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— 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.

泛舟是游客操纵小艇游历湍急河流的过程,为了给游客更多的自由,多日泛舟已逐渐流行起来,随之而来的避免不同游客相遇前提下行程安排问题亟待解决。该项目提出了泛舟者模型来描述一个叫做大长河的国家公园中,游客(泛舟者)的行为并据此计划小艇的出发时间。基于此模型研究者完成了一个模拟泛舟者决策的算法和一个对小艇出发时刻表的评价系统,继而结合二者提出了最佳出发时刻表的算法并解决了该问题。

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.

对来享受大自然自由的小艇泛舟者而言,像列车时刻表一样详细的计划并不适用于大长河国家公园的情况,小艇的出发时刻应当仅包含出发时间和皮划艇类型。研究者们总结了泛舟者在各个关键节点处做决定的过程从而形成了泛舟者模型,基于此的仿真算法能够在给定出发计划下模拟出游客们详细的实际行程。

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.

利用层次分析法获得的权重因子和仿真出来的详细行程,评价系统能够对发艇计划给予评价。基于此评价系统而构建的适应函数,通过遗传算法的方式实现了最佳出发时刻表算法。

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.

最终,研究者计算出了最佳的出发时刻表并与现有的研究结果进行了对照从而验证了本模型。泛舟者模型易于理解和实现并且贴近实际情况。此研究成果获得数学建模竞赛的荣誉提名奖(二等奖)。

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