Abstract
In this paper, we investigate the use of low-discrepancy sequences to generate an initial population for population-based optimization algorithms. Previous studies have found that low-discrepancy sequences generally improve the performance of a population-based optimization algorithm. However, these studies generally have some major drawbacks like using a small set of biased problems and ignoring the use of non-parametric statistical tests. To address these shortcomings, we have used 19 functions (5 of them quasi-real-world problems), two popular low-discrepancy sequences and two well-known population-based optimization methods. According to our results, there is no evidence that using low-discrepancy sequences improves the performance of population-based search methods.
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Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: IEEE Swarm Intelligence Symposium, pp. 120–127 (2007)
Bratley, P., Fox, B.: Algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 14, 88–100 (1988)
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 Trans. Evol. Comput. 10(6), 646–657 (2006)
Brits, R., Engelbrecht, A.P., van den Bergh, F.: A niching particle swarm optimizer. In: Proceedings of the Fourth Asia Pacific Conference on Simulated Evolution and Learning, pp. 692–696 (2002)
Das, S., Suganthan, P.: Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Technical report, Jadavpur University, Nanyang Technological University (2010)
Derrac, J., Garcia, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011)
Eberhart, R., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: IEEE International Conference on Evolutionary Computation, pp. 81–86 (2001)
Gacôgne, L.: Benefit of a steady state genetic algorithm with adaptive operators. Mendel University, Brno, Czech, pp. 236–242 (2000)
Gentle, E.: Random Number Generation and Monte Carlo Methods. Springer, Berlin (1998)
Georgieva, A., Jordanov, I.: Hybrid metaheuristics for global optimization using low-discrepancy sequences of points. Comput. Oper. Res. 37(3), 456–469 (2010)
Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 1942–1948. IEEE Press, New York (1995)
Kucherenko, S., Sytsko, Y.: Application of deterministic low-discrepancy sequences in global optimisation. Comput. Optim. Appl. 30, 297–318 (2005)
Marsaglia, G., Zaman, A.: A new class of random number generators. Ann. Appl. Probab. 3, 462–480 (1991)
Michalewicz, Z., Fogel, D.: How to Solve It: Modern Heuristics. Springer, Berlin (2000)
Monica, T., Rajasekhar, A., Pant, M., Abraham, A.: Enhancing the local exploration capabilities of artificial bee colony using low discrepancy Sobol sequence. Commun. Comput. Inf. Sci. 168, 158–168 (2011)
Monson, C., Seppi, K.: Exposing origin-seeking bias in PSO. In: GECCO’05, pp. 241–248 (2005)
Nguyen, Q.U., Nguyen, X.H., Mckay, R., Tuan, P.: Initializing PSO with randomized low-discrepancy sequences: The comparative results. In: Proceedings of IEEE Congress on Evolutionary Algorithms, pp. 1985–1992 (2007)
Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39, 459–472 (2007)
Kimura, S., Matsumura, K.: Genetic algorithms using low discrepancy sequences. In: Proceedings of GEECO, pp. 1341–1346 (2005)
Pant, M., Thangaraj, R., Grosan, C., Abraham, A.: Improved particle swarm optimization with low-discrepancy sequences. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3011–3018 (2008)
PSC. Particle Swarm Central. http://www.particleswarm.info. (Visited 3 July 2012)
Sandgren, E.: Non linear integer and discrete programming in mechanical design optimization. J. Mech. Des. 112(2), 223–229 (1990)
Shi, Y., Eberhart, C.: A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, Alaska, pp. 69–73 (1998)
Sobol, I.: On the systematic search in a hypercube. SIAM J. Numer. Anal. 16(5), 790–792 (1979)
Spears, W., Green, D., Spears, D.: Biases in particle swarm optimization. Int. J. Swarm Intell. Res. 1(2), 34–57 (2010)
Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, International Computer Science Institute, Berkeley, CA (1995)
Suganthan, P., Hansen, N., Liang, J., Deb, K., Chen, Y., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technology University, Singapore (2005)
Thangaraj, R., Pant, M., Abraham, A., Badr, Y.: Hybrid evolutionary algorithm for solving global optimization problems. In: Proceedings of the 4th International Conference on Hybrid Artificial Intelligence Systems, pp. 310–318 (2009)
Van Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. Kluwer Academic, Dordrecht (1987)
Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)
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Omran, M.G.H., al-Sharhan, S., Salman, A. et al. Studying the effect of using low-discrepancy sequences to initialize population-based optimization algorithms. Comput Optim Appl 56, 457–480 (2013). https://doi.org/10.1007/s10589-013-9559-2
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DOI: https://doi.org/10.1007/s10589-013-9559-2