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Study of Genetic Algorithms with Crossover Based on Confidence Intervals as an Alternative to Classical Least Squares Estimation Methods for Nonlinear Models

  • Domingo Ortiz-Boyer
  • César Harvás-Martínez
  • José Muñoz-Pérez
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

Genetic algorithms are optimization techniques especially useful in functions whose nonlinearity makes an analytical optimization impossible. This kind of functions appear when using least squares estimators in nonlinear regression problems. Least squares optimizers in general, and the Levenberg-Marquardt method in particular, are iterative methods especially designed to solve this kind of problems, but the results depend on both the features of the problem and the closeness to the optimum of the starting point. In this paper we study the least squares estimator and the optimization methods that are based on it. Then we analyze those features of real-coded genetic algorithms that can be useful in the context of nonlinear regression. Special attention will be devoted to the crossover operator, and a new operator based on confidence intervals will be proposed. This crossover provides an equilibrium between exploration and exploitation of the search space, which is very adequate for this kind of problems. To analyze the fitness and robustness of the proposed crossover operator, we will use three complex nonlinear regression problems with search domains of different amplitudes and compare its performance with that of other crossover operators and with the Levenberg-Marquardt method using a multi-start scheme.

Keywords

Real coded genetic algorithms Nonlinear regression Confidence interval based crossover. 

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Domingo Ortiz-Boyer
    • 1
  • César Harvás-Martínez
    • 1
  • José Muñoz-Pérez
    • 2
  1. 1.Department of Computer ScienceUniversity of CórdobaCórdobaSpain
  2. 2.Department of Languages and Computer ScienceUniversity of MálagaMálagaSpain

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