2011 HiMCM B题特等奖学生论文下载3192

2011 HiMCM B题特等奖学生论文下载3192

 

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论文摘要如下：

 

Losing objects is an inevitability of human existence. We lose objects, and occasionally, we lose ourselves.

 

In the first section of the problem, we were tasked with finding a lost object in Hopkinton State Park with only a pen flashlight at our disposal and the sun quickly setting. We constructed four different scenarios that tailor our model to an individual’s search, depending on what the pre-existing conditions exist. Our four models take into account various contingencies, considering whether or not the individual knows generally where the object is, and whether or not the individual stayed on the path. In situations where the individual stayed on the path, we aimed to maximize efficiency by minimizing redundant edge traversal through the use of Euler Circuits and Paths. If the individual knew a general area in which the object may be, we instead maximized area, increasing the probability that the object would be found by using an Archimedean Spiral, which has been shown to be the most efficient search pattern for an open area. We established 100%, 100%, 70.46%, and 2.21% certainty that our object would be found for each of the four scenarios. In the scenario with the the lowest probability, the low level of certainty is due to the complete lack of parameters for search; in this case, we maximized the area covered.

 

The second part of the problem asked us to devise a model for finding a jogger who has gotten lost at night in Fort Ord, using the pen flashlight as our only light source. We determined that the jogger’s intention of going on a 5.0 mile run meant that he or she is no more than 5.5 miles deep into the park, with 0.5 miles accounting for any wandering on the part of the jogger. For this scenario, we constructed two models: one that accounts for when the jogger is stationary and another for when the jogger is mobile. If the jogger is unconscious (and therefore stationary), the searcher must travel along the Euler path that extends a maximum of 5.5 miles in trails into the park depending on the jogger’s point of origin. If conscious, the jogger could rationally decide to remain in the same position, wander frantically, or wander out and return to the same starting point. Because we did not have any basis to accurately predict the behavior of the jogger, we made certain assumptions about the jogger’s path of travel. We once again used Eulerization to calculate the optimal search path to find a jogger moving in the park, based on his or her starting area. If this area-specific search along the Euler path is unsuccessful, then we decided that the searcher should travel along the most popular and prominent paths in the entire park. The combination of both methods greatly increases the efficiency and likelihood of finding the lost jogger, regardless of whether the jogger is conscious or unconscious.

 

While there were several limitations, such as the exclusion of terrain from our consideration, we believe that we have developed an optimal model with the given information that satisfies our logical assumptions. Our plan encompasses a variety of plausible scenarios,while minimizing total search time and maximizing probability of success.

 

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