2016 HiMCM A题特等奖学生论文下载6453

2016 HiMCM A题特等奖学生论文下载6453

 

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论文摘要如下：

19th Annual High School Mathematical Contest in Modeling (HiMCM)

Summary Sheet

(Please make this the first page of your electronic Solution Paper.)
Team Control Number: 6453

Problem Chosen: A

Summary

In order to achieve the goal of reducing road congestion and ensuring participants proceed without hindrance, at the same time solve the problem of minimizing the competition time, this paper adopts the following 3 models to obtain solution:

First of all, in model1, according to the analysis of data from the last year competition, we extract the mean and standard deviation as basis of classification. We apply Cluster Analysis to divide all the participants into 6 groups, combining several original groupings and let the athletes at the similar level to be on the same group; the strengths of doing this are: reduce the total time of competition (avoid the time issue due to the overmuch division originally given by the question), ensure the participants will not cause hindrance to each other (competitors with similar level will not cause hindrance), and reduce the problem of road congestion.

In model 2, we apply the Genetic Algorithm to optimize the starting order and exact starting time of every group. We make the total time to be smallest under the condition of athletes in every group will not disturb mutually, no road congestion. The result turns out to be: the total competition time can be controlled within 4.5 hours, which achieves the goal of organizer. This algorithm can be applied to find the optimum solution in the shortest amount of time. This model can be used in common scheduling problem because of strong representation.

In model 3, we apply linear programming. First, we use variable-controlling method, under the result of optimum starting sequence of athletes derived in model 2; we consider the influence that distances of races will exert on road congestion and total competition time. For only minimizing the distances of race to optimize the total time is meaningless, this paper assumes the constricted condition of race distances and finally derives the linear programming model. The result shows, adjusted distance can farthest reduce the waiting time, which is set for the purpose of avoiding road congestion and mutual disturbance; as a result, maximize the efficiency of using time.

In conclusion, this paper solves and gives complete solution of the problem of reducing road congestion and minimizing total competition time, successfully achieve the goal of question. This paper has strong generality therefore can be applied to daily scheduling problem.

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