This is about Comparative Analysis of Artificial Bee Colony and Improve Cuckoo Search algorithm, a thesis work done by us. Finally it is published on February-10-2015 on IJARAI. Here you will find the basic of ABC algorithm, ICS algorithm and the comparison between them.

2. 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

3. 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.

4. 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.

5. 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.

6. 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.

7. Cuckoo Search

8. 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.

9. 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

10. 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.

11. 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

12. Artificial Bee Colony

13. 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

14. 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.

15. Equations Used In ABC
1. xij = xminj + rand[0, 1](xmaxj − xminj )
2. vij = xij + φij (xij − xkj )

16. 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

17. Comparison Analysis

18. Comparison Analysis
Function Dim ABC ICS
F1
5 + -
10 - +
15 + -
25 - +
F2
5 = =
10 + -
15 = =
25 + -
F3
5 + -
10 - +
15 - +
25 - +

19. Comparison Analysis
Function Dim ABC ICS
F4
5 - +
10 - +
15 - +
25 - +
F5
5 - +
10 - +
15 - +
25 - +
F6
5 - +
10 + -
15 + -
25 + -
Total 8 14

20. 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.

21. Graph Analysis

22. Graph Analysis
Fig: 3D surface plots (2 view) of Rosenbrock function that best for ICS.
Rosenbrock Function that gives the best result for ICS

23. Fig: 3D surface plots (2 view) of Ackley function that best for ICS.
Graph Analysis
Ackley Function that gives the best result for ICS

24. Fig: 3D surface plots (2 view)of Rastrigin function that best for ICS.
Graph Analysis
Rastrigin Function that gives the best result for ICS

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

26. 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

27. Fig: 2D plot of ICS vs ABC algorithm.
Graph Analysis
Comparison Graph for ABC Vs ICS

28. Fig: 3D plot of Rosenbrock Function Of ICS algorithm.
Graph Analysis
Comparison Graph For ICS Between Rosenbrock Function

29. 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

30. 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.

31. 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

32. 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.

33. References

34. 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.

35. 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 putation
and 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.

36. References
[11] D. Karaboga, "An Idea Based on Honey Bee Swarm for Numerical Optimization.Technical
Report-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.

37. 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.

38. 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.

39. 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.