一种针对收敛性问题的改进进退法及其仿真验证

进退法是最优化方法中一种常用且简单的一维单峰试探搜索算法.针对进退法的收敛性和收敛速率展开研究,在讨论了进退法的算法原理及其实施步骤的基础上,针对原算法在某些情况不收敛的问题,提出了一种改进的进退法,将原算法每次进退迭代中的转向步长变为与前一步长和迭代次数有关的函数, 这样可以克服原算法不收敛的缺点.通过严格的理论推导证明了改进进退法的正确性,并利用实例仿真验证了其有效性.结果表明:进退法收敛速率不稳定,依不同初始参数而不同,改进进退法以降低收敛速率为代价而保证收敛性.

An Improved Advance-Retreat Method Aimed at Convergency and Simulation Proof

Advance-retreat method is a one-dimension searching algorithm of the optimal theory and a method for single peak function, which is very simple and in common use. The main work of this paper aims at the problem of convergence and convergent speed stated as follows. Firstly, the theory and process of advance-retreat method is discussed. Secondly, an improved advance-retreat method is proposed for conquering the drawback that the original method is not convergent at some conditions. By the improved method, the alternative step changes to a function of forehead step and iterative time. Thirdly, by a strict theoretical derivation the correctness of the method is proved. Fourthly, the effectiveness of the method is verified by simulation results. Finally, the results show that the convergence speed of the advance-retreat method is changeable with the different initial parameters and by using the improved advance-retreat method, the convergence is guaranteed at any case at the cost of decreasing the convergence speed.