New Methods of Studying Valley Fitness Landscapes
This work addresses a foundational gap in evolutionary optimization by providing formal tools for analyzing fitness landscapes, though it appears incremental as it builds on existing concepts like homeomorphism and PCA.
The paper tackles the problem of rigorously defining and identifying valleys in high-dimensional fitness landscapes, presenting two methods: a topological definition of valleys as one-dimensional manifolds and a statistical algorithm using PCA to locate and orient valleys.
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.