Diversity Enhancement via Magnitude

• URL: http://arxiv.org/abs/2201.10037v1
• Date: Tue, 25 Jan 2022 01:38:53 GMT
• Title: Diversity Enhancement via Magnitude
• Authors: Steve Huntsman
• Abstract summary: We use the recently developed theory of magnitude to construct a gradient flow and similar notions that systematically manipulate finite subsets of Euclidean space to enhance their diversity. We demonstrate diversity enhancement on benchmark problems using leading algorithms, and discuss extensions of the framework.
• Score: 7.005458308454871
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Promoting and maintaining diversity of candidate solutions is a key requirement of evolutionary algorithms in general and multi-objective evolutionary algorithms in particular. In this paper, we use the recently developed theory of magnitude to construct a gradient flow and similar notions that systematically manipulate finite subsets of Euclidean space to enhance their diversity, and apply the ideas in service of multi-objective evolutionary algorithms. We demonstrate diversity enhancement on benchmark problems using leading algorithms, and discuss extensions of the framework.

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