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A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems.

Bo Song1, Victor O K Li2

  • 1Department of Electrical and Electronic Engineering, the University of Hong Kong, Pokfulam, Hong Kong bsong@connect.hku.hk.

Evolutionary Computation
|February 6, 2019
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Summary
This summary is machine-generated.

Infinite population models in evolutionary algorithms have flawed convergence proofs. A new framework rigorously analyzes these models, proving convergence for mutation and recombination operators with independent initial populations.

Keywords:
Evolutionary algorithmsconvergence in distributioninfinite population modelspopulation dynamicstheoretical analysis.

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Area of Science:

  • Computer Science
  • Evolutionary Computation
  • Theoretical Computer Science

Background:

  • Infinite population models are crucial for understanding evolutionary algorithm dynamics.
  • These models typically derive from Markov chains, assuming infinite population size and individual symmetries.
  • Existing convergence proofs for these models have been found to be problematic and incomplete.

Purpose of the Study:

  • To critically re-evaluate the theoretical foundations of infinite population models for continuous optimization problems.
  • To address limitations in previous studies regarding convergence proofs and operator analysis.
  • To develop a mathematically rigorous framework for analyzing infinite population models.

Main Methods:

  • Demonstrating flaws in existing convergence proofs for infinite population models.
  • Establishing that the exchangeability assumption is insufficient for deriving transition equations.
  • Developing a new analytical framework based on convergence in distribution for infinite sequences.
  • Utilizing the framework to prove convergence for mutation and n-ary recombination operators.

Main Results:

  • Identified and corrected problematic convergence proofs in prior research.
  • Showcased the inadequacy of the exchangeability assumption for deriving transition equations.
  • Introduced a novel, rigorous framework for analyzing infinite population models.
  • Successfully proved the convergence of infinite population models for key evolutionary operators.

Conclusions:

  • The new analytical framework provides a robust foundation for studying infinite population models.
  • The proven convergence of mutation and recombination operators offers accurate predictions for large populations.
  • Accurate predictions are contingent upon the initial population being identically and independently distributed.