2022年美国大学生数学建模-【美赛】A题：Game Theory in Cycling（附获奖论文）

目录

Summary

1 Introduction

1.1 Problem Background

1.2 Restatement of the Problem

1.3 Our Work

2 Assuptions and Justififications

3 The Data

4 Notations

5 Analysis and Modeling

5.1 Model I: Power Output and Recovery

5.1.1 Power Curve

5.1.2 Power Profifiles of Three Typical Riders

5.2 Model II: Optimal Power Distribution

5.2.1 Power and Energy Analysis

5.2.2 Weather Condition Analysis

5.2.3 Dynamic Analysis

5.2.4 Optimization of Power Distribution

5.3 2021 Olympic Time Trial course

5.4 2021 UCI World Championship time trial course

5.5 Self-Designed Course

6 Sensitivity Analysis

6.1 Weather Conditions

6.2 Deviations From Target Power Distribution

7 Extend Our Model

7.1 Simplifified Situation

7.2 Complex Situation

8 Discussion

8.1 Strengths and Weaknesses

8.2 Future Work

9 Guidance

 References

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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 inflfluential factors. We