1. Firefly
Algorithm
by Mr
Zamani
&
Hosseini

2. Isfahan University of Technology. Fall 2010

3. Isfahan University of Technology. Fall 2010
Outline
Abstract
Introduction
Particle Swarm Optimization
Firefly Algorithm
Comparison of FA with PSO and GA
Conclusions
References
Isfahan University of Technology. Fall 2010

4. Isfahan University of Technology. Fall 2010
Abstract
Nature-inspired algorithms are among the most powerful algorithms for optimization
We will try to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications
We will compare the proposed firefly algorithm with other metaheuristic algorithms such as particle swarm optimization
Finally we will discuss its applications
and implications for further research
Isfahan University of Technology. Fall 2010

5. Isfahan University of Technology. Fall 2010
Introduction
PSO
Particle swarm optimization (PSO) was developed by Kennedy and Eberhart in 1995
based on the swarm behavior such as fish and bird schooling in nature, the so-called swarm intelligence
Though particle swarm optimization has many similarities with genetic algorithms, but it is much simpler because it does not use mutation/crossover operators
Instead, it uses the real-number randomness and the global communication among the swarming particles. In this sense, it is also easier to implement as it uses mainly real numbers FA
particle swarm optimization is just a special class of the
firefly algorithms
Isfahan University of Technology. Fall 2010

6. Particle Swarm Optimization(PSO)
The PSO algorithm searches the space of the objective functions by adjusting the trajectories of individual agents, called particles, as the piecewise paths formed by positional vectors in a quasi-stochastic manner
The particle movement has two major components
stochastic component
deterministic component
Isfahan University of Technology. Fall 2010

7. Isfahan University of Technology. Fall 2010
PSO
Isfahan University of Technology. Fall 2010

8. Isfahan University of Technology. Fall 2010
PSO
Isfahan University of Technology. Fall 2010

9. Behavior of Fireflies
The flashing light of fireflies is an amazing sight in the summer sky in the tropical and temperate regions
There are about two thousand firefly species, and most fireflies produce short and rhythmic flashes
The pattern of flashes is often unique
for a particular species
Isfahan University of Technology. Fall 2010
Isfahan University of Technology. Fall 2010

10. Isfahan University of Technology. Fall 2010
Behavior of Fireflies
Two fundamental functions of such flashes are
to attract mating partners (communication)
to attract potential prey
Females respond to a male’s unique pattern of flashing in the same species
We know that the light intensity at a particular distance ‘r’ from the light source obeys the inverse square law
The air absorbs light which becomes weaker and weaker as the distance increases
The flashing light can be formulated in such
a way that it is associated with the
objective function
Isfahan University of Technology. Fall 2010

11. Isfahan University of Technology. Fall 2010
Firefly Algorithm
For simplicity in describing our new FA we now use the following three idealized rules:
all fireflies are unisex so that one firefly will be attracted to other fireflies regardless of their sex
Attractiveness is proportional to their brightness, thus 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 affected or determined by the landscape of the objective function. For a maximization problem, the brightness can simply
be proportional to the value of the
objective function
Isfahan University of Technology. Fall 2010

12. Isfahan University of Technology. Fall 2010
Firefly Algorithm
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13. Isfahan University of Technology. Fall 2010
Attractiveness
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14. Isfahan University of Technology. Fall 2010
Attractiveness
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15. Isfahan University of Technology. Fall 2010
Distance and Movement
Isfahan University of Technology. Fall 2010

16. Scaling and Asymptotic Cases
It is worth pointing out that the distance r defined above is not limited to the Euclidean distance
There are two important limiting cases when
Isfahan University of Technology. Fall 2010

17. Isfahan University of Technology. Fall 2010
Validation
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18. Isfahan University of Technology. Fall 2010
Validation
Isfahan University of Technology. Fall 2010

19. Isfahan University of Technology. Fall 2010
Validation
Isfahan University of Technology. Fall 2010

20. Comparison of FA with PSO and GA
Isfahan University of Technology. Fall 2010

21. Isfahan University of Technology. Fall 2010
Conclusions
we have formulated a new firefly algorithm and analyzed its similarities and differences with particle swarm optimization
We then implemented and compared these algorithms
Our simulation results for finding the global optima of various test functions suggest that particle swarm often outperforms traditional algorithms such as genetic algorithms, while the new
firefly algorithm is superior to both PSO and
GA in terms of both efficiency and
success rate
Isfahan University of Technology. Fall 2010

22. Isfahan University of Technology. Fall 2010
Levy Flights
Flight behavior of many animals and insects
Fruit flies explore their landscape using a series of straight flight paths punctuated by a sudden 90 degree turn.
Applied to optimization and optimal search
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23. Isfahan University of Technology. Fall 2010
Levy Flights (Cont.)
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24. Isfahan University of Technology. Fall 2010
Levy Flights Example
Left: example of 1000 steps of levy flight
Right: example of 1000 steps of an approximation to a Brownian motion type of Levy flight
Isfahan University of Technology. Fall 2010

25. Levy-Flight Firefly Algorithm (LFA)
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26. Isfahan University of Technology. Fall 2010
LFA Tests
Initial locations of 40 fireflies (left) and their locations after 5 iterations (right) on 2D Ackley function.
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27. Isfahan University of Technology. Fall 2010
LFA vs. PSO
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28. Isfahan University of Technology. Fall 2010
Eagle Strategy (ES)
Based on the foraging behavior of eagles such as golden eagles.
An eagle forages in its own territory by flying freely in a random manner much like the Levy flights.
Once the prey is sighted, the eagle will change its search strategy to an intensive chasing tactics so as to catch the prey as efficiently as possible.
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29. Isfahan University of Technology. Fall 2010ES
Perform Levy walks in whole domain.
If find a prey change to a chase strategy.
Chase strategy can be considered as an intensive local search.
We can use any optimization technique.
We can use FA.
Isfahan University of Technology. Fall 2010

30. Isfahan University of Technology. Fall 2010

31. Isfahan University of Technology. Fall 2010
ES vs. PSO
Isfahan University of Technology. Fall 2010

32. Glowworm Swarm Optimization (GSO)
Glowworm == immature firefly
Similar to FA but with little differences.
introduced by K.N. Krishnanand and D. Ghose in 2005.
Multimodal optimization
Isfahan University of Technology. Fall 2010

33. Dynamic Decision Range
Effect of distant glowworms are discounted when a glowworm has sufficient number of neighbors or the range goes beyond the range of perception of the glowworms.
Every glowworm has a neighborhood range
Agents depend only on information available in their neighborhood
Isfahan University of Technology. Fall 2010

34. Dynamic Decision Range(Cont.)
Neighborhood is bounded by a radial sensor range.
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35. Dynamic Decision Range(Cont.)
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GSO vs. PSO
Isfahan University of Technology. Fall 2010

39. Isfahan University of Technology. Fall 2010
GSO vs. PSO (Cont.)
Isfahan University of Technology. Fall 2010

40. flow shop scheduling problem (FSSP)
a complex combinatorial optimization problem
set of n jobs (1, …, n)
set of m machines (1, …, m)
Set of n jobs to be processed in a set of m machines in the same order
minimization of makespan, mean flow, etc.
Isfahan University of Technology. Fall 2010

41. Isfahan University of Technology. Fall 2010
FSSP Cont.
NP-Complete
(n!)m schedules need to be considered
Many attempts to solve this problem using different methods including EAs.
FA can be used
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42. Isfahan University of Technology. Fall 2010
Discretization of FA
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43. Discrete Firefly Algorithm (DFA)
Use the sigmoid function to convert real values to binary values
Outperforms an ACO implementation named MHD-ACS.
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44. Isfahan University of Technology. Fall 2010
References
Isfahan University of Technology. Fall 2010

45. Isfahan University of Technology. Fall 2010
References
Isfahan University of Technology. Fall 2010

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