Göç Eden Kuşlar Algoritmasinda Kaos Fonksiyonlarinin Kullanilmasi

Olasılıksal eniyileme algoritmaları çalışmalarının birçok aşamasında rastlantısal veri kullanmaktadırlar ve performansları büyük oranda bu rastlantısal verinin dağılımına göre değişiklik göstermektedir. Bu noktadan hareketle farklı rastlantısal veri kaynaklarının eniyileme algoritmalarının performansına etkisi son zamanlardaki birçok çalışmanın odak noktası olmuştur. Kaotik eşlem fonksiyonları matematiksel özellikleri sonucu rastlantısal veri kaynağı olarak kullanılmaya oldukça elverişlidir. Bu çalışmada kaotik eşlem fonksiyonlarının popülasyon tabanlı evrimsel bir algoritma olan göç eden kuşlar algoritmasına etkisi bilgisayar mimarisinin güncel problemlerinden biri olan görev dağıtım problemi üzerinde deneysel olarak incelenmiştir. Deneyler neticesinde bir kısım kaotik eşlem fonksiyonlarının ele alınan problem için uygun olmadığı gözlense de, klasik rastlantısal veri üretme algoritmaları ile başa baş performans sergileyen kaotik eşlem fonksiyonlarının da bulunduğu görülmüştür

Use Of Chaos Functions in Migrating Birds Optimization Algorithm

Stochastic optimization algorithms use randomly generated data heavily in various steps. The form of this randomly generated data affects the performance of stochastic optimization algorithms significantly. Therefore, the effect of different random data sources on the performance of optimization algorithms is a common focus of many recent studies. Thanks to their mathematical properties, chaotic map functions are very convenient for being used as random data sources. In this work, an empirical analysis is provided in order to show the effect of chaotic map functions on the performance of migrating birds optimization algorithm. This empirical analysis is based on the task allocation problem which is a recent computer architecture problem. According to our experimental results, it is observed that some chaotic map functions perform inefficiently. On the other hand, it is also observed that there are some particular chaotic map functions that can compete with the classical random data generators

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[1] Copponetto R., Fazzino S. ve Xibillia M. G., "Chaotic Sequences to Improve the Performance of Evolutionary Algorithms", IEEE Transactions On Evolutionary Computation, Cilt 7, No 3, 289-304, 2003.
[2] Schuster H. G., "Deterministic Chaos", Wiley, New York, 1988.
[3] Shabika A., Hooshmandasl M. ve Meybodi M., “Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials”, Int J Bifurc Chaos, Cilt:26, No 7,1650112, 2016.
[4] Farajallah M., El Assad S. ve Deforges O., “Fast and Secure Chaos-Based Cryptosystem for Images”, Int J Bifurc Chaos, Cilt:26, No 2, 1650021, 2016.
[5] Tang B., Xiao Y., Tang S. ve Cheke R., “A Feedback Control Model of Comprehensive Therapy for Treating Immunogenic Tumours”, Int J Bifurc Chaos, Cilt:26, No 3, 1650039, 2016.
[6] Mariani V., Duck A., Guerra F., Coelho L., Rao R., “A chaotic quantum-behavedparticle swarm approach applied to optimization of heat exchangers”, Appl. Therm. Eng., Cilt 42, 119-128, 2012.
[7] Senkerik R., Pluhacek M., Davendra D., Zelinka I., Kominkova Z., “Chaos driven evolutionary algorithm: a new approach for evolutionaryoptimization”, Int. J. Mathematics and Computers in Simulation, Cilt 7, No 3, 363-368, 2013
[8] Liu D. ve Cao Y.A.,“Chaotic genetic algorithm for fuzzy grid job scheduling” IEEE International Conferenceon Computational Intelligence and Security, Guangzhou,Cilt 1, 320–323, Kasım 2006.
[9] Alataş B., Akın E. ve Özer B., “Chaos embedded particle swarm optimization algorithms”, Chaos, Solitons & Fractals; Cilt 40, 1715–1734, 2009.
[10] Pluhacek M., Senkerik R. ve Davendra D.,”Chaos particle swarm optimization with Eensemble of chaotic systems”, Swarm and Evolutionary Computation, Cilt 25, 29-35, 2015.
[11] Metlicka M. ve Davendra D. “Chaos driven discrete artificial bee algorithm for location and assignment optimisation problems”, Swarm and Evolutionary Computation, Cilt 25, 15-28, 2015.
[12] Shatz, S., Wang, J.P. ve Goto, M.,“Task allocation for maximizing reliability of distributed computer systems” IEEE Transactions on Computers, Cilt 41, 1156–1168, 1992.
[13] Kang Q., He H. ve Deng R., “Bi-objective task assignment in heterogeneous distributed systems using honeybee mating optimization”, Applied Mathematics and Computation, Cilt 219, 2589– 2600, 2012.
[14] Salman A., Ahmad I. ve Al-Madani, S.,“Particle swarm optimization for task assignment problem”, Microprocessors and Microsystems, Cilt 26, 363 - 371, 2002.
[15] Attiya G. ve Hamam Y.,“Task allocation for maximizing reliability of distributed systems: A simulated annealing approach”, Journal of Parallel and Distributed Computing, Cilt 66, 1259–1266, 2006.
[16] Duman E., Uysal M. ve Alkaya A. F.,“Migrating birds optimization: Anew metaheuristic approach and its performance on quadratic assignment problem”, Information Sciences, Cilt 217, 65–77, 2012.
[17] Yin P. Y., Yu S.-S., Wang P. ve Wang, Y. T,“Multiobjective task allocationin distributed computing systems by hybrid particle swarm optimization”, AppliedMathematics and Computation, Cilt 184, 407–420, 2007.
[18] Lin S.W., Ying K.C. ve Huang C.- Y.,“Multiprocessor task schedulingin multistage hybrid flowshops: A hybrid artificial bee colony algorithm with bidirectional planning”, Computers and Operations Research, Cilt 40, 1186–1195, 2013.
[19] Pan Q.K. ve Dong Y.,“An improved migrating birds optimisation for a hybridflowshop scheduling with total flowtime minimisation”,Information Sciences, Cilt 277,643–655, 2014.
[20] Pendharkar P. C.,“An ant colony optimization heuristic for constrained taskallocation problem”, Journal of Computational Science, Cilt 7, 37–47, 2015.
[21] Stone H. S., “Multiprocessor scheduling with the aid of network flow algorithms”, IEEE Transactions Software Engineering, Cilt 3, 85–93, 1977.
[22] Hansen J. V. ve Giauque W. C.,“Task allocation in distributed processing systems”, Operations Research Letters, Cilt 5, 137-143, 1986
[23] Chen, W.-H., & Lin, C.-S.,“A hybrid heuristic to solve a task allocation problem”, Computers & Operations Research, Cilt 27, 287-303, 2000.
[24] Peitgen H., Jurgens H., Saupe D.,“Chaos and fractals New Frontiers of Science”, Springer-Verlag, Berlin, 1992.
[25] Peterson G. “Arnold’s cat map”, Math 45 - Linear algebra,1997.
[26] Burgers J., “Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion”, Selected Papers of J. M. Burgers, Springer, Netherlands, 281–334, 1995.