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Evolving intervening variables for response surface approximations

Evolving intervening variables for response surface approximations
Evolving intervening variables for response surface approximations
Genetic Programming (GP) is a powerful string processing technique based on the Darwinian paradigm of natural selection. Although initially conceived with the more general aim of automatically producing computer code for complex tasks, it can also be used to evolve symbolic expressions, provided that we have a fitness criterion that measures the quality of an expression. In this paper we present a GP approach for generating functions in closed analytic form that map the input space of a complex function approximation problem into one where the output is more amenable to linear regression. In other words, intervening variables are evolved in each dimension, such that the final approximation model has good generalization properties and at the same time, due to its linearity, can easily be incorporated into further calculations. We employ least squares and cross-validation error measures to derive the fitness function that drives the evolutionary process. Results are presented for a one-dimensional test problem to illustrate some of the proposed ideas – this is followed by a more thorough empirical study, including multi-dimensional approximations and an engineering design problem.
1-12
American Institute of Aeronautics and Astronautics
Sobester, Andras
096857b0-cad6-45ae-9ae6-e66b8cc5d81b
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
Sobester, Andras
096857b0-cad6-45ae-9ae6-e66b8cc5d81b
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def

Sobester, Andras, Nair, P.B. and Keane, A.J. (2004) Evolving intervening variables for response surface approximations. In Proceedings of the 10th AIAA/ISSMO multi-disciplinary analysis and optimization conference. American Institute of Aeronautics and Astronautics. pp. 1-12 .

Record type: Conference or Workshop Item (Paper)

Abstract

Genetic Programming (GP) is a powerful string processing technique based on the Darwinian paradigm of natural selection. Although initially conceived with the more general aim of automatically producing computer code for complex tasks, it can also be used to evolve symbolic expressions, provided that we have a fitness criterion that measures the quality of an expression. In this paper we present a GP approach for generating functions in closed analytic form that map the input space of a complex function approximation problem into one where the output is more amenable to linear regression. In other words, intervening variables are evolved in each dimension, such that the final approximation model has good generalization properties and at the same time, due to its linearity, can easily be incorporated into further calculations. We employ least squares and cross-validation error measures to derive the fitness function that drives the evolutionary process. Results are presented for a one-dimensional test problem to illustrate some of the proposed ideas – this is followed by a more thorough empirical study, including multi-dimensional approximations and an engineering design problem.

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More information

Published date: 2004
Additional Information: AIAA 2004-4379
Venue - Dates: Multidisciplinary Analysis and Optimization Conference, 2004-08-30 - 2004-09-01

Identifiers

Local EPrints ID: 22962
URI: https://eprints.soton.ac.uk/id/eprint/22962
PURE UUID: 669746bb-b39c-4dc7-bbd4-38d9c5123706
ORCID for Andras Sobester: ORCID iD orcid.org/0000-0002-8997-4375

Catalogue record

Date deposited: 03 Apr 2006
Last modified: 20 Jul 2019 01:03

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