1. Scientific Research Group in Egypt (SRGE)
Swarm Intelligence (6)
Firefly algorithm
Scientific Research Group in Egypt (SRGE)
Dr. Ahmed Fouad Ali
Suez Canal University,
Dept. of Computer Science, Faculty of Computers and informatics
Member of the Scientific Research Group in Egypt

2. Scientific Research Group in Egypt

3. Outline 1.Firefly algorithm (History and main idea)
2. Behavior of fireflies
3. Characteristics of firefly algorithm
4. The basic steps of the firefly Algorithm
5. Application of the firefly Algorithm
6. References

4. Firefly algorithm (History and main idea)
Firefly Algorithm (FA) was first developed by Xin-She Yang in late 2007, which was based on the flashing patterns and behavior of fireflies
Firefly algorithm is a metaheuristic population based method.

5. Behavior of fireflies
The sky filled with the light of fireflies is a marvelous sight in the summer in the moderately temperature regions.
There are near to two thousand firefly species, and most of them produce short and rhythmic flashes.
The pattern observed for these flashes is unique for most of the times for a specific species.
Females of a species respond to individual pattern of the male of the same species.

6. Characteristics of firefly algorithm
Fireflies are unisex so that one firefly will be attracted to other fireflies regardless of their sex.
The attractiveness is proportional to the brightness, and they both decrease as their distance increases.
For any two flashing fireflies, the less brighter one will move towards the brighter one.
If there is no brighter one than a particular firefly, it will move randomly.
The brightness of a firefly is determined by the landscape of the objective function.

7. The basic steps of the firefly Algorithm (attractiveness )
The light intensity I (r) varies following the inverse square law
Where I0 represents the light intensity at the source.
The combined effect the inverse square law and absorption can be approximated using the following Gaussian form:

8. The basic steps of the firefly Algorithm (attractiveness )
As a firefly’s attractiveness is proportional to the light intensity seen by adjacent fireflies, the attractiveness function of the firefly is established by:
Where β0 is the firefly attractiveness value at r = 0 and γ is the media light absorption coefficient.

9. The basic steps of the firefly Algorithm (movement )
Fireflies movement is based on the principles of attractiveness: when firefly j is more attractive than firefly i the movement is determined by the following equation:
where k =1,2,...,D (D is dimension of problem), α and Sk are the scaling parameters and randik rand is random number between 0 and 1.

10. The basic steps of the firefly Algorithm (distance )
Distance rij between fireflies i and j is obtained by Cartesian distance form by:

11. The basic steps of the firefly Algorithm (special case )
If β0 = 0, it becomes a simple random walk.
On the other hand, if γ = 0, it reduces to a variant of particle swarm optimization

12. The basic steps of the firefly Algorithm (algorithm)

13. Application of the firefly Algorithm
Digital Image Compression and Image Processing
Feature selection and fault detection
Antenna Design
Structural Design
Scheduling
Semantic Web Composition
Chemical Phase equilibrium
Clustering
Dynamic Problems
Rigid Image Registration Problems

14. References
X. S. Yang, “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, 2008.
Xin-She Yang, Firefly Algorithms for Multimodal Optimization, 2010
Xin-She Yang, Comparative Study of Firefly Algorithm and Particle Swarm Optimization for Noisy Non-Linear Optimization Problems, 2010, ISBN:

15. Thank you