Abstract—The roughness grade analysis on fitness landscape is helpful for obtaining the difficulty of the multi-dimensional function optimization problem, improving the optimization algorithms, and finding all local minima. Firstly, comparison studies are carried out on several commonly used indicators that depict the roughness of fitness landscape, such as autocorrelation function index, the improved fitness distance correlation (FDC) coefficient index, which are calculated using samples instead of differentiability of the function. A comprehensive index called roughness grade (RG) is constructed to measure the roughness of the fitness landscape by utilizing indices such as total variation of the function, rate of decline, FDC, etc. The advantages and disadvantages of the roughness indicators are summarized according to the results of experiments, which show that the improved FDC index and RG index are qualified for measuring different aspects of the roughness characteristics, and the improved FDC index has advantages over RG on fixed value range, less samples required, and simple calculation, thus can be used as main index, while RG index can be used as aided index for designing roughness grade based optimization algorithms of multi-dimensional function.
Index Terms—Fitness landscape, fitness distance correlation (FDC), multi-dimensional function, roughness grade.
S. H. Wu is with the Equipment Management and UAV Engineering College, Air Force Engineering University, China (e-mail: wu_s_h82@sina.com).
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Cite: Shi Hui Wu, "Roughness Grade Analysis on Fitness Landscape for Optimization Problem of Multi-Dimensional Function," International Journal of Modeling and Optimization vol. 10, no. 3, pp. 97-103, 2020.
Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
(CC BY 4.0).
