New Methods of Studying Valley Fitness Landscapes

Jun He; Tao Xu

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arXiv · 1805.00092

New Methods of Studying Valley Fitness Landscapes

Jun He·Tao Xu

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Abstract

The word "valley" is a popular term used in intuitively describing fitness landscapes. What is a valley on a fitness landscape? How to identify the direction and location of a valley if it exists? However, such questions are seldom rigorously studied in evolutionary optimization especially when the search space is a high dimensional continuous space. This paper presents two methods of studying valleys on a fitness landscape. The first method is based on the topological homeomorphism. It establishes a rigorous definition of a valley. A valley is regarded as a one-dimensional manifold. The second method takes a different viewpoint from statistics. It provides an algorithm of identifying the valley direction and location using principle component analysis.

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Jun He, Tao Xu. 2018-04-30. New Methods of Studying Valley Fitness Landscapes. https://arxiv.org/abs/1805.00092

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