Summary
The particle swarm optimization (PSO) algorithm has gained increasing popularity in the last few years mainly because of its relative simplicity and its good overall performance, particularly in continuous optimization problems. As PSO is adopted in more types of application domains, it becomes more important to have well-established methodologies to assess its performance. For that purpose, several test problems have been proposed. In this chapter, we review several state-of-the-art test function generators that have been used for assessing the performance of PSO variants. As we will see, such test problems sometimes have regularities which can be easily exploited by PSO (or any other algorithm for that sake) resulting in an outstanding performance. In order to avoid such regularities, we describe here several basic design principles that should be followed when creating a test function generator for single-objective continuous optimization.
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References
Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. John Wiley & Sons, Chichester (2006)
Salomon, R.: Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. a survey of some theoretical and practical aspects of genetic algorithms. Biosystems 39(3), 263–278 (1996)
Rönkkönen, J., Li, X., Kyrki, V., Lampinen, J.: A generator for multimodal test functions with multiple global optima. In: Li, X., Kirley, M., Zhang, M., Green, D., Ciesielski, V., Abbass, H.A., Michalewicz, Z., Hendtlass, T., Deb, K., Tan, K.C., Branke, J., Shi, Y. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 239–248. Springer, Heidelberg (2008)
Liang, J., Suganthan, P., Deb, K.: Novel composition test functions for numerical global optimization. In: Proceedings of the 2005 IEEE Swarm Intelligence Symposium (SIS 2005), pp. 68–75 (June 2005)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (December 1995)
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of the 1998 IEEE International Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence, pp. 69–73 (May 1998)
Shi, Y., Eberhart, R.: Empirical study of particle swarm optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), vol. 3, p. 1950 (1999)
Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6(1), 58–73 (2002)
Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science (MHS 1995), pp. 39–43 (October 1995)
Kennedy, J.: Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), vol. 3, p. 1938 (1999)
Kennedy, J., Mendes, R.: Population structure and particle swarm performance. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), Washington, DC, USA, pp. 1671–1676. IEEE Computer Society, Los Alamitos (2002)
Passaro, A., Starita, A.: Particle swarm optimization for multimodal functions: a clustering approach. Journal Artificial Evolution and Applications 8(2), 1–15 (2008)
Bird, S., Li, X.: Enhancing the robustness of a speciation-based pso. In: IEEE Congress on Evolutionary Computation (CEC 2006), pp. 843–850 (2006)
Liang, J., Qin, A., Suganthan, P., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation 10(3), 281–295 (2006)
de Oca, M.M., Stützle, T., Birattari, M., Dorigo, M.: Frankenstein’s PSO: A Composite Particle Swarm Optimization Algorithm. IEEE Transactions on Evolutionary Computation 13(5), 1120–1132 (2009)
Harrington, S.: Computer Graphics: A Programming Approach, 2nd edn. Mcgraw-Hill College Press, New York (1987)
Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE Swarm Intelligence Symposium (SIS 2007), pp. 120–127 (April 2007)
Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation (GECCO 2006), New York, NY, USA, pp. 1305–1312. ACM, New York (2006)
Deb, K., Goldberg, D.E.: An Investigation of Niche and Species Formation in Genetic Function Optimization. In: Schaffer, J.D. (ed.) Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, California, George Mason University, pp. 42–50. Morgan Kaufmann Publishers, San Francisco (June 1989)
Gallagher, M., Yuan, B.: A general-purpose tunable landscape generator. IEEE Transactions on Evolutionary Computation 10(5), 590–603 (2006)
Morrison, R., Jong, K.D.: A test problem generator for non-stationary environments. In: Proceedings of the 1999 Congress Evolutionary Computation (CEC 99). Volume 3. (1999) 2053
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Barrera, J., Coello Coello, C.A. (2011). Test Function Generators for Assessing the Performance of PSO Algorithms in Multimodal Optimization. In: Panigrahi, B.K., Shi, Y., Lim, MH. (eds) Handbook of Swarm Intelligence. Adaptation, Learning, and Optimization, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17390-5_4
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DOI: https://doi.org/10.1007/978-3-642-17390-5_4
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