抢渡长江模型

摘  要

本文就竞渡策略问题建立了竞渡路线优化模型。首先,就题中前2问所提出的问题给出了较精确的答案。然后分析了1934年和2002年能到达终点的人数的百分比差别之大的原因,并给出了能够成功到达终点的选手的条件。在对随后问题的分析过程中,本文提出了依据水速的变化来改变竞渡者速度方向的思路,并建立了模型2、模型3。模型2提出了1种比较理想化的竞渡策略,即依据水速的'变化随时变换人的速度方向,并根据所得的结果给出了1个较合理的水速分布函数,再根据实际情况得出1个更为合理的分布函数,建立了改进后的模型3。利用LINGO和Mathematica数学软件编程算出了问题的最优解。最后将本文所建立的模型做了1些推广,它们可以应用到航空,航天和航海等领域。

关键词：非线性规划; 3角函数; 逼近法

Abstract

The optimal model for crossing issue was established. At the beginning, exact results are presented on the first two questions given in the article. I also analyze the main reason for the percentages different of people who can succeed in reaching the opposite bank in 1934 and in 2002 and gives the necessary requirements for those who can reach the destination successfully. In 2002 the minimal speed of those successful competitors was 1. 43m/s. In the process of analyzing the latter problems, the idea that adjusting the competitors flat - out direction as current changes is brought forward to establish Model Ⅱ and Model Ⅲ. Model Ⅱ provides an ideal crossing way in the case that one can adjust his flat - out direction at any time as current changes and gives a relatively rational distribution function of water speed. By analyzing water speed on the foundation of the real condition , we get a more rational distribution function of water speed and build Model Ⅲ . The LINGO and MATHE-MATICA software are .

Key words: Nonlinear programming; trigonometric function; approximation method