2015 HiMCM B题特等奖学生论文下载6129

2015 HiMCM B题特等奖学生论文下载6129

 

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论文摘要如下：

18th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet (Please attach a copy of this page to your Solution Paper.)

Team Control Number: 6129 Problem Chosen: B

Please paste or type a summary of your results on this page. Please remember not to include the name of your school, advisor, or team members on this page.

Summary
Our task was to analyze the safety of My City given crime data of the city. In analyzing the city, it is important to be able to compare the city to other similar sized cities. Simply giving a value for the safety of a single city is meaningless without comparing it to other cities. In order to do this, we designed a simple model and extended model to process different specificities of crime data and return a bounded index of city safety.

 

Our model assigns a cumulative safety index from 0 to 100, in which an index of 100 indicates absolute safety and lower indices signify increased levels of danger. We categorized and weighted crimes based on their severity in the calculation, and, to calculate our safety index, we inputted the crime rate of a crime category into a logistic function.

 

We opted to use logistic functions to describe the effect of crime rate on the safety of a city. We believe that this approach yields an effective model because logistic functions are monotonic, meaning that they are either always increasing or always decreasing. This aligns with our assumption that the addition of a crime either negatively impacts the safety of a city or does not affect it. Furthermore, a logistic function is bounded above and below, yielding a bounded safety index. This allows one to make meaningful comparisons between the safety indices of different cities or other populaces.

 

We choose our solution set of logistic functions using a genetic algorithm,This process iterates over many generations, gradually shifting the set toward better fits for the predetermined data and eventually converging to a single solution if the conditions are selective enough.

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