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中文摘要：
针对信赖域方法求解多峰值优化不能收敛到全局最优的问题，提出了一种信赖域遗传算法，该算法将遗传算法和信赖域方法进行了结合。利用了遗传算法繁殖算子的随机性和信赖域方法求解二次优化问题的高效性，该算法能够克服信赖域方法的缺点同时能够有效求解一类欺骗性问题。最后证明了算法的收敛性，通过数值试验说明了算法的有效性。
英文摘要：
To overcome the shortcoming of general trust region method which cannot converge the global optimum of multi-peak optimization problems. Genetic algorithm based on trust region method is presented which combines genetic algorithm and trust region method. Using the randomicity of reproduce operators of genetic algorithm and the high efficiency of trust region method to solve quadratic optimizations, the proposed algorithm can overcome the limitation of trust region method and solve efficiently a class of deceptive problems. Finally, the convergence is proved and numerical experiments show that the algorithm works well.
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Three symmetric solutions for a class of elliptic equations involving the p-Laplacian with discontin
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