Fractal Analysis of the Optimal Objective Function

Abstract:

The fractals of the optimization problems are first discussed. The multi-fractal parameters of the optimal objective function are computed by the Detrended Fluctuation Analysis (DFA) method. The multi-fractal general Hurst Index is related to the difficulty to solve the optimization problem. These features are verified by analyzing the first six test functions proposed on 2005 IEEE Congress on Evolutionary Computation. The results show that the different objective functions have obvious different multifractal and the general Hurst Index can be used to evaluate the difficulty to solve the optimization problem.

• Periodical: Applied Mechanics and Materials (Volumes 519-520)
• Pages: 811-815
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.519-520.811
• Online since: February 2014
• Authors: Xiao Hong Qiu*, Yong Bo Tan, Bo Li
• Keywords: Algorithm (GA), Detrended Fluctuation Analysis, Fractal, Objective Function, Optimization

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