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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 97
Edited by: Y. Tsompanakis, B.H.V. Topping
Paper 43

Control of Physical Consistency in Metamodel Building by Genetic Programming

U. Armani1, Z. Khatir2, A. Khan1, V.V. Toropov1,2, A. Polynkin1, H. Thompson2, N. Kapur2 and C.J. Noakes1

1School of Civil Engineering, 2School of Mechanical Engineering,
University of Leeds, United Kingdom

Full Bibliographic Reference for this paper
U. Armani, Z. Khatir, A. Khan, V.V. Toropov, A. Polynkin, H. Thompson, N. Kapur, C.J. Noakes, "Control of Physical Consistency in Metamodel Building by Genetic Programming", in Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 43, 2011. doi:10.4203/ccp.97.43
Keywords: genetic programming, high-fidelity design optimisation, metamodel, mathematical structure, non-linear system, analytical expression, engineering applications.

Soft computing has grown in importance in recent years, allowing engineers to handle more and more complex problems. Computer power has made different classes of computationally intensive techniques viable and successful alternatives to other established methods. Algorithms based on machine learning, data mining and genetically inspired methods are in some cases the only choice when the knowledge of the problem is scarce.

Genetic programming (GP) [1] can be considered one of the latest techniques to have appeared in the range of soft computing tools. It is a genetically-inspired method able to generate from a data set global metamodels describing the relationship between a system's input and output data. Typically, genetic operators are used to recombine parts of mathematical expressions in a randomised but directed way until a high quality metamodel (i.e. a model of a model) is found. The major strength of genetic programming lies in its ability to provide explicit metamodels, making possible the use of traditional analytical methods for the subsequent analysis and optimisation.

A problem arises that the stochastic nature of GP reduces the possibility of controlling the consistency of the generated metamodels. It is not uncommon in a conventional GP experiment to obtain expressions that despite showing low errors cannot be used in an application as their response is not consistent with the assumptions imposed by the problem's nature.

In this paper it is described how control of the "physical consistency" of the generated metamodels can be improved using some basic knowledge regarding the problem at hand by imposing constraints in the problem formulation. The benefits of the new strategy are shown through a benchmark problem. Two case studies where genetic programming has been successfully applied to optimise the ventilation design of an industrial bread baking oven and of a hospital ward are also presented. In both cases data provided by computational fluid dynamics (CFD) simulations were used to generate a metamodel and genetic algorithm techniques were used to find the optimum of the modelled response. Validation of the optimal point performed using data generated by additional CFD simulations confirmed the high quality of the metamodels. In a case study the optimum found by genetic programming matches the optimum found by another metamodelling technique.

J.R. Koza, "Genetic programming: on the programming of computers by means of natural selection", MIT press, Cambridge, USA, 1992.

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