Abstract—In order to overcome the inefficiency shortcoming of traditional step-based searching method for extremum seeking in two-dimensional fractional Fourier domain, some typical intelligent optimization methods such as genetic algorithms, continuous ant colony algorithm, particle swarm optimization and chaos optimization method are introduced and applied successfully in fractional Fourier transform. To accelerate the convergence further, three optimization methods containing two improved chaos optimization methods and another hybrid method combing chaos optimization and Quasi-Newton method are proposed. The performances of the proposed optimization methods are verified by comparing with step-based method and other intelligent optimization methods based on simulation. Results show that the presented hybrid optimization algorithm is much more preferable considering computation efficiency, precision and resolution in all the abovementioned optimization methods.
Index Terms—the fractional Fourier transform; genetic algorithms; continuous ant colony algorithm; particle swarm optimization; chaos optimization algorithm; Quasi-Newton algorithm; extremum seeking
Wei Hongkai is with Navy University of Engineering, Wuhan, China (email: email@example.com).
Cai Zhiming is with Navy University of Engineering, Wuhan, China (email: firstname.lastname@example.org).
Wang Pingbo is with Navy University of Engineering, Wuhan, China (email: email@example.com).
Fu Yinfeng is with Shanghai marine electronic equipment research institute, Shanghai, China (email: firstname.lastname@example.org).
Cite: Wei Hongkai, Cai Zhiming, Wang Pingbo and Fu Yinfeng, "Study of Intelligent Optimization Methods Applied in the Fractional Fourier Transform," International Journal of Computer Theory and Engineering vol. 2, no. 4, pp. 532-537, 2010.