Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Journal of Global Optimization
Parameter identification of chaotic systems using evolutionary programming approach
Expert Systems with Applications: An International Journal
Accelerating Differential Evolution Using an Adaptive Local Search
IEEE Transactions on Evolutionary Computation
Computers & Mathematics with Applications
Comparison of evolutionary-based optimization algorithms for structural design optimization
Engineering Applications of Artificial Intelligence
Artificial bee colony algorithm and pattern search hybridized for global optimization
Applied Soft Computing
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Parameter identification of chaotic systems is an important issue in nonlinear science and has attracted increasing interest from a variety of research and application fields. Essentially, parameter identification can be formulated as a multi-dimensional optimization problem. By combining differential evolution (DE) and Nelder-Mead (NM) simplex search, an effective hybrid algorithm named NMDE is proposed in this paper. By suitably fusing the DE-based evolutionary search and NM simplex-based local search, exploration and exploitation abilities can be well balanced and satisfactory optimization performances can be achieved. The NMDE hybrid algorithm is applied to parameter identification of several typical chaotic systems. Numerical simulation and comparisons with some typical existing algorithms demonstrate the effectiveness and robustness of the proposed hybrid NMDE algorithm. Moreover, the effects of noise and population size on the performances of NMDE are investigated as well.