EAGER: Physical Flow and other Industrial Challenges

动机。在许多社会挑战的核心，特别是考虑到可持续性和效率，有困难的优化问题。虽然这些潜在问题可以使用优化方法解决较小的设置，但实际问题的规模仍然令人望而却步。除了规模带来的直接挑战外，在当今快节奏和相互交织的经济中，我们还面临着解决实时方面的挑战；否则，得到的解决方案可能不再适用：问题变化的速度比解决的速度快。这个EAGER解决了由社会挑战引起的特定优化问题，并将激励对潜在优化问题的研究。为此，在连续和离散优化以及机器学习和随机化的交叉点将开发新的方法。知识价值。pi着手研究一般的解决方案策略，以解决问题的规模，实时需求，以及使用理论计算机科学和现代优化理论的最新发展的不确定性方面。该提案的核心是研究与货船路线、码垛、车辆和移动机器人路线及相关问题相关的现实挑战。与传统方法的一个主要区别是，实时需求不会被添加到顶部，而是集成到整个设计过程中，这可能会产生更好的算法。除了上述问题带来的挑战外，pi还打算开发一个在线专家系统——Ask Minmax。该平台将利用机器学习技术，为面临具有挑战性的优化问题的行业和其他人员提供优化方法和工具的理论。更广泛的影响。这项建议的一个关键目标是外联。EAGER将开发一种咨询工具，使工业界和更广泛的社会了解算法和优化中最有用的方法。特别是，该工具旨在帮助用户决定哪些方法最可能适用于他们的问题：该工具将以交互方式从用户那里收集有关其优化问题的信息。然后，系统将确定最可能的模型并提供信息。码垛和路由中的大规模挑战需要各种启发式和算法的组合。将对行业产生重大影响的第二个组成部分是为此类算法制定关键绩效指标。这些指标将有助于衡量特定启发式和/或算法的效率，当算法在更大的解决方案中组合时，这将非常重要。指导一名研究生、一名跨多个EAGERs共享的博士后学生并与之合作，以及在数学与应用研究所（IMA）举办相关前沿主题的研讨会，这些都是该EAGER更广泛影响的一部分。

Motivation. At the core of many societal challenges, particularly in view of sustainability and efficiency, there are hard optimization problems. While these underlying problems can be solved for smaller setups using optimization methods, realistic problem sizes are still prohibitive. Apart from the immediate challenges arising from sheer size, in today's fast-paced and intertwined economies we additionally face the challenge of addressing real-time aspects; otherwise, the obtained solutions might not apply anymore: the problem changed faster than it was solved. This EAGER addresses specific optimization problems arising from societal challenges and will motivate the study of the underlying optimization problems. For this, new methods at the intersection of continuous and discrete optimization as well as machine learning and randomization will be developed. Intellectual Merit. PIs set out to investigate general solution strategies to address problem size, real-time requirements, as well as uncertainty aspects using recent developments from theoretical computer science and modern optimization theory. At the core of this proposal is the study of real-world challenges related to cargo-vessel routing, palletizing, vehicle and mobile bot routing and related problems. A main difference to classical approaches is that the real-time requirements will not be added on top but will be integral to the whole design process, which is likely to result in better algorithms. Apart from the challenges from the aforementioned problems, PIs intend to develop an online expert system - Ask Minmax. This platform will leverage machine learning techniques to make the theory of optimization methods and tools accessible to industry and other personnel that face challenging optimization problems. Broader Impact. A key objective of this proposal is outreach. This EAGER will develop a consulting tool that will allow industry and the broader society to learn about most useful methods in algorithms and optimization. In particular, this tool is geared towards helping the user to make a decision regarding which methods are most likely to be applicable to their problem: in an interactive way the tool will collect information from the user about their optimization problem. The system will then determine the most likely model and provide information. Large-scale challenges in palletizing and routing require the combination of various heuristics and algorithms. A second component that will significantly impact industry is the developing of key performance indicators for such algorithms. These metrics will help to gauge efficiency of a particular heuristic and/or algorithms, which will be important when algorithms are combined within a larger solution. Mentoring and collaborating with a graduate student, a shared postdoctoral student across multiple EAGERs, as well as hosting a workshop in relevant frontier topics at the Institute for Mathematics and Applications (IMA) are all parts of the broader impact of this EAGER.