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搶渡長江模型
摘 要
本文就競渡策略問題建立了競渡路線優化模型。首先,就題中前2問所提出的問題給出了較精確的答案。然后分析了1934年和2002年能到達終點的人數的百分比差別之大的原因,并給出了能夠成功到達終點的選手的條件。在對隨后問題的分析過程中,本文提出了依據水速的變化來改變競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種比較理想化的競渡策略,即依據水速的變化隨時變換人的速度方向,并根據所得的結果給出了1個較合理的水速分布函數,再根據實際情況得出1個更為合理的分布函數,建立了改進后的模型3。利用LINGO和Mathematica數學軟件編程算出了問題的最優解。最后將本文所建立的模型做了1些推廣,它們可以應用到航空,航天和航海等領域。
關鍵詞：非線性規劃; 3角函數; 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
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