Abstract
Due to conventional differential evolution algorithm is often trapped in local optima and premature convergence in high dimensional optimization problems, a State Evaluation Adaptive Differential Evolution algorithm (SEADE) is proposed in this paper. By using independent scale factor on each dimension of optimization problem, and evaluating the distribution of population on each dimension, the SEADE correct the control parameters adaptively. External archive and a moving window evaluation mechanism on evolution state are introduced in SEADE to detect whether the evolution is stagnation or not, and with the help of opposition-based population, the algorithm can jump out of local optima basins. The results of experiments on several benchmarks show that the proposed algorithm is capable of improving the search performance of high dimensional optimization problems. And it is more efficient in design FIR digital filter using SEADE than conventional method like Parks-McClellan algorithm.
Highlights
FIR digital filter is an important component of digital signal processing system [1]
With the characteristics of system stability, easy to achieve linear phase, allowing to design of multi passband/stopband and easy to implement in hardware, FIR digital filter has been widely used in communications, voice and image processing, radar, biomedical systems, consumer electronics system, seismic exploration and other fields [2]
Similar to other evolutionary algorithms, Differential Evolution (DE) is easy to fall into local optima and premature convergence in solving high dimensional optimization problems
Summary
FIR digital filter is an important component of digital signal processing system [1]. The frequency sampling method and the window function method are simple, but it is difficult to accurately determine boundary frequency of passband and stopband of the filter Uniform approximation method, such as Parks-McClellan algorithm [6], can obtain better passband and stopband performance, and can accurately specify the passband and stopband edge, but the amplitude error relative value of frequency band is specified by the weighting function rather than by the deviation of FIR digital filter. We present a State Evaluation Adaptive Differential Evolution algorithm (SEADE), aiming at the shortcomings of DEs in solving high dimensional optimization problems. SEADE correct the control parameters using the feedback of the state of population and evolution, and jump out of local optima basins through external archive and opposition-based population. Where Vi,G is the mutation vector generated by Xi,G, r1i , r2i and r3i are mutually exclusive indices randomly chosen from solution space, which are different from i, and F is the scaling factor which control the magnitude of the difference component
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