地球物理反演中的高效混沌优化改进算法

AN EFFICIENT AND IMPROVED CHAOS OPTIMIZATION ALGORITHM IN GEOPHYSICAL INVERSION

混沌方法已成为一种新颖且有潜力的优化工具。之前出现的几种基于混沌优化改进算法,其改进的核心就是在混沌优化搜索过程中,用已具有一定精度的当前最优解为中心,不断缩小优化变量的搜索区间,调整、细化参数,使搜索更快、更有效地向最优解收敛。但这些改进算法也存在明显的不足,当搜索起始点选择不合适、遍历区间很大或控制参数选取不合适时,搜索结果很难达到或接近最优解,上述算法也可能需要花费很长的时间才能取得较好的优化性能,同样易再次陷入局部解。针对上述问题,提出一种通过不断初始化初始参数,充分利用混沌的遍历性,无需在迭代中修改搜索空间但又可迅速得到最优解的优化方法,经对几个复杂函数及泊松比反演的测试表明,其方法为快速高效的优化算法,有望在地球物理反演中广泛应用。

Chaos method is a new and potential optimization tool. The cores of the previous several improved algorithms based on chaos optimization is taking the optimum solution with certain precision as the center to reduce the searching interval of the optimizing variable continuously during the searching process, to adjust and refine the parameters to gain the convergence of the optimum solution rapidly and effectively. However, there are some evident shortcomings in these improved algorithm; if the start point of the searching is not proper, and the ergodic interval is very large or the control parameters is not selected properly, the searching result can't reach or approach the optimum solution, and it will take a long time to make the algorithm have good optimizing capability, moreover, the algorithm is easy to be trapped in the local optimum solution. Aimed at the problems mentioned above, the paper put forward an optimizing method that initialized the initial parameters continuously, fully applied the ergodic property of the chaos, and did't need to modify the searching interval during the iteration, at the same time, could gain the optimum solution rapidly. The tests for several complicated functions and Poisson's ratio inversion indicates that this method is a rapid and effective optimizing algorithm, which will be widely applied in the geophysical inversion.