Abstract
Sampling has been often employed by evolutionary algorithms to cope with noise when solving noisy real-world optimization problems. It can improve the estimation accuracy by averaging over a number of samples, while also increasing the computation cost. Many studies focused on designing efficient sampling methods, and conflicting empirical results have been reported. In this paper, we investigate the effectiveness of sampling in terms of rigorous running time, and find that sampling can be ineffective. We provide a general sufficient condition under which sampling is useless (i.e., sampling increases the running time for finding an optimal solution), and apply it to analyzing the running time performance of (1+1)-EA for optimizing OneMax and Trap problems in the presence of additive Gaussian noise. Our theoretical analysis indicates that sampling in the above examples is not helpful, which is further confirmed by empirical simulation results.
This research was supported by the National Science Foundation of China (61375061, 61333014) and the Jiangsu Science Foundation (BK2012303).
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References
Aizawa, A.N., Wah, B.W.: Scheduling of genetic algorithms in a noisy environment. Evolutionary Computation 2(2), 97–122 (1994)
Arnold, D.V.: Noisy Optimization with Evolution Strategies. Kluwer, Norwell (2002)
Auger, A., Doerr, B.: Theory of Randomized Search Heuristics: Foundations and Recent Developments. World Scientific, Singapore (2011)
Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)
Bartz-Beielstein, T., Blum, D., Branke, J.: Particle swarm optimization and sequential sampling in noisy environments. In: Metaheuristics. Operations Research/Computer Science Interfaces Series, vol. 39, pp. 261–273. Springer, Heidelberg (2007)
Beyer, H.G.: Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice. Computer Methods in Applied Mechanics and Engineering 186(2), 239–267 (2000)
Branke, J., Schmidt, C.: Selection in the presence of noise. In: Proceedings of the 5th ACM Conference on Genetic and Evolutionary Computation, Chicago, IL, pp. 766–777 (2003)
Branke, J., Schmidt, C.: Sequential sampling in noisy environments. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 202–211. Springer, Heidelberg (2004)
Branke, J., Schmidt, C., Schmec, H.: Efficient fitness estimation in noisy environments. In: Proceedings of the 3rd ACM Conference on Genetic and Evolutionary Computation, San Francisco, CA, pp. 243–250 (2001)
Cantú-Paz, E.: Adaptive sampling for noisy problems. In: Proceedings of the 6th ACM Conference on Genetic and Evolutionary Computation, Seattle, WA, pp. 947–958 (2004)
Doerr, B., Goldberg, L.A.: Adaptive drift analysis. Algorithmica 65, 224–250 (2013)
Doerr, B., Johannsen, D., Winzen, C.: Multiplicative drift analysis. Algorithmica 64, 673–697 (2012)
Doerr, B., Hota, A., Kötzing, T.: Ants easily solve stochastic shortest path problems. In: Proceedings of the 14th ACM Conference on Genetic and Evolutionary Computation, Philadelphia, PA, pp. 17–24 (2012)
Droste, S.: Analysis of the (1+1) EA for a noisy OneMax. In: Proceedings of the 6th ACM Conference on Genetic and Evolutionary Computation, Seattle, WA, pp. 1088–1099 (2004)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1-2), 51–81 (2002)
He, J., Yao, X.: Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence 127(1), 57–85 (2001)
Iacca, G., Neri, F., Mininno, E.: Noise analysis compact differential evolution. International Journal of Systems Science 43(7), 1248–1267 (2012)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments-a survey. IEEE Transactions on Evolutionary Computation 9(3), 303–317 (2005)
Neumann, F., Witt, C.: Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity. Springer, Berlin (2010)
Park, T., Ryu, K.R.: Accumulative sampling for noisy evolutionary multi-objective optimization. In: Proceedings of the 13th ACM Conference on Genetic and Evolutionary Computation, Dublin, Ireland, pp. 793–800 (2011)
Qian, C., Yu, Y., Zhou, Z.-H.: On algorithm-dependent boundary case identification for problem classes. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 62–71. Springer, Heidelberg (2012)
Sano, Y., Kita, H.: Optimization of noisy fitness functions by means of genetic algorithms using history of search with test of estimation. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation, Honolulu, HI, pp. 360–365 (2002)
Siegmund, F., Ng, A.H., Deb, K.: A comparative study of dynamic resampling strategies for guided evolutionary multi-objective optimization. In: Proceedings of the 2013 IEEE Congress on Evolutionary Computation, Cancun, Mexico, pp. 1826–1835 (2013)
Stagge, P.: Averaging efficiently in the presence of noise. In: Proceedings of the 5th International Conference on Parallel Problem Solving from Nature, Amsterdam, The Netherlands, pp. 188–197 (1998)
Syberfeldt, A., Ng, A., John, R.I., Moore, P.: Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling. European Journal of Operational Research 204(3), 533–544 (2010)
Yu, Y., Zhou, Z.-H.: A new approach to estimating the expected first hitting time of evolutionary algorithms. Artificial Intelligence 172(15), 1809–1832 (2008)
Zhang, Z., Xin, T.: Immune algorithm with adaptive sampling in noisy environments and its application to stochastic optimization problems. IEEE Computational Intelligence Magazine 2(4), 29–40 (2007)
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Qian, C., Yu, Y., Jin, Y., Zhou, ZH. (2014). On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_30
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DOI: https://doi.org/10.1007/978-3-319-10762-2_30
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