【作者】 胡行华；

【导师】 高雷阜；

【作者基本信息】 辽宁工程技术大学 ， 管理科学与工程， 2008， 硕士

【摘要】 混沌是非线性确定性系统所产生的类似随机的运动,研究表明混沌序列具有遍历性、非周期性、随机性等特性。由于混沌序列的这些特性,我们可以将混沌序列引入到优化领域中。自李兵将混沌序列应用到优化领域以来,取得了较快的发展。然而大多数的混沌序列都局限于用Logistic映射产生,由于Logistic映射所产生序列极不均匀,因此大大地浪费了计算的时间。本文对Logistic映射、立方映射和无限折叠映射进行了比较,并分析了他们的混沌特性,通过实验仿真和数据统计,发现后两种映射所产的混沌序列更均匀些,加快了搜索全局最优解的速度。传统的优化算法能够很好地解决单极点的优化问题,但对于多极点的优化问题往往很难达到令人满意的结果;而混沌优化算法在解决多极点的优化问题时能够体现出它的优势。本文对传统的优化算法和混沌优化算法进行比较,并应用于求解多极点的全局最优解和实际经济问题所建立的数学模型,得出的结论是,在解决多极点的优化问题时,混沌优化算法明显优于传统的优化算法。最后,对于混沌优化算法进行了总结,提出其不足之处和有待进一步研究的方向。更多还原

【Abstract】 Chaos is kind of similar to random movement that generated from nonlinear- uncertainty system. Studies have shown that chaotic sequence was characterized with ergodicity, non-cyclical and randomness etc. As a result of these characteristics, we may introduce the chaos sequence in the optimization field. Since the chaos sequence applied in the optimization field by Li Bing, it has made the rapid development. However, the majority of chaos sequences was limited in generation of Logistic-map, because the sequence generated from Logistic-map was extremely non uniform, a large amount of computing work has been cost. Logistic map, cube mapping and unlimited folded maps were compared in this paper and the characteristics of their chaotic were analyzed, through simulation and statistics, it was found that the last two maps generated the more evenly chaotic sequence and faster search for global optimal solution.Traditional optimization algorithms can perfectly solve the optimization problem of unipolar, however, it was unsatisfied for multi-polar. Chaotic optimization algorithms take its advantages of resolving the problem. In this paper, the traditional and chaotic optimization algorithms were compared, and applied for resolving the multi-target extreme values and mathematical model for the actual economic problems. It was concluded that chaotic optimization algorithms was superior to the traditional. Finally, it was summarized regarding the shortcomings of chaos optimization algorithm and proposed further studies.更多还原