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| Comparative study on chaos optimization algorithm for nonlinear function |
| Revised:December 08, 2002 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20043048 |
| KeyWord:global optimization,chaos optimization algorithm,nonlinear functions,chaotic/stochastic sequences,probability density function |
| Yang Dixiong Li Gang Cheng Gengdong* |
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| Abstract: |
| The chaos optimization algorithms in the published papers were almost based on Logistic map. However, the probability density function of chaotic sequence for Logistic map is Chebyshev-type function, which maybe affect the global searching capacity and computational efficiency of chaos optimization algorithm severely. Considering the statistical property of chaotic sequence of Logistic map, the improved hybrid chaos-BFGS optimization algorithm is presented in this paper by eliminating the bad design points during the chaos searching. Since the probability density function of chaotic sequence for Kent map is the uniform function on interval (0,1), the hybrid chaos optimization-BFGS algorithm is established on basis of Kent map. Five nonlinear functions (three low-dimensional and two high-dimensional functions) are employed to test the performance and efficiency of five hybrid optimization algorithms, which are improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, unimproved Logistic map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, and mesh-BFGS algorithm. The global optimization performance of these algorithms is compared, and the performance discrepancy of optimization algorithms is discussed. It is concluded that the chaos optimization algorithm is one kind of stochastic method similar to Monte Carlo method, and the computational performance of hybrid optimization algorithms is affected by the following factors: the statistical property of chaotic/stochastic sequences generated from optimization algorithms, and the position of global optimum of nonlinear functions. |
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