Cuckoo Search via Lvy flights X. S. Yang and Suash Deb NABIC, - PowerPoint PPT Presentation

Cuckoo Search via Lévy flights X. S. Yang and Suash Deb NABIC, 2009, IEEE Presented by Cihan Kaya

What is cuckoo search with Levy flights? v A meta-heuristic method v Global optimization v Based on obligate brood parasitic behavior of cuckoo birds Wikipedia

Brood parasitism of cuckoo birds v Lay their eggs in the nest of a host bird. v Imitate the colors and patterns of host eggs. v Increase their survival and productivity. Aidala et. al, (2010) Nature Education Knowledge 3(10):53

What if egg is discovered? v Discovered foreign egg will be thrown or host will leave nest. v Nests with eggs are selected. v Cuckoo eggs will hatch earlier than host egg. Aidala et. al, (2010) Nature Education Knowledge 3(10):53

Then what? v Cuckoo chick will evict all host eggs. v Increased food share. Anderson et. al, (2009) Plos One 4 (11), e7725

Laying eggs and evolutionary arm race • Video Cuckoo infiltration Egg destruction

Levy flights v Food search in nature is random or quasi-random. v Foraging path is random walk and depends on current location and transition probability. v Since next direction is based on probability, it can be modeled mathematically.

Difference from random walk Wikipedia

Biological inspiration v Eggs in nests : set of solutions v Cuckoo egg : new solution. v New and better solutions will replace, less fit solutions. v Cuckoo’s change position with Levy flights after leaving nest.

Rules of implementation v Each cuckoo can lay one egg at each time step. v High quality nests will carry onto next generations. v # of host nests is fixed and p a is the probability of discovery of an alien egg. v Host bird can throw away egg or leave nest.

Initialization v Parameters v n : number of host nests v p a : probability of discovery of alien egg v MaxIter : maximum number of iterations v Initialization ($) v Generate initial n host, 𝑦 " ($) ) v Evaluate 𝑔(𝑦 "

Iterations v Generate a new solution ($'() = 𝑦 " ($) + 𝛽 ⨁ 𝑀𝑓 0 𝑤𝑧(𝜇) v 𝑦 " ($'() ) v Evaluate 𝑔(𝑦 " v Choose a nest x j randomly ($) ) < 𝑔(𝑦 " ($'() ) v If 𝑔(𝑦 4 ($) with 𝑦 " ($'() v Replace 𝑦 4 v Abandon a fraction of p a worse nests. v Build new nests with Levy flights v Keep the best solutions

Realisation and Verification v Bivariate Michaelwicz function 𝑦 = 2𝑧 = 𝑔 𝑦, 𝑧 = − sin 𝑦 𝑡𝑗𝑜 => − sin 𝑧 𝑡𝑗𝑜 => 𝜌 𝜌

Realisation and Verification • Easom Test Function

Comparison with other algorithms

Traveler Salesman Solution (DCS) • N cities and D is distance matrix. DE( 𝑔 𝜌 = A 𝑒 C(")C("'() + 𝑒 C(D)C(() "F( • Eggs and nests: Order of cities • Movements 2-opt move Ouaarab et. al, (2010) Neural Computing and Double bridge move Applications , 24 (7-8), 1659-1669

Traveler Salesman Solution Ouaarab et. al, (2010) Neural Computing and Applications , 24 (7-8), 1659-1669

Advantages v Simple v T wo parameters, p a and n. v Easy to implement.

Other use areas v Engineering optimization problems v NP-hard combinatorial optimization problems v Data fusion in wireless sensor networks v Neural network training v Manufacturing scheduling v Nurse scheduling