1 Firefly Algorithm by Mr Zamani & Hosseini. 2 Isfahan University of Technology. Fall 2010.

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Firefly Algorithm

by Mr Zamani

&Hosseini

2

Isfahan University of Technology. Fall 2010

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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

• 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 researchIsfahan University of Technology. Fall 2010

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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– 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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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. Fall 2010Isfahan 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 above 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

• 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


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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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Levy Flights (Cont.)

•


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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 flightIsfahan University of Technology. Fall 2010

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Levy-Flight Firefly Algorithm (LFA)

•


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LFA Tests

• Initial locations of 40 fireflies (left) and their locations after 5 iterations (right) on 2D Ackley function.


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LFA vs. PSO


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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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ES

• 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.


30Isfahan University of Technology. Fall 2010

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ES vs. PSO


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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


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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


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Dynamic Decision Range(Cont.)

• Neighborhood is bounded by a radial sensor range.


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Dynamic Decision Range(Cont.)

•


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GSO vs. PSO


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GSO vs. PSO (Cont.)


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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.


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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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Discretization of FA

•


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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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References


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References


1 Firefly Algorithm by Mr Zamani & Hosseini. 2 Isfahan University of Technology. Fall 2010.

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