The document presents an overview of swarm intelligence algorithms, with a focus on the bees algorithm and ant colony optimization. It explains how these algorithms mimic natural behaviors to find optimal solutions and provides detailed examples of each method. The potential applications and advantages of these algorithms are also discussed.

1. Swarm Intelligence
Algorithms
Dr. Hossam Mahmoud Moftah
Beni Suef University,
Dept. of Multimedia, Faculty of Computers and information
‫بنى‬ ‫حاسبات‬ ‫ثالثة‬ ‫لسنة‬ ‫متخصصة‬ ‫محاضرات‬
‫سوزيف‬

2. 2
Agenda
• Introduction
• Bees Algorithms
• Ant colony optimization

3. 3
Introduction
• Swarm intelligence (SI) is the collective behavior
of decentralized, self-organized systems, natural
or artificial.

4. 4
Swarm Intelligence (SI)
An artificial intelligence (AI) technique
based on the collective behavior in
decentralized, self-organized systems
Generally made up of agents who
interact with each other and the
environment
No centralized control structures
Based on group behavior found in
nature

5. 5
Swarm-based Optimisation Algorithms
SOAs include:
The Ant Colony Optimisation (ACO)
algorithm
The Genetic Algorithm (GA)
The Particle Swarm Optimisation (PSO)
algorithm (for example the flocking of birds
and the schooling of fish)
Others……(Bees (BA), BAT, Firefly
Algorithms)

6. 6
Examples of Swarms in Nature:
Classic Example: Swarm of Bees
Can be extended to other similar systems:
Ant colony
Agents: ants
Traffic
Agents: cars
Crowd
Agents: humans
Flock of birds
Agents: birds
Immune system
Agents: cells
and molecules

7. 7
Bees algorithm
• the Bees Algorithm is a
population-based search
algorithm which was
developed in 2005. It
mimics the food
foraging behaviour of
honey bee colonies.
• The only condition for
the application of the
Bees Algorithm is that
some measure of
topological distance
between the solutions is
defined.

8. 8
Bees in Nature
1- A colony of honey bees can extend itself over
long distances in multiple directions (more than 10
km)

9. 9
Bees in Nature
2- Scout bees search randomly from one patch to
another

10. 10
Bees in Nature
3- The bees who return to the hive, evaluate the
different patches depending on certain quality
threshold (measured as a combination of some
elements, such as sugar content)

11. 11
Bees in Nature
4- They deposit their nectar or pollen go to the
“dance floor” to perform a “waggle dance”

12. 12
Bees in Nature
5- Bees communicate through this waggle dance
which contains the following information:
1. The direction of flower patches (angle
between the sun and the patch)
2. The distance from the hive (duration of
the dance)
3. The quality rating (fitness) (frequency of
the dance)

13. 13
Bees in Nature
These information helps the colony to send its bees
precisely
6- Follower bees go after the dancer bee to the patch
to gather food efficiently and quickly

14. 14
Bees in Nature
7- The same patch will be advertised in the
waggle dance again when returning to the hive is
it still good enough as a food source (depending
on the food level) and more bees will be recruited
to that source
8- More bees visit flower patches with plentiful
amounts of nectar or pollen

15. 15
Bees algorithm

16. 16
Bees algorithm

17. 17
Bees algorithm

18. 18
Example
• n = 100 number of scout bees
• m = 10 number of sites selected out of n visited sites
• e = 2 number of best sites out of m selected sites
• nep = 40 number of bees recruited for best e sites
• nsp = 20 number of bees recruited for other (m-e)
selected sites
• ngh = 3 neighbourhood size

19. 19
Simple Example: Function Optimisation
• Here are a simple example about how Bees
algorithm works
• The example explains the use of bees algorithm to
get the best value representing a mathematical
function (functional optimal)

20. 20
Simple Example
• The following figure shows the mathematical
function

21. 21
• 1- The first step is to initiate the population with
any 10 scout bees with random search and evaluate
the fitness. (n=10)
Simple Example

22. 22
Graph 1. Initialise a Population of (n=10) Scout Bees
with random Search and evaluate the fitness.
x
y
*
*
*
*
*
*
*
*
*
*
Simple Example

23. 23
• 2- Population evaluation fitness:
• an array of 10 values in constructed and ordered in
ascending way from the highest value of y to the
lowest value of y depending on the previous
mathematical function
Simple Example

24. 24
• 3- The best m site is chosen randomly ( the best
evaluation to m scout bee) from n
• m=5, e=2, m-e=3
Simple Example

25. 25
Graph 2. Select best (m=5) Sites for Neighbourhood Search:
(e=2) elite bees “▪” and (m-e=3) other selected bees“▫”
x
y
▪
▫
▪
▫
▫
*
*
**
*
me
Simple Example

26. 26
• 4- Select a neighborhood search site upon ngh size:
• Assign random neighborhood ngh as follow
Simple Example

27. 27
x
y
▪
▫
▪
▫
▫
Graph 3. Determine the Size of Neighbourhood (Patch Size ngh)
Simple Example

28. 28
• 5- recruits more bees to the selected sites and
evaluate the fitness to the sites:
• Sending bees to e sites (rich sites) and m-e sites
(poor sites).
• More bees will be sent to the e site.
• n2 = 4 (rich)
• n1 = 2 (poor)
Simple Example

29. 29
x
y
▪
▫
▪
▫
▫
*
* *
*
Graph 4. Recruit Bees for Selected Sites
(more Bees for the e=2 Elite Sites)
*
*
*
*
*
*
*
*
*
*
* *
* *
* *
Simple Example

30. 30
• 6- Select the best bee from each location (higher
fitness) to form the new bees population.
• Choosing the best bee from every m site as follow:
Simple Example

31. 31
x
y
▪
▫
▪
▫
▫
*
* *
*
Graph 5. Select the Fittest Bee * from Each Site
*
*
*
*
*
*
*
*
*
*
Simple Example

32. 32
• 7- initializes a new population:
• Taking the old values (5) and assigning random
values (5) to the remaining values n-m
Simple Example

33. 33
x
y
*
Graph 6. Assign the (n–m) Remaining Bees to Random Search
*
*
*
o
*
o
o
o
o
m
e
Simple Example

34. 34
• 8- the loop counter will be reduced and the steps
from two to seven will be repeated until reaching
the stopping condition (ending the number of
repetitions imax)
• At the end we reach the best solution as shown in
the following figure
• This best value (best bees from m) will represent
the optimum answer to the mathematical function
Simple Example

35. 35 35
x
y
*
Graph 7. Find The Global Best point
*
*
*
*
Simple Example

36. 36
• 8- the loop counter will be reduced and the steps
from two to seven will be repeated until reaching
the stopping condition (ending the number of
repetitions imax)
• At the end we reach the best solution as shown in
the following figure
• This best value (best bees from m) will represent
the optimum answer to the mathematical function
Simple Example

37. 37
BA pros and cons
The advantages of the BA
Very efficient in finding optimal solutions
The disadvantages of the BA
It is using a number of tunable parameters

38. 38
Ant Colony Optimization
• Ant Colony Optimization is an
efficient method to finding
optimal solutions to a graph
• Using three algorithms based on
choosing a city, updating
pheromone trails and pheromone
trail decay, we can determine an
optimal solution to a graph
• Ant Colony Optimization has
been used to figure out solutions
to real world problems, such as
truck routing

39. 39
Ant Colony Optimization
• Cooperative search by pheromone trails
1
2
3
4
5
6

40. 40
A simple TSP example
A
E
D
C
B
1
[]
4
[]
3
[]
2
[]
5
[]
dAB =100;dBC = 60…;dDE =150

41. 41
Iteration 1
A
E
D
C
B
1
[A]
5
[E]
3
[C]
2
[B]
4
[D]

42. 42
How to choose next city?
A
E
D
C
B
1
[A]
1
[A]
1
[A]
1
[A]
1
[A,D]
otherwise0
allowedjif k






∈
∑=
∈ kallowedk
ikik
ijij
k
ij
][)]t([
][)]t([
)t(p
βα
βα
ητ
ητ

43. 43
Iteration 2
A
E
D
C
B
3
[C,B]
5
[E,A]
1
[A,D]
2
[B,C]
4
[D,E]

44. 44
Iteration 3
A
E
D
C
B
4
[D,E,A]
5
[E,A,B]
3
[C,B,E]
2
[B,C,D]
1
[A,D,C]

45. 45
Iteration 4
A
E
D
C
B
4
[D,E,A,B]
2
[B,C,D,A]
5
[E,A,B,C]
1
[A,DCE]
3
[C,B,E,D]

46. 46
Iteration 5
A
E
D
C
B
1
[A,D,C,E,B]
3
[C,B,E,D,A]
4
[D,E,A,B,C]
2
[B,C,D,A,E]
5
[E,A,B,C,D]

47. 47
Path and Trace Update
1
[A,D,C,E,B]
5
[E,A,B,C,D]
L1 =300





∈
=∆
otherwise0
bestTour),(
,
jiif
L
Q
k
k
jiτ
L2 =450
L3 =260
L4 =280
L5 =420
2
[B,C,D,A,E]
3
[C,B,E,D,A]
4
[D,E,A,B,C]

48. 48
Path and Trace Update
ijijij tt τρττ ∆+=+ )()1(





∈
=∆
otherwise0
bestTour),(
,
jiif
L
Q
k
k
jiτ
otherwise0
allowedjif k






∈
∑=
∈ kallowedk
ikik
ijij
k
ij
][)]t([
][)]t([
)t(p
βα
βα
ητ
ητ

49. 49
Conclusions
Thanks