Tobias Friedrich
Timo Kötzing
ABSTRACT
Practical optimization problems frequently include uncertainty about the quality measure, for example due to noisy evaluations. Thus, they do not allow for a straightforward application of traditional optimization techniques. In these settings, randomized search heuristics such as evolutionary algorithms are a popular choice because they are often assumed to exhibit some kind of resistance to noise. Empirical evidence suggests that some algorithms, such as estimation of distribution algorithms (EDAs) are robust against a scaling of the noise intensity, even without resorting to explicit noise-handling techniques such as resampling.
In this paper, we want to support such claims with mathematical rigor. We introduce the concept of graceful scaling in which the run time of an algorithm scales polynomially with noise intensity. We study a monotone fitness function over binary strings with additive noise taken from a Gaussian distribution. We show that myopic heuristics cannot efficiently optimize the function under arbitrarily intense noise without any explicit noise-handling. Furthermore, we prove that using a population does not help. Finally we show that a simple EDA called the Compact Genetic Algorithm can overcome the shortsightedness of mutation-only heuristics to scale gracefully with noise. We conjecture that recombinative genetic algorithms also have this property.
This extended abstract summarizes our work "The Benefit of Recombination in Noisy Evolutionary Search," which appeared in Proceedings of International Symposium on Algorithms and Computation (ISAAC), 2015, pp. 140--150.
- H.-G. Beyer, "Evolutionary Algorithms in Noisy Environments: Theoretical Issues and Guidelines for Practice," Computer Methods in Applied Mechanics and Engineering, vol. 186, no. 2--4, pp. 239--267, 2000.Google Scholar
- T. Friedrich, T. Kötzing, M. S. Krejca, and A. M. Sutton, "The benefit of recombination in noisy evolutionary search," in Proceedings of International Symposium on Algorithms and Computation (ISAAC), 2015, pp. 140--150.Google Scholar
- Prügel-Bennett, J. Rowe, and J. Shapiro, "Run-time analysis of population-based evolutionary algorithm in noisy environments," in Proceedings of Foundations of Genetic Algorithms (FOGA). ACM, 2015, pp. 69--75. Google ScholarDigital Library
Index Terms
- The Benefit of Recombination in Noisy Evolutionary Search
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