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Firefly Algorithm by Mr Zamani & Hosseini

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**Isfahan University of Technology. Fall 2010**

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**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

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**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

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**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

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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 Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

PSO Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

PSO Isfahan University of Technology. Fall 2010

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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 2010 Isfahan University of Technology. Fall 2010

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**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

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**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

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**Isfahan University of Technology. Fall 2010**

Firefly Algorithm Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Attractiveness Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Attractiveness Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Distance and Movement Isfahan University of Technology. Fall 2010

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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 Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Validation Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Validation Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Validation Isfahan University of Technology. Fall 2010

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**Comparison of FA with PSO and GA**

Isfahan University of Technology. Fall 2010

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**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

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**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 Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Levy Flights (Cont.) Isfahan University of Technology. Fall 2010

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**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

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**Levy-Flight Firefly Algorithm (LFA)**

Isfahan University of Technology. Fall 2010

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**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. Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

LFA vs. PSO Isfahan University of Technology. Fall 2010

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**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. Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

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. Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

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**Isfahan University of Technology. Fall 2010**

ES vs. PSO Isfahan University of Technology. Fall 2010

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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 Isfahan University of Technology. Fall 2010

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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 Isfahan University of Technology. Fall 2010

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**Dynamic Decision Range(Cont.)**

Neighborhood is bounded by a radial sensor range. Isfahan University of Technology. Fall 2010

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**Dynamic Decision Range(Cont.)**

Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

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**Isfahan University of Technology. Fall 2010**

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**Isfahan University of Technology. Fall 2010**

GSO vs. PSO Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

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

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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. Isfahan University of Technology. Fall 2010

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**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 Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

Discretization of FA Isfahan University of Technology. Fall 2010

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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. Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

References Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

References Isfahan University of Technology. Fall 2010

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**Isfahan University of Technology. Fall 2010**

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