Fuzzy multiobjective optimization with multivariate regression trees

We introduce a new methodology in which multiobjective optimization is formulated as unsupervised learning through induction of multivariate regression trees. In particular, it is shown that learning of Pareto-optimal solutions can be efficiently accomplished by using a number of fuzzy tree partitioning criteria. These include: a newly formulated fuzzy method based on Kendall´s nonparametric measure of association (G. Simon, 1977), Bellman-Zadeh´s approach to multiobjective decision making utilized in an inductive framework (R.E. Bellman and L.A. Zadeh, 1970), and finally, multidimensional fuzzy entropy (B. Kosko, 1990). For purposes of comparison, the efficiency of learning with fuzzy partitioning criteria is compared with that of two conventional multivariate statistical techniques based on dispersion matrices. The widely used problem of design of a three bar truss is presented to highlight advantages of our new approach