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The Robustness of Hybrid Algorithms in Multimodal Functions Optimization

The Robustness of Hybrid Algorithms in Multimodal Functions Optimization. 姓名: 何怡偉 元智工業工程與管理博士班. The characteristic of Nelder-Mead simplex method. A simple direct search technique. Easy to use and does not need the derivatives of the function.

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The Robustness of Hybrid Algorithms in Multimodal Functions Optimization

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  1. The Robustness of Hybrid Algorithms in Multimodal Functions Optimization 姓名: 何怡偉 元智工業工程與管理博士班

  2. The characteristic of Nelder-Mead simplex method • A simple direct search technique. • Easy to use and does not need the derivatives of the function. • Very sensitive to the choice of initial points and not guaranteed to attain the global optimum.

  3. The characteristic of evolutionary computation technique • Eventually locate the desired solution. • The high computational cost of the slow convergence rate. • Do not utilize much local information to determine a most promising search direction.

  4. Nelder-Mead Simplex Operations

  5. The Structure of hybrid NM-GA

  6. The Structure of hybrid NM-PSO

  7. The populations design for the five algorithms

  8. The surface plot of the Himmelblau function

  9. The contour plot of the Himmelblau function

  10. Computational results on the Himmelblau function

  11. A surface plot of the peaks function

  12. A contour plot of the peaks function

  13. Computational Results on the peak function for searching the global maximum

  14. Summary • The proposed hybrid NM-GA and NM-PSO are indeed effective, reliable, efficient and robust at locating best-practice optimum solutions for multimodal functions. • Stochastic Optimization

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