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Generating Uniformly Distributed Points on a Unit Simplex for Evolutionary Many-Objective

Updated: Sep 17, 2021

Deb, K., Bandaru, S., & Seada, H. (2019). Generating uniformly distributed points on a unit simplex for evolutionary many-objective optimization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11411 LNCS, pp. 179–190). Springer Verlag.


Most of the recently proposed evolutionary many-objective optimization (EMO) algorithms start with a number of predefined reference points on a unit simplex. These algorithms use reference points to create reference directions in the original objective space and attempt to find a single representative near Pareto-optimal point around each direction. So far, most studies have used Das and Dennis’s structured approach for generating a uniformly distributed set of reference points on the unit simplex. Due to the highly structured nature of the procedure, this method does not scale well with an increasing number of objectives. In higher dimensions, most created points lie on the boundary of the unit simplex except for a few interior exceptions. Although a level-wise implementation of Das and Dennis’s approach has been suggested, EMO researchers always felt the need for a more generic approach in which any arbitrary number of uniformly distributed reference points can be created easily at the start of an EMO run. In this paper, we discuss a number of methods for generating such points and demonstrate their ability to distribute points uniformly in 3 to 15-dimensional objective spaces. Access publication.

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