Combinatorial optimization design for the identification and classification of mathematical knots**

通过竞赛和基于游戏的数学内容，驯鹿竞赛激发了对数学的热情，并激发了学生学习的更高成就。在不断增长的教育游戏市场中，驯鹿竞赛不断面临着开发新的有趣的互动数学挑战的需求，以保持领先于竞争对手，并抓住和保持儿童的注意力。为此，Caribou Contests想开发一个新的，独特的和互动的STEM教育模块，关于结，在三维空间中的字符串闭环。尽管存在几个关于结的网页，但允许人们交互式使用结的网站还不存在。这种类型的交互式格式非常适合接触年轻学生，在在线课程内容和数学竞赛中探索结理论中的空间概念。* 该研究项目是开发一种用于结识别的计算机搜索，使结相互变形，从而在其他方法无法做到的情况下证明它们的等效性。有两个密切相关的计算挑战：第一，找到“最简单”的图表示一个给定的结，第二，以确定是否两个给定的结是等效的。两种搜索策略，遗传算法和模拟退火，将被应用到这个研究问题。我们的方法是创新的，因为如果成功的话，它将提供结身份的证明，并可以在视觉上翻译为在线教育材料，以吸引学生。该程序产生的变形序列也可用于研究目的。*该项目的结果将使驯鹿竞赛开发一个关于纽结理论的应用程序，为在线竞赛创建问题，并在其电子商店中作为迷你课程出售，从而为通常对数学不感兴趣的学生打开数学之门，并进一步激励已经对数学着迷的学生。 ************************

Through competition and game-based math content, Caribou Contests stimulates enthusiasm for math and inspires higher achievement in student learning. In the growing market of educational games, Caribou Contests is continually faced with the need to develop new and interesting interactive mathematical challenges to stay ahead of competitors and to grasp and hold on to the attention of children. To this end, Caribou Contests would like to develop a new, unique and interactive STEM educational module about knots, closed loops of string in three-dimensional space. Although several web pages on knots exist, a web site that allows one to work with knots interactively does not yet exist. This type of interactive format is ideally suited to reach out to young students to explore spatial concepts in knot theory in online course content and math competitions. ****The research project is to develop a computer search for knot identification, enabling the deformation of knots into each other and thus prove their equivalence when other methods cannot. There are two closely related computational challenges: first to find the "simplest" diagram representing a given knot, and second to identify whether two given knots are equivalent. Two search strategies, Genetic Algorithms and Simulated Annealing, will be applied to this research problem. Our approach is innovative because, if successful, it will provide a proof of knot identities and can be translated visually to online education materials to engage students. The resulting deformation sequences from this program are also useful for research purposes.****Results of the project will enable Caribou Contests to develop an application about knot theory to create questions for online contests and to sell as a mini-course in their e-shop, thereby opening the door to mathematics for students normally not interested in it, and further motivating students already fascinated by mathematics. ************************