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Firefly Algorithm

ByRasool Tavakoli

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Outline

• 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

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• 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

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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

Isfahan University of Technology. Dec 2011Isfahan University of Technology. Fall 2010

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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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PSO

𝛽 (𝑟 )❑→𝛿(𝑟 )

Random Search

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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

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[1] Kennedy, J. and Eberhart, R. C. (1995) ‘Particle swarm optimization’, Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ. pp. 1942-1948.

[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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