— Optimal Set-Off Diagram Algorithm based on Raftsman Model

The Consortium for Mathematics and Its ApplicationsIt is a research teamwork finished during the Mathematical Contest in Modeling by COMAP in 2012. 这是2012年由美国数学与应用数学组织举办的数学建模竞赛的小组研究成果。
Rafting is a popular outdoor activity using rafts to navigate a river on a white water, which makes the raft passengers excited. Giving much more freedom to travelers, multi-day trips become popular these days. As the growing of travelers flow, the arrangement of rafting trips to avoid different rafts meet has been a critical problem. This project proposes Raftsman Model to describe the behavior of tourists (raftsman) and schedules the rafts’ departure in a national park called Big Long River. Based on Raftsman Model, the researchers come up a simulation algorithm of raftsman’s decisions and evaluation system on set-off diagrams of rafts. The problem is solved by Optimal Set-Off Diagram Algorithm combined with the simulation and the evaluation.


To the tourists go rafting pursuing for the freedom in wilderness, the train-diagram-like sophisticated schedule should not be suitable or economical for the Big Long River. The suitable schedule should only consist of the time to set off and the type of rafts. This researchers summarized the process of raftsmen making-decisions on the critical points, which constitutes Raftsman Model, upon which the Simulation Algorithm of Raftsmen’s Decisions simulates the detail journeys under a specific rafts schedule.


A Calculated Rafts Timetable (一个计算出的出发时刻表)

With the weights of factors calculated by Analytic Hierarchy Process and the detail journeys simulated upon a schedule, Evaluation System gives the rating of a set-off diagram. With the fitness function based on the ratings of set-off diagrams, Genetic Algorithm constitutes Optimal Set-Off Diagram Algorithm. Then, an optimal set-off schedule is obtained.


Finally, the researchers computed the optimal diagram and conducted a comparison with present research to verify their model. The framework of the Raftsman Model is easy to understand and implement. It is close to the reality, which makes it extensible. This research won the Honorable Mentioned Prize of Mathematical Contest in Modeling by COMAP.


* COMAP is the trademark of COMAP. COMAP是美国数学与应用数学组织的注册商标。


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