Cuckoo Search & Firefly Algorithms


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metaheuristic algorithms - Cuckoo Search & Firefly Algorithms
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Cuckoo Search & Firefly Algorithms

  1. 1. Cuckoo Search & Firefly Algorithms By: Mustafa Salam
  2. 2. Cuckoo Search Algorithm
  3. 3. Overview Cuckoo search (CS) is an optimization algorithm developed by Xin-she Yang and Suash Deb in 2009. Cuckoos have an aggressive reproduction strategy that involves the female laying her fertilized eggs in the nest of another species so that the surrogate parents unwittingly raise her brood. Sometimes the cuckoo's egg in the host nest is discovered (eggs are not its owns), the surrogate parents either throw it out or abandon the nest and builds their own brood elsewhere.
  4. 4. Cuckoo Behavior  Some cuckoo species have evolved in such a way that female parasitic cuckoos are often very specialized in the mimicry in color and pattern of the eggs of a few chosen host species. This reduces the probability of eggs being abandoned and increases their reproductively.
  5. 5. Cuckoo Behavior  Parasitic cuckoos often choose a nest where the host bird just laid its own eggs. In general, the cuckoo eggs hatch slightly earlier than their host eggs.
  6. 6. Cuckoo Behavior  Once the first cuckoo chick is hatched, the first instinct action it will take is to evict the host eggs by blindly propelling the eggs out of the nest, which increases the cuckoo chick’s share of food provided by its host bird.
  7. 7. Cuckoo Rules & Parameters 1) Each cuckoo lays one egg at a time, and dumps it in a randomly chosen nest. 2) The best nests with high quality of eggs (solutions) will carry over to the next generations. 3) The number of available host nests is fixed, and a host can discover an alien egg with a probability pa ∈ [0, 1]. In this case, the host bird can either throw the egg away or abandon the nest so as to build a completely new nest in a new location.
  8. 8. • As a further approximation, this last assumption can be approximated by a fraction pa of the n nests being replaced by new nests (with new random solutions at new locations). • For a maximization problem, the quality or fitness of a solution can simply be proportional to the objective function. Other forms of fitness can be defined in a similar way to the fitness function in genetic algorithms.
  9. 9. Lévy Flights A Lévy flight is a random walk in which the step-lengths are distributed according to a heavy-tailed probability distribution. After a large number of steps, the distance from the origin of the random walk tends to a stable distribution.
  10. 10. Lévy Flights When generating new solutions flight is performed x(t+1) for, say cuckoo i, a L´evy xi(t+1) = xi(t) + α ⊕ L´evy(λ) New Solution Current Location …….. (1) The transition probability Where α > 0 is the step size, which should be related to the scales of the problem of interest. In most cases, we can use α= 1
  11. 11. Lévy Flights L v flig tses n lly p v eara d mwlk w ileth ir ra d m ´e y h se tia ro id no a h e no s p a d w fro aL v d trib tio fo la es p te s re ra n m ´e y is u n r rg te s L´evy ∼ u = t−λ, (1 < λ ≤ 3) ……… (2) Which has an infinite variance with an infinite mean. Here the steps essentially form a random walk process with a power-law step-length distribution with a heavy tail. Some of the new solutions should be generated by L´evy walk around the best solution obtained so far, this will speed up the local search.
  12. 12. Lévy Flights However, a substantial fraction of the new solutions should be generated by far field randomization and whose locations should be far enough from the current best solution, this will make sure the system will not be trapped in a local optimum.
  13. 13. Pseudo code of Cuckoo Search algorithm Begin Objective function f(x), x = (x1, ..., xd)T ; Initial a population of n host nests xi (i = 1, 2, ..., n); while (t <MaxGeneration) or (stop criterion) Get a cuckoo (say i) randomly by Lévyflights; Evaluate its quality/fitness Fi; Choose a nest among n (say j) randomly; if (Fi > Fj) Replace j by the new solution; end Abandon a fraction (pa) of worse nests and build new ones at new locations via L´evy flights; Keep the best solutions (or nests with quality solutions); Rank the solutions and find the current best; end while Postprocess results and visualization; End
  14. 14. Cuckoo Applications a) Spring design and Welded beam design problems. b) Solve nurse scheduling problem. c) An efficient computation for data fusion in wireless sensor networks. d) A new quantum-inspired cuckoo search was developed to solve Knapsack problems. e) Efficiently generate independent test paths for structural software testing and test data generation. f) Applied to train neural networks with improved performance.
  15. 15. Firefly Algorithm
  16. 16. Firefly Algorithm The firefly algorithm (FA) is a metaheuristic algorithm, developed by Xin-She Yang in late 2007 and 2008 , which was based on the flashing patterns and behavior of fireflies.
  17. 17. Behavior of Fireflies 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. The flashing light is produced by a process of bioluminescence, and the true functions of such signaling systems are still debating.  However, two fundamental functions of such flashes are to attract mating partners (communication), and to attract potential prey.
  18. 18. Behavior of Fireflies  In addition, flashing may also serve as a protective warning mechanism.  The rhythmic flash, the rate of flashing and the amount of time form part of the signal system that brings both sexes together.  Females respond to a male’s unique pattern of flashing in the same species, while in some species such as photuris, female fireflies can mimic the mating flashing pattern of other species so as to lure and eat the male fireflies who may mistake the flashes as a potential suitable mate.
  19. 19. Firefly Rules & Parameters  Fireflies are unisex so that one firefly will be attracted to other fireflies regardless of their sex.  The attractiveness is proportional to the brightness, and they both decrease as their distance increases. 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 determined by the landscape of the objective function.
  20. 20. Firefly Rules & Parameters  The light intensity at a particular distance (r) from the light source obeys the inverse square law. That is to say , the light intensity (I) decreases as the distance (r) increases in terms of ( I ∝ 1/ r2 ).  Furthermore, the air absorbs light which becomes weaker and weaker as the distance increases.
  21. 21. The algorithm In the firefly algorithm, there are three important formulas in firefly algorithm, which are:  Attractiveness The form of attractiveness function of a firefly is the following monotonically decreasing function. r Where e rm m 1 r is the distance between any two fireflies, is a fixed light absorption coefficient. ………… (1) is the attractiveness at r = 0 and
  22. 22. The algorithm  Distance The distance between any two fireflies i and j at Xi and Xj, respectively, is the Cartesian distance as follows: Where xi,k is the (k)th component of the spatial coordinate Xi of (i)th firefly and d is the number of dimensions.
  23. 23. The algorithm  Movement The movement of a firefly i is attracted to another more attractive (brighter) firefly j is determined by following equation: Where the second term is due to the attraction while the third term is ran d omi zati on wi th being the randomization parameter. rand is a random number generator uniformly distributed in [0, 1]. For most cases in the implementation, 1 and 0,1 . 0
  24. 24. Pseudo code of the firefly algorithm Begin Objective function f (x), x = (x1 , ..., xd )T Generate initial population of fireflies xi (i = 1, 2, ..., n) Light intensity Ii at xi is determined by f ( xi ) Define light absorption coefficient γ while (t <MaxGeneration) for i = 1 : n all n fireflies for j = 1 : i all n fireflies ( inner loop ) if ( Ij > Ii ) Move firefly i towards j ; end if Attractiveness varies with distance r via e−γr Evaluate new solutions and update light intensity end for j end for i Rank the fireflies and find the current best end while Postprocess results and visualization End
  25. 25. Performance Comparison
  26. 26. Firefly Applications  Digital Image Compression and Image Processing  Feature selection  Antenna Design  Structural Design  Scheduling  Clustering
  27. 27. References [1] Xin-She Yang, Suash Deb: “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, (2008). [2] Nitesh Sureja ,”New Inspirations in Nature: A Survey “, G H Patel College of Engineering & Technology, Vallabh Vidyanagar (Gujarat), INDIA (2012). [3] Shakti Kumar, Parvinder Kaur, Amarpartap Singh,” Fuzzy Model Identification: A Firefly Optimization Approach”, Department of Electronics & Communications, SLIET, Longowal, Punjab, INDIA(2012).
  28. 28. Thank You