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Runtime Analysis of Restricted Tournament Selection for Bimodal Optimisation.

Edgar Covantes Osuna1, Dirk Sudholt2,3

  • 1School of Engineering and Sciences, Tecnológico de Monterrey, Monterrey, 64849, México edgar.covantes@tec.mx.

Evolutionary Computation
|October 8, 2021
PubMed
Summary
This summary is machine-generated.

Restricted tournament selection (RTS) efficiently finds both optima on the TwoMax function with a large window size. However, small window sizes cause RTS to fail, highlighting the importance of niche size in evolutionary algorithms.

Keywords:
Niching methodsevolutionary algorithmrestricted tournament selectionruntime analysis

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Area of Science:

  • Evolutionary Computation
  • Algorithm Analysis
  • Optimization

Background:

  • Niching methods are crucial for maintaining population diversity and preventing genetic drift in evolutionary algorithms.
  • Investigating multiple peaks in parallel requires effective selection mechanisms that balance exploration and exploitation.

Purpose of the Study:

  • To provide the first rigorous runtime analysis of restricted tournament selection (RTS) within a (μ+1) evolutionary algorithm.
  • To evaluate the effectiveness of RTS in finding both optima of the bimodal TwoMax function.

Main Methods:

  • Restricted Tournament Selection (RTS): An offspring competes against the closest individual within a randomly selected window of population members.
  • Theoretical analysis of RTS runtime complexity on the TwoMax problem.
  • Experimental studies to complement theoretical findings and explore parameter spaces.

Main Results:

  • RTS efficiently finds both optima on the TwoMax function when the window size (w) is sufficiently large.
  • With a small window size, RTS fails to find both optima, even with exponential time, with high probability.
  • A variant of RTS using selection without replacement enhances diversity but slows convergence when niches collapse.

Conclusions:

  • The effectiveness of RTS is highly dependent on the window size parameter for maintaining population diversity and achieving convergence.
  • Theoretical results demonstrate a critical threshold for window size, beyond which efficient optimization is guaranteed.
  • Experimental validation supports theoretical findings and suggests further research directions for RTS parameter tuning.