Abstract

A tutorial is presented on Global Approximation, a mathematical procedure useful for the optimisation of complex systems. The state-of-the art numerical algorithms that can be exploited within a Global Approximation approach are reviewed. Some original numerical procedures are also proposed, such as using Low Discrepancy Sequences to train Multilayer Perceptron Neural Network (MLPNN) or Radial Basis Function Neural Network (RBFNN). The final aim of the research is to find a mathematical algorithm for Global Approximation which requires a minimum of expertise to be effectively used. A number of candidate algorithms for such a kind of Global Approximation are comparatively tested with reference to a vehicle design optimisation problem. The result is that the RBFNN can be as efficient as the MLPNN, which is much harder to train, when used to find a satisfactory approximation of the relationships among design variables and objective functions which define the road holding and handling performance of a race car. It is envisaged that in the future Global Approximation could be used to derive the relationship between Pareto-optimal design variable values and Pareto-optimal objective function values.

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