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A Self-adaptive Mixed Distribution Based Uni-variate Estimation of Distribution Algorithm for Large Scale Global Optimization

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Nature-Inspired Algorithms for Optimisation

Part of the book series: Studies in Computational Intelligence ((SCI,volume 193))

Abstract

Large scale global optimization (LSGO), which is highly needed for many scientific and engineering applications, is a very important and very difficult task in optimization domain. Various algorithms have been proposed to tackle this challenging problem, but the use of estimation of distribution algorithms (EDAs) to it is rare. This chapter aims at investigating the behavior and performances of uni-variate EDAs mixed with different kernel probability densities via fitness landscape analysis. Based on the analysis, a self-adaptive uni-variate EDA with mixed kernels (MUEDA) is proposed. To assess the effectiveness and efficiency of MUEDA, function optimization tasks with dimension scaling from 30 to 1500 are adopted. Compared to the recently published LSGO algorithms, MUEDA shows excellent convergence speed, final solution quality and dimensional scalability.

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References

  1. Bosman, P.A.N.: Design and application of iterated density-estimation evolutionary algorithms. Ph.D. dissertation, Universiteit Utrecht, The Netherlands (2003)

    Google Scholar 

  2. Bosman, P.A.N., Grahl, J.: Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms. Eur. J. Oper. Res. 185, 1246–1264 (2008)

    Article  MATH  Google Scholar 

  3. Bosman, P.A.N., Grahl, J., Rothlauf, F.: SDR: A better trigger for adaptive variance scaling in normal EDAs. In: Proc. Genetic and Evolutionary Computation Conference (GECCO), London, United Kingdom, pp. 492–499 (2007)

    Google Scholar 

  4. Bosman, P.A.N., Thierens, D.: Expanding from discrete to continuous Estimation Of Distribution Algorithms: The IDEA. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 767–776. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Brest, J., Zamuda, A., Boskovic, B., Maucec, M.S., Zumer, V.: High-dimensional real-parameter optimization using self-adaptive Differential Evolution algorithm with population size reduction. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 2032–2039 (2008)

    Google Scholar 

  6. Gnedenko, B., Kolmogorov, A.: Limit distribution for sums of independent random variables. Addison Wesley, Cambridge (1954)

    Google Scholar 

  7. Grahl, J., Bosman, P.A.N., Minner, S.: Convergence phases, variance trajectories, and runtime analysis of continuous EDAs. In: Proc. Genetic and Evolutionary Computation Conference (GECCO), pp. 516–522 (2007)

    Google Scholar 

  8. Grahl, J., Bosman, P.A.N., Rothlauf, F.: The correlation Ctriggered adaptive variance scaling idea. In: Proc. Genetic and Evolutionary Computation Conference (GECCO), pp. 397–404 (2006)

    Google Scholar 

  9. Hansen, N., Gemperle, F., Auger, A., Koumoutsakos, P.: When do heavy-tail distributions help? In: Parallel Problem Solving From Nature IX (PPSN IX), pp. 62–71. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Hsieh, S., Sun, T., Liu, C., Tsai, S.: Solving large scale global optimization using improved particle swarm optimizer. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 1777–1784 (2008)

    Google Scholar 

  11. Larranga, P.: A review on estimation of distribution algorithms. In: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, ch. 3, pp. 57–100. Springer, Heidelberg (2001)

    Google Scholar 

  12. Larranga, P., Etxeberria, R., Lozano, J.A., Pena, J.M.: Optimization in continuous domains by learning and simulation of Gaussian networks. In: Proc. Genetic and Evolutionary Computation Conference Workshop Program, pp. 201–204 (2000)

    Google Scholar 

  13. Lee, C.Y., Yao, X.: Evolutionary programming using mutations based on the Lévy Probability Distribution. IEEE Trans. Evol. Comput. 8(1), 1–13 (2004)

    Article  Google Scholar 

  14. Lévy, P.: Theorie de l’Addition des Veriables Aleatoires. Paris, France, Gauthier-Villars (1937)

    Google Scholar 

  15. Liu, Y., Yao, X., Zhao, Q., Higuchi, T.: Scaling up fast evolutionary porgramming with cooperative coevolution. In: Proc. IEEE Congress on Evolutionary Computation (CEC), pp. 1101–1108 (2001)

    Google Scholar 

  16. Lu, Q., Yao, X.: Clustering and learning Gaussian Distribution for continuous optimization. IEEE Trans. Systems Man and Cybernetics 35(2), 195–204 (2005)

    Article  Google Scholar 

  17. MaCnish, C., Yao, X.: Direction matters in high-dimensional optimisation. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 2377–2384 (2008)

    Google Scholar 

  18. Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive models for breeder genetic algorithm. Evol. Comput. 1(1), 25–49 (1993)

    Article  Google Scholar 

  19. Mühlenbein, H., Schomisch, M., Born, J.: The parallel genetic algorithm as function optimizer. Parallel Comput. 17, 25–49 (1991)

    Article  Google Scholar 

  20. Panait, L., Luke, S., Wiegand, R.: Biasing coevolutionary search for optimal multiagent behaviors. IEEE Trans. Evol. Comput. 10(6), 629–645 (2006)

    Article  Google Scholar 

  21. Pardalos, P.: Large-Scale nonlinear optimization. In: Nonconvex Optimization and Its Applications. Springer, The Netherlands (2006)

    Google Scholar 

  22. Potter, A.M., Jong, K.A.D.: A cooperative co-evolutionary approach to function optimization. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 249–257. Springer, Heidelberg (1994)

    Google Scholar 

  23. Potter, A.M., Jong, K.A.D.: Cooperative coevolution: An architecture for evolving coadapted subcomponents. Evol. Comput. 8(1), 1–29 (2000)

    Article  Google Scholar 

  24. Rudlof, S., Koppen, M.: Stochastic hill climbing with learning by vectors of normal distributions. In: Proc. First Online Workshop on Soft Computing (WSC1), Nagoya, Japan, pp. 60–70 (1996)

    Google Scholar 

  25. Sebag, M., Ducoulombier, A.: Extending population-based incremental learning to continuous search spaces. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 418–427. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  26. Shi, Y., Teng, H., Li, Z.: Cooperative co-evolutionary differential evolution for function optimization. In: Proc. First International Conference on Natural Computation, pp. 1080–1088 (2005)

    Google Scholar 

  27. Sinha, N., Chakrabarti, R., Chattopadhyay, P.K.: Evolutionary programming techniques for economic load dispatch. IEEE Trans. Evol. Comput. 7(1), 83–94 (2003)

    Article  Google Scholar 

  28. Smith, T., Husbands, P., Layzell, P., OShea, M.: Fitness landscapes and evolvability. Evol. Comput. 10(1), 1–34 (2002)

    Article  Google Scholar 

  29. Stadler, P.F.: Fitness landscapes. In: Biological Evolution and Statistical Physics, pp. 187–207. Springer, Heidelberg (2002)

    Google Scholar 

  30. Szu, H., Hartley, R.: Fast simulated annealing. Phys. Lett. A 122(3,4), 157–162 (1987)

    Article  Google Scholar 

  31. Tang, K., Yao, X., Suganthan, P.N., MacNish, C., Chen, Y.P., Chen, C.M., Yang, Z.Y.: Benchmark functions for the CEC 2008 special session and competition on large scale global optimization. Technical Report for IEEE Congress of Evolutionary Computation (CEC) (2008) (special issue)

    Google Scholar 

  32. Tseng, L., Chen, C.: Multiple trajectory search for large scale global optimization. In: Proc. IEEE Congress on Evolutionary Computation (CEC), pp. 3052–3059 (2008)

    Google Scholar 

  33. Wang, Y., Li, B.: A restart uni-variable estimation of distribution algorithms: Sampling under mixed Gaussian and Levy Probability Distribution. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 3218–3225 (2008)

    Google Scholar 

  34. Wright, S.: The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In: Proc. 6th Congr. Genetics, vol. 1, p. 365 (1932)

    Google Scholar 

  35. Yang, Z., He, J.S., Yao, X.: Making a difference to differential evolution. In: Michalewicz, Z., Siarry, P. (eds.) Advances in Metaheuristics for Hard Optimization, pp. 397–414. Springer, Heidelberg (2007)

    Google Scholar 

  36. Yang, Z., Tang, K., Yao, X.: Differential evolution for high-dimensional function optimization. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Singapore, pp. 3523–3530 (2007)

    Google Scholar 

  37. Yang, Z., Tang, K., Yao, X.: Large scale evolutionary optimization using cooperative coevolution. Inf. Sci. 178(15), 2985–2999 (2008)

    Article  MathSciNet  Google Scholar 

  38. Yang, Z., Tang, K., Yao, X.: Multilevel cooperative coevolution for large scale optimization. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 1663–1670 (2008)

    Google Scholar 

  39. Yao, X.: An overview of evolutionary computation. Chinese J. Adv. Software Res. 3(1), 12–29 (1996)

    Google Scholar 

  40. Yao, X., Liu, Y.: Fast evolutionary programming. In: Proc. Fifth Annual Conference on Evolutionary Programming (EP 1996), pp. 451–460. MIT Press, San Diego (1996)

    Google Scholar 

  41. Yao, X., Liu, Y.: Fast evolution strategies. Control and Cybern 26(3), 467–496 (1997)

    MATH  MathSciNet  Google Scholar 

  42. Zamuda, A., Brest, J., Boskovic, B., Zumer, V.: Large scale global optimization using differential evolution with self adaptation and cooperative co-evolution. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 3719–3726 (2008)

    Google Scholar 

  43. Zhao, S., Liang, J.J., Suganthan, P.N., Tasgetiren, M.F.: Dynamic multi-swarm particle swarm optimizer with local search for large scale global optimization. In: Proc. IEEE Congress on Evolutionary Computation (CEC), Hong Kong, pp. 3845–3852 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Nature Inspired Computation and Application Laboratory (NICAL), University of Science and Technology of China,  

    Yu Wang & Bin Li

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  1. Yu Wang
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  2. Bin Li
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  1. Swinburne University of Technology, Sarawak Campus, Jalan Simpang Tiga, 93350, Kuching, Sarawak, Malaysia

    Raymond Chiong

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Wang, Y., Li, B. (2009). A Self-adaptive Mixed Distribution Based Uni-variate Estimation of Distribution Algorithm for Large Scale Global Optimization. In: Chiong, R. (eds) Nature-Inspired Algorithms for Optimisation. Studies in Computational Intelligence, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00267-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-00267-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00266-3

  • Online ISBN: 978-3-642-00267-0

  • eBook Packages: EngineeringEngineering (R0)

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