2019建模美赛B题(派送无人机)M奖论文
本文末尾附上了题目以及论文的链接,可以直接打开的(好多人找我要论文,懵了)~
昨天上午出了建模美赛的结果,我们小组获得的是M奖,感觉挺开心的。我一直觉得拿O奖那种是个概率事件,需要天时地利人和的各种因素都合适才行,所以看到自己是M奖,感觉自己的能力已经得到了认可就很满意了。今天看了下比赛结果分析,看到今年M奖和O奖比例分别为7.09%和15.35%,大部分同学只拿到了S奖(成功参赛奖),中国学生获奖比例更是少的可怜,感觉挺惊讶的,今后的同志们继续加油吧~
关于美赛,我感觉它和国赛的差别还是挺大的。表面上看是任务量加大了很多,以及增加了语言上的阻碍(阅读和表达),但实质上差别更在于两者的问题指向不同,两者的思路是完全不同的。具体说来,国赛是把来源于实际的问题抽象简化到适合直接运用数学模型解决,因此国赛做出来的结果是确定以及准确的,而美赛则直接把实际中问题拿来研究,它可能本身就是一个“不可解决”的问题,没有模型的模型,需要我们置身于实际问题当中,设法去解决它。这更多的是需要一种“启发式”的方法,你没办法得到真正的最优,但你可以根据合理的“启发”,找出我们人类能够找到的最优解。
这就像是中国要划分34个省,美国有50个州一样,尽管这种划分与整体达到最大效益并无联系,甚至可能会导致效益降低,但若不作划分,中央哪能直接管理这么大片的地方?问题便无解了。而在划分后,再去求每区域的最优解,还有可能在解决问题过程中再对这种划分做调整,就像是我们的直辖市、自治区等等,这便是启发式方法的最佳体现了。
可能是我领悟的太慢,在集中准备美赛的12天和正式比赛的4天中,我一直在以国赛的思路尝试解决美赛的问题,结果发现难以拿出一个合适的模型,能够求得当前问题的最优解。比赛当中,总感觉这些问题是“按下葫芦浮起瓢”,这句话恐怕会是很多参加过美赛的人共同感受吧~我是在最后的时间里才意识到我思维进入的坑,理解了老美的思路后我豁然开朗,但来不及重新开始建模也让我感觉遗憾。
由于比赛那几天我始终没有进入那种集中思考的状态,而且美赛的任务量大到超过我的预期,所以论文其实是匆匆赶完的,瑕疵很多,不满意的地方也很多。不过最近实在太忙,待到清闲时我再针对我们的原论文及对比一些O奖论文做一些评注总结,以及对我们的原论文做一次修改,让它更完美一些。
英文摘要如下,全文请移步文末复制连接下载,有问题可留言或通过QQ交流~
An Optimal strategy of Aerial Disaster Relief Response System
Summary
Analyzing the influence of the hurricane in Puerto Rico, we recommend a transportable disaster response system to the HELP, Inc., including number and locations of Cargo containers. And we make strategy for medical packages delivery and video reconnaissance of road networks.
We cluster cities on the island and select three areas according to the limitation of the number of containers and the level of urgency. Then we establish a relief utility-cost model, which can measure the profitability according to the severity of the disaster in different areas and the population density of the area. Optimizing the utility-cost model, we determine the number of the containers in each area.
In order to determine the locations of containers from many ports around each area, we establish a multi-objective optimization model with two objectives: minimizing the cost of medical packages delivery and the cost of video reconnaissance of road networks. We determine the best locations of containers by optimizing the multi-objective program.
Aiming at two missions in relief, we select drones according to their medical packages delivery ability and video reconnaissance ability. By means of the AHP method, we select type B drone and type F drone as the best types in road reconnaissance and medical delivery respectively. And with the constraints of the demand in each area and the limitation capacity of containers and cargo bays, we determine the number of drones and medical packages.
Constructing the graph of main roads in each area, we define the value of each edge measured by the length of corresponding road. Applying genetic algorithm to maximize the value of roads to be videoed, we design the best flight route of video reconnaissance.
The sensitivity analysis shows the strong robustness of our model. Variation of key parameters cause moderate changes to the computing result.
Keywords: relief utility-cost model; multi-objective optimization; AHP method; graph; Genetic Algorithm
原题目下载连接:https://files.cnblogs.com/files/qujunhui/2019_MCM_Problem_B.rar
原论文下载连接:https://files.cnblogs.com/files/qujunhui/1906843.rar
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