Polynomial genetic programming for response surface modeling Part 1: a methodology

Created by W.Langdon from gp-bibliography.bib Revision:1.4420

  author =       "Y. S. Yeun and Y. S. Yang and W. S. Ruy and 
                 B. J. Kim",
  title =        "Polynomial genetic programming for response surface
                 modeling Part 1: a methodology",
  journal =      "Structural and Multidisciplinary Optimization",
  year =         "2005",
  volume =       "29",
  number =       "1",
  pages =        "19--34",
  month =        jan,
  keywords =     "genetic algorithms, genetic programming, directional
                 derivative-based smoothing, extended data-set method,
                 high-order polynomial, interpolation,
                 overfitting,response surface",
  ISSN =         "1615-147X",
  URL =          "http://www.springerlink.com/app/home/contribution.asp?wasp=pggkrvwxwq5hf4uqva6q&referrer=parent&backto=issue,2,6;journal,2,60;linkingpublicationresults,1:102504,1;",
  DOI =          "doi:10.1007/s00158-004-0460-6",
  abstract =     "The second-order polynomial is commonly used for
                 fitting a response surface but the low-order polynomial
                 is not sufficient if the response surface is highly
                 nonlinear. Based on genetic programming (GP), this
                 paper presents a method with which high-order smooth
                 polynomials, which can model nonlinear response
                 surfaces, can be built. Since in many cases small
                 samples are used to fit the response surface, it is
                 inevitable that the high-order polynomial shows serious
                 overfitting behaviors. Moreover, the high-order
                 polynomial shows infamous wiggling, unwanted
                 oscillations, and large peaks. To suppress such
                 problematic behaviors, this paper introduces a novel
                 method, called directional derivative-based smoothing
                 (DDBS) that is very effective for smoothing a
                 high-order polynomial. The role of GP is to find
                 appropriate terms of a polynomial through the
                 application of genetic operators to GP trees that
                 represent polynomials. The GP tree is transformed into
                 the standard form of a polynomial using the translation
                 algorithm. To estimate the coefficients of the
                 polynomial quickly the ordinary least-square (OLS)
                 method that incorporates the DDBS and extended data-set
                 method is devised.

                 Also, by using the classical Lagrange multiplier
                 method, the modified OLS method enabling interpolation
                 is presented. Four illustrative numerical examples are
                 given to demonstrate the performance of GP with DDBS.",

Genetic Programming entries for Yun Seog Yeun Young-Soon Yang Won-Sun Ruy B J Kim