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Fireworks Algorithm pp 37–58Cite as

Modeling and Theoretical Analysis of FWA

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Abstract

In order to describe the convergence analysis of FWA, a Markov stochastic process modeling Fireworks Algorithm has been defined and established, in the first part of this chapter, then to prove the global convergence of FWA and analyze the time complexity of FWA based on an absorbing Markov stochastic process of FWA. After that, the computation of the approximation region of expected convergence time of Fireworks Algorithm has also been given through a detailed derivation procedure. In the second part of this chapter, we will present 13 commonly used random number generators (RNGs) and also try to discuss the impact of the RNGs on the performance of FWA.

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References

  1. Y. Tan, Y. Zhu, Fireworks algorithm for optimization, in Advances in Swarm Intelligence (Springer, Berlin, 2010), pp. 355–364

    Google Scholar 

  2. H. Huang, Z. Hao, Y. Qin, Time complexity of evolutionary programming. J. Comput. Res. Dev. 45(11), 1850–1857 (2008)

    Google Scholar 

  3. H. Huang, Z. Hao, W. Chunguo, Y. Qin, Time convergence speed of ant colony optimization. J. Comput. 30(8), 1344–1353 (2007)

    Google Scholar 

  4. D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (Amsterdam, London, 1969)

    Google Scholar 

  5. P. L’Ecuyer, Random number generation, in Handbook of Computational Statistics. Springer Handbooks of Computational Statistics, ed. by J.E. Gentle, W.K. Hardle, Y. Mori (Springer, Berlin, 2012), pp. 35–71. doi:10.1007/978-3-642-21551-3_3. ISBN: 978-3-642-21550-6

  6. P. L’Ecuyer, R. Simard, TestU01: A C library for empirical testing of random number generators. ACM Trans. Math. Softw. 33(4), (2007). doi:10.1145/1268776.1268777. ISSN: 0098-3500

  7. M. Clerc, List-based optimisers: experiments and open questions. Int. J. Swarm Intell. Res. (IJSIR) 4(4), 23–38 (2013)

    Article  Google Scholar 

  8. C.J.A. Bastos-Filho, J.D. Andrade, M.R.S. Pita, A.D. Ramos, Impact of the quality of random numbers generators on the performance of particle swarm optimization, in IEEE International Conference on Systems, Man and Cybernetics, SMC 2009 (2009), pp. 4988–4993. doi:10.1109/ICSMC.2009.5346366

  9. C.J.A. Bastos-Filho, M.A.C. Oliveira, D.N.O. Nascimento, A.D. Ramos, Impact of the random number generator quality on particle swarm optimization algorithm running on graphic processor units, in 2010 10th International Conference on Hybrid Intelligent Systems (HIS) (2010), pp. 85–90

    Google Scholar 

  10. G. Marsaglia, Xorshift RNGs. J. Stat. Softw. 8(14), 1–6 (2003)

    Article  Google Scholar 

  11. L. Howes, D. Thomas, Efficient random number generation and application using CUDA, GPU Gems 3 (Addison-Wesley Professional, Boston, 2007), pp. 805–830

    Google Scholar 

  12. J.A. Rice, Mathematical Statistics and Data Analysis (Thomson Higher Education, Belmont, 2007)

    Google Scholar 

  13. P. L’Ecuyer, Tables of linear congruential generators of different sizes and good lattice structure. Math. Comput. 68(225), 249–260 (1999). doi:10.1090/S0025-5718-99-00996-5. ISSN: 0025-5718

    Article  MATH  MathSciNet  Google Scholar 

  14. The Numerical Algorithms Group Ltd, NAG Library Manual. Mark 23, (2011)

    Google Scholar 

  15. P. L’Ecuyer, Good parameters and implementations for combined multiple recursive random number generators. Oper. Res. 47(1), 159–164 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Matsumoto, T. Nishimura, Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. (TOMACS) 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  17. M. Saito, M. Matsumoto, SIMD-oriented fast mersenne twister: a 128-bit pseudorandom number generator, in Monte Carlo and Quasi-Monte Carlo Methods 2006, ed. by A. Keller, S. Heinrich, H. Niederreiter (Springer, Berlin, 2008), pp. 607–622. doi:10.1007/978-3-540-74496-2_36. ISBN: 978-3-540-74495-5

  18. M. Saito, M. Matsumoto, Variants of mersenne twister suitable for graphic processors. ACM Trans. Math. Softw. 39(2), 12:1–12:20 (2013). doi:10.1007/978-3-540-74496-2_36. ISBN: 978-3-540-74495-5

  19. S. Kirkpatrick, E.P. Stoll, A very fast shift-register sequence random number generator. J. Comput. Phys. 40(2), 517–526 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Matsumoto, T. Nishimura, Dynamic creation of pseudorandom number generators, in Monte Carlo and Quasi-Monte Carlo Methods 1998, ed. by H. Niederreiter, J. Spanier (Springer, Berlin, 2000), pp. 56–69

    Chapter  Google Scholar 

  21. AMD Inc. Core Math Library (ACML)

    Google Scholar 

  22. The Boost Random Number Library

    Google Scholar 

  23. W.B. Langdon, A fast high quality pseudo random number generator for NVIDIA CUDA, in Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, GECCO’09 (ACM, New York, 2009), pp. 2511–2514. doi:10.1145/1570256.1570353. ISBN: 978-1-60558-505-5

  24. Intel Corp. The Math Kernel Library

    Google Scholar 

  25. NVIDIA Corp. CURAND Library Programming Guide v5.5 (2013)

    Google Scholar 

  26. K. Ding, Y. Tan, cuROB: A GPU-based Test Suit for Real-Parameter Optimization, in Advances in Swarm Intelligence. Lecture Notes in Computer Science, vol. 8794, ed. by Y. Tan, Y.H. Shi, C.A. Coello Coello (Springer, Berlin, 2014), pp. 66–78

    Google Scholar 

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Authors and Affiliations

  1. Peking University, Beijing, China

    Ying Tan

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  1. Ying Tan
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Tan, Y. (2015). Modeling and Theoretical Analysis of FWA. In: Fireworks Algorithm. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46353-6_3

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  • DOI: https://doi.org/10.1007/978-3-662-46353-6_3

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  • Print ISBN: 978-3-662-46352-9

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