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Multidimensional Scaling and Genetic Algorithms: A Solution Approach to Avoid Local Minima

Stefan Etschberger and Andreas Hilbert

No 181, Arbeitspapiere zur mathematischen Wirtschaftsforschung from Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie

Abstract: Multidimensional scaling is very common in exploratory data analysis. It is mainly used to represent sets of objects with respect to their proximities in a low dimensional Euclidean space. Widely used optimization algorithms try to improve the representation via shifting its coordinates in direction of the negative gradient of a corresponding fit function. Depending on the initial configuration, the chosen algorithm and its parameter settings there is a possibility for the algorithm to terminate in a local minimum. This article describes the combination of an evolutionary model with a non-metric gradient solution method to avoid this problem. Furthermore a simulation study compares the results of the evolutionary approach with one classic solution method.

Date: 2002
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