Pareto multi-objective optimization for high locality-preserving space-filling curve identification

Abstract

Space-filling curves are widely used in applications that take advantage of the locality-preserving property. The pattern (the first order curve) plays a central role in locality preserving property. This was highlighted in previous works well-received by the community. A formulation was established leading to defined new patterns, including competitive patterns, i.e., patterns carrying comparable (and sometimes better) locality-preserving level than the Hilbert curve, so far the reference. Nevertheless, the number of pattern solutions resulting from the given formulation exponentially grows up with the space dimension.

In this article, with the help of an evolutionary algorithm, an original approach dedicated to the identification of high locality-preserving multidimensional patterns is proposed. Our idea is to embed the problem in a multi-objective optimization framework guided by Pareto optimality. In a such framework, each locality score (through a standard criteria) obtained by a pattern at a specific radius value can be processed as an objective function (to be minimized). The overall multi-objective function then illustrates how well the objectives are met, i.e. how the locality is achieved as progressively the space is filled. So, several space radii of interest are taken into account in the locality estimation and not a single one. This track contributes to define an accurately process of pattern identification.

Comparative experimental results led on dimensions upper than three, seem to confirm that the proposed approach is Reliable, Efficient and Flexible. The results showed that the classical RBG pattern is not Pareto optimal in the 5-D case and alternative patterns are emerging. Finally, being able to identify patterns that preserve locality at a competitive level compare to the referent Hilbert curve (RBG pattern-based) constitutes a real contribution and could greatly improve the effectiveness of applications.