Population-Based Continuous Optimization, Probabilistic Modelling and Mean Shift

  • Authors:
  • Marcus Gallagher;Marcus Frean

  • Affiliations:
  • School of Information Technology and Electrical Engineering, University of Queensland, Brisbane QLD 4072, Australia;School of Mathematical and Computing Sciences, Victoria University, PO Box 600, Wellington, New Zealand

  • Venue:
  • Evolutionary Computation
  • Year:
  • 2005

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Abstract

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.