2022年美赛特等奖论文-2022-2022年A题获奖论文合集.pdf
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Problem Chosen
A
2022
MCM/ICM
Summary Sheet
Team Control Number
2200289
Game Theory in Cycling
Summary
The rider’s strategy has a huge impact on the outcome of the race. In this article, we
analyze the physiological and dynamic model of the rider’s power output, on the basis of which
we obtain the optimal power output strategy over the entire course using Simulated Annealing
Algorithm. We then conduct sensitivity analysis of possible influential factors. We extend our
model to Team time trial.
In Model 1, we establish a model describing the rider’s power limit and physical strength
based on physiology. By fitting the data in the literature, we obtain the quantitative parameters
of rider’s physical ability. Then a model describing the relation between power output and
duration is established and utilized to give power profiles of three different types of riders.
In model 2, the courses are divided into 1164 sections. We first conduct analysis of power
output, dynamic model and weather condition to quantitatively solve for energy and speed
variation and time for each section of the course. We use Simulated Annealing Algorithm to
optimize the power distr ibution over the course with the optimization objective of reducing the
total race time. We then apply the model to two realistic courses and one self-designed course
and give the optimal power distributions accordingly. All the results are properly explained.
In sensitivity analysis, we first examine the influence of wind speed and wind direction
on results in Model 2 by changing the two parameters in two different types of courses. And
we find that the closer the course gets to the circle ,the less sensitive our model is to weather
conditions.
When analyzing the sensitivity of the optimized results of the model to the deviations of
cyclis ts’ power distribution, We find that the total time is positively correlated with the variance
of disturbance and is fairly sensitive to it. Then we conduct sensitivity analysis on each road
section in turn to determine which road sections are the key parts and inversely solve for the
possible range of expected split times at key parts.
In the Extension part, we first study the simplified situation to consider the team as a whole.
We establish a model to describe the aerodynamic drag on each rider in all permutations. We
then study the comple x model that applies the strategy of sacrificing tw o wind breakers at cer tain
point. Based on Model 2, we change the objective function and add the dropping point as a
decision variable to extend our model to TTT.
Finally, we give a racing guidance for a certain course to introduce our model and demon-
strate how to use it.
Keywords: Physiology; Dynamics; Simulated Annealing Algorithm;
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