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On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments.

Chao Qian1, Yang Yu2, Ke Tang3

  • 1UBRI, School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230027, China; National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210023, China chaoqian@ustc.edu.cn.

Evolutionary Computation
|December 17, 2016
PubMed
Summary

Sampling can significantly accelerate noisy evolutionary optimization. By rigorously analyzing running times, this study proves sampling can reduce exponential to polynomial time complexity for problems like OneMax and LeadingOnes, especially under high noise levels.

Keywords:
Robust optimizationcomputational complexity.evolutionary algorithmsoptimization in noisy environmentsrunning time analysis

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Optimization

Background:

  • Real-world optimization often involves noisy objective functions due to uncertainties.
  • Evolutionary algorithms are frequently used for noisy optimization, necessitating effective noise-handling strategies.
  • Sampling, estimating fitness via multiple evaluations, is a common but theoretically unclear noise-handling technique.

Purpose of the Study:

  • To theoretically analyze the impact of sampling on the performance of evolutionary algorithms in noisy environments.
  • To determine if sampling can improve the efficiency of evolutionary algorithms when dealing with noisy fitness functions.

Main Methods:

  • Rigorous running time analysis of the (1+1)-EA on OneMax and LeadingOnes problems.
  • Investigation of both prior and posterior noise models, including additive Gaussian noise.
  • Comparative analysis of sampling against other noise-robust strategies like parent populations and threshold selection.

Main Results:

  • Sampling can accelerate noisy evolutionary optimization exponentially, reducing running time from exponential to polynomial under high noise.
  • A small difference in the number of samples can lead to an exponential difference in expected running time, highlighting the importance of careful selection.
  • Sampling proves more effective for noise handling than parent populations and threshold selection in illustrative examples.

Conclusions:

  • Sampling is a powerful theoretical tool for accelerating evolutionary optimization in the presence of significant noise.
  • The effectiveness of sampling is contingent on the noise level and necessitates careful parameter tuning.
  • Sampling's benefits are demonstrated in specific noisy optimization scenarios, though it may be ineffective when noise is not detrimental.