Induction of Multivariate Regression Trees for Design Optimization

B. Forouraghi, L. W. Schmerr, G. M. Prabhu

In this paper we introduce a methodology within which multiobjective design optimization is approached from an entirely new perspective. Specifically, we demonstrate that multiple-objective optimization through induction of multivariate regression trees is a powerful alternative to the conventional vector optimization techniques. Furthermore, in an attempt to investigate the effect of various types of splitting rules on the overall performance of the optimizing system, we present a tree partitioning algorithm which utilizes a number of techniques derived from diverse fields of statistics and fuzzy logic. These include: three multivariate statistical approaches based on dispersion matrices, two newly-formulated fuzzy splitting rules based on Pearson’s parametric and Kendall’s nonparametric measures of association, Bellman and Zadeh’s fuzzy decision-maximizing approach within an inductive framework, and finally, the multidimensional extension of a widely-used fuzzy entropy measure. In terms of potential application areas, we highlight the advantages of our methodology by presenting the problem of multiobjective design optimization of a beam structure.


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