri, Turkey, Erciyes University, Intelligent Systems Research Group, Department of Computer Engineering.

[24] G. YAN and Chuangqin, "Effective Refinement Artificial Bee Colony Optimization algorithm Based On Chaotic Search and Application for PID Control Tuning," Taiyuan, China, College of Information Engineering, Taiyuan University of Technology.

[25] IJCIT, International Journal of Communications and Information Technology, vol. 1, Dec. 2011.

References

[26] IJAIA, "International Journal of Artificial Intelligence & Applications," vol. 2, July 2011.

[27] IJAIS, International Journal of Applied Information Systems, vol. 7, no. ISSN: 2249-0868, September 2014.

[28] S. Rainer and P. Kenneth, "Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces," in Journal of Global Optimization, Kluwer Academic Publishers, 1997, pp. 341-357.

[29] R. Poli, J. Kennedy and T. Blackwell, "Particle Swarm Optimization," Springer Science, vol.

1, pp. 33-57, 1 August 2007.

[30] K. Abdullah, D. W. Coit and A. E. Smith, "Multi-objective optimisation using genetic

algorithms," A tutorial.Reliability Engineering and System Safety, no. 992–1007, 2006.