Transcript A ladybird on a branch

Firefly
Algorithm
By
Rasool Tavakoli
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Outline
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Abstract
Introduction
Particle Swarm Optimization
Firefly Algorithm
Comparison of FA with PSO and GA
Conclusions
References
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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.
• Finally we will compare the proposed firefly
algorithm with other metaheuristic algorithms
such as particle swarm optimization by the
implementation results.
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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
– was developed by Xin-She Yang at Cambridge University in 2007
– particle swarm optimization is just a special class of the
firefly algorithms
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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
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PSO
𝑥𝑖∗
Denotes the best xi in the history
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PSO
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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
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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.
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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
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Firefly Algorithm
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Attractiveness
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Attractiveness
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Distance and Movement
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Scaling and Asymptotic Cases
• It is worth pointing out that the distance r
defined in previous slide is not limited to the
Euclidean distance.
• There are two important limiting cases when
–
–
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Validation
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Validation
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Validation
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Comparison of FA
with PSO and GA
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Conclusions
• New firefly algorithm have some similarities and
differences with particle swarm optimization
• Flying to other fireflies replaced with crossoover.
• 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
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References
[1] Kennedy, J. and Eberhart, R. C. (1995) ‘Particle swarm optimization’, Proc. of
IEEE International Conference on Neural Networks, Piscataway, NJ. pp. 19421948.
[2] Yang X. S.: Firefly algorithms for multimodal optimization. in: Stochastic
Algorithms: Foundations and Applications (Eds. O. Watanabe and T. Zeugmann),
Springer, SAGA 2009, Lecture Notes in Computer Science, 5792, 169-178 (2009).
[3] Yang, X. S., (2010) ‘Firefly Algorithm, Stochastic Test Functions and Design
Optimization’, Int. J. Bio-Inspired Computation, Vol. 2, No. 2, pp.78–84.
[4] X.-S. Yang, “Firefly algorithm, L´evy flights and global optimization”, in: Research
and Development in Intelligent Systems XXVI (Eds M. Bramer, R. Ellis, M.
Petridis), Springer London, pp. 209-218 (2010).
[5] Yang, X. S. Nature-Inspired Metaheuristic Algorithms, Luniver Press, UK, 2008.
[6] Engineering Optimization -An Introduction with Metaheuristic Applications, Wiley,
UK, 2010.
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