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Random Lines: A Novel Population Set-Based Evolutionary Global Optimization Algorithm

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Genetic Programming (EuroGP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6621))

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Abstract

In this paper, we present a new population set-based evolutionary optimization algorithm which aims to find global minima of cost functions. This algorithm creates random lines passing through pairs of points (vectors) in population, fits a quadratic function based on three points on each line, and then applies the crossover operation to extrema of these quadratic functions, and lastly performs the selection operation. We refer to the points determining random lines as parent points and the extremum of a quadratic model as the descendant or mutated point under some conditions. In the crossover operation, some entries of a descendant vector are randomly replaced with the corresponding entries of one parent vector and some other entries of the descendant vector are replaced with the corresponding entries of the other parent vector based on the crossover constant. The above crossover and mutation operations make this algorithm robust and fast converging. One important property of this algorithm is that its robustness in general increases with increasing population size which may become useful when more processing units are available. This algorithm achieves comparable results with the well-known Differential Evolution (DE) algorithm over a wide range of cost functions.

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References

  1. Törn, A., Zilinskas, A.: Global Optimization. Springer, New York (1989)

    Book  MATH  Google Scholar 

  2. Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: New perspectives on some classical and modern methods. SIAM Review 45(3), 385–482 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hooke, R., Jeeves, T.A.: Direct Search Solution of Numerical and Statistical Problems. Journal of the ACM 8(2), 212–229 (1961)

    Article  MATH  Google Scholar 

  4. Nelder, J.A., Mead, R.: A Simplex Method for Function Minimization. Computer Journal 7(4), 308–313 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ali, M.M., Törn, A.: Population Set-based Global Optimization Algorithms: Some Modifications and Numerical Studies. Computers and Operations Research 31(10), 1703–1725 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Back, T., Schewefel, H.P.: An Overview of Evolutionary Algorithms for parameter optimization. Evolutionary Computation 1(1), 1–23 (1993)

    Article  Google Scholar 

  7. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, New York (2003)

    Book  MATH  Google Scholar 

  8. Yao, X., Liu, Y., Lin, G.: Evolutionary Programming Made Faster. IEEE Transactions on Evolutionary Computation 3(2), 82–102 (1999)

    Article  Google Scholar 

  9. Back, T., Hammel, U., Schwefel, H.P.: Evolutionary Computation: Comments on the History and Current State. IEEE Transactions on Evolutionary Computation 1(1), 3–17 (1997)

    Article  Google Scholar 

  10. Fogel, D.B.: What Is Evolutionary Computation? IEEE Spectrum 37(2), 28–32 (2000)

    Article  Google Scholar 

  11. Hinterding, R., Michalewicz, Z., Eiben, A.E.: Adaptation in Evolutionary Computation: A Survey. In: IEEE International Conference on Evolutionary Computation, pp. 65–69. IEEE Press, Los Alamitos (1997)

    Google Scholar 

  12. Storn, R., Price, K.: Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  14. Veenhuis, C.B.: Tree Based Differential Evolution. In: Vanneschi, L., Gustafson, S., Moraglio, A., De Falco, I., Ebner, M. (eds.) EuroGP 2009. LNCS, vol. 5481, pp. 208–219. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Transactions on Evolutionary Computation 10(6), 646–657 (2006)

    Article  Google Scholar 

  16. Montgomery, J., Chen, S.: An Analysis of the Operation of Differential Evolution at High And Low Crossover Rates. In: IEEE Congress on Evolutionary Computation, pp. 1–8. IEEE Press, Los Alamitos (2010)

    Google Scholar 

  17. Caponio, A., Neri, F.: Differential Evolution with Noise Analyzer. In: Giacobini, M., Brabazon, A., Cagnoni, S., Di Caro, G.A., Ekárt, A., Esparcia-Alcázar, A., Farooq, M., Fink, A., Machado, P. (eds.) EvoWorkshops 2009. LNCS, vol. 5484, pp. 715–724. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Liu, G., Li, Y.X., He, G.L.: Design of Digital FIR Filters Using Differential Evolution Algorithm Based on Reserved Genes. In: IEEE Congress on Evolutionary Computation, pp. 1–7. IEEE Press, Los Alamitos (2010)

    Google Scholar 

  19. Das, S., Konar, A.: Automatic Image Pixel Clustering with an Improved Differential Evolution. Applied Soft Computing 9(1), 226–236 (2009)

    Article  Google Scholar 

  20. Shi, Y., Teng, H., Li, Z.: Cooperative Co-evolutionary Differential Evolution for Function Optimization. In: Wang, L., Chen, K., Ong, Y.S. (eds.) ICNC 2005. LNCS, vol. 3611, pp. 1080–1088. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-Based Differential Evolution. IEEE Transactions on Evolutionary Computation 12(1), 64–79 (2008)

    Article  Google Scholar 

  22. Kundu, D., Suresh, K., Ghosh, S., Das, S., Abraham, A., Badr, Y.: Automatic Clustering Using a Synergy of Genetic Algorithm and Multi-objective Differential Evolution. In: Corchado, E., Wu, X., Oja, E., Herrero, Á., Baruque, B. (eds.) HAIS 2009. LNCS, vol. 5572, pp. 177–186. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Abbass, H.A., Sarker, R., Newton, C.: PDE: a Pareto-frontier Differential Evolution Approach for Multi-objective Optimization Problems. In: Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, South Korea, vol. 2, pp. 971–978. IEEE Press, Los Alamitos (2001)

    Google Scholar 

  24. Vesterstroem, J., Thomsen, R.: A Comparative Study of Differential Evolution, Particle Swarm Optimization, and Evolutionary Algorithms on Numerical Benchmark Problems. Proc. Congr. Evol. Comput. 2, 1980–1987 (2004)

    Google Scholar 

  25. Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc., Englewood Cliffs (1983)

    MATH  Google Scholar 

  26. More, J.J., Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease. ACM Transactions on Mathematical Software 20, 286–307 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  27. Mohan, C., Shanker, K.: A Controlled Random Search Technique for Global Optimization Using Quadratic Approximation. Asia-Pacific Journal of Operational Research 11, 93–101 (1994)

    MathSciNet  MATH  Google Scholar 

  28. Thangaraj, R., Pant, M., Abraham, A.: New Mutation Schemes for Differential Algorithm and Their Application to the Optimization of Directional Over-current Relay Settings. Applied Mathematics and Computation 216, 532–544 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Liu, J., Lampinen, J.: A Fuzzy Adaptive Differential Evolution Algorithm. Soft Computing-A Fusion of Foundations, Methodologies and Applications 9(6), 448–462 (2005)

    MATH  Google Scholar 

  30. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Selfadapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Transactions on Evolutionary Computation 10(6), 646–657 (2006)

    Article  Google Scholar 

  31. Storn, R.: On the Usage of Differential Evolution for Function Optimization. In: Proc. Biennial Conf. North Amer. Fuzzy Inf. Process. Soc., pp. 519–523 (1996)

    Google Scholar 

  32. More, J.J., Garbow, B.S., Hillstrom, K.E.: Testing Unconstrained Optimization Software. ACM Transactions on Mathematical Software 7(1), 17–41 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  33. Ali, M.M., Khompatraporn, C., Zabinsky, Z.B.: A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems. Journal of Global Optimization 31, 635–672 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. Pierre, D.A.: Optimization Theory with Applications. Dover Publications Inc., Mineola (1969)

    MATH  Google Scholar 

  35. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Maryland, Room 2123, Chemical and Nuclear Engineering Building (Bldg 90), College Park, MD, 20742-2115, USA

    İsmet Şahin

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  1. İsmet Şahin
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Editor information

Editors and Affiliations

  1. INESC-ID Lisboa, Rua Alves Redol 9, 1000-029, Lisboa, Portugal

    Sara Silva

  2. Department of Biological Sciences, University of Idaho, ID 83844-3051, Moscow, USA

    James A. Foster

  3. University College Dublin, UCD CASL, Belfield, Dublin 4, Ireland

    Miguel Nicolau

  4. Faculty of Sciences and Technology, Department of Informatics Engineering, University of Coimbra, Pólo II - Pinhal de Marrocos, 3030-290, Coimbra, Portugal

    Penousal Machado

  5. Department of Animal Production Epidemiology and Ecology, University of Torino, Via Leonardo da Vinci 44, 10095, Grugliasco (TO), Italy

    Mario Giacobini

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Şahin, İ. (2011). Random Lines: A Novel Population Set-Based Evolutionary Global Optimization Algorithm. In: Silva, S., Foster, J.A., Nicolau, M., Machado, P., Giacobini, M. (eds) Genetic Programming. EuroGP 2011. Lecture Notes in Computer Science, vol 6621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20407-4_9

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  • DOI: https://doi.org/10.1007/978-3-642-20407-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20406-7

  • Online ISBN: 978-3-642-20407-4

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