Analysis of selection algorithms: A markov chain approach

  • Authors:
  • Uday Kumar Chakraborty;Kalyanmoy Deb;Mandira Chakraborty

  • Affiliations:
  • Reader Department of Computer Science and Engineering Jadavpur University Calcutta 700032, India uday@jadav.ernet.in;Assistant Professor Department of Mechanical Engineering Indian Institute of Technology Kanpur, UP 208016, India deb@iitk.ernet.in;Lecturer Department of Computer Science and Engineering Jadavpur University Calcutta 700032, India mc@jadav.ernet.in

  • Venue:
  • Evolutionary Computation
  • Year:
  • 1996

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Abstract

A Markov chain framework is developed for analyzing a wide variety of selection techniques used in genetic algorithms (GAs) and evolution strategies (ESs). Specifically, we consider linear ranking selection, probabilistic binary tournament selection, deterministic s-ary (s = 3,4,...) tournament selection, fitness-proportionate selection, selection in Whitley's GENITOR, selection in (μ, λ)-ES, selection in (μ + λ)-ES, (μ, λ)-linear ranking selection in GAs, (μ + λ)-linear ranking selection in GAs, and selection in Eshelman's CHC algorithm. The analysis enables us to compare and contrast the various selection algorithms with respect to several performance measures based on the probability of takeover. Our analysis is exact---we do not make any assumptions or approximations. Finite population sizes are considered. Our approach is perfectly general, and following the methods of this paper, it is possible to analyze any selection strategy in evolutionary algorithms.