AI Planning and Mathematical Programming

人们和组织的许多日常活动都需要计划和安排：决定采取什么行动来实现一系列目标，以及决定何时应该采取行动以及使用什么资源。每天的通勤可能包括决定一个人最晚什么时候可以离开家准时到达一个重要的会议，同时考虑不同的出行方式(自行车、汽车、公共交通)，每种出行方式需要的时间，以及与其他目标的相互作用(例如，如果我开车，我下班后就不能和同事喝一杯了)。另一个例子是，像亚马逊这样的公司必须使用劳动力、仓库空间、卡车和燃料来协调货物的接收、储存、订单接收、包装和交付。*人工智能规划在过去15年中取得了长足进步，主要解决了采取什么行动的问题。相比之下，处理有关操作的时间和资源选择的选择的最成功的技术来自数学编程和约束编程学科。随着人工智能规划技术越来越多地被用于现实世界的应用，它必须越来越多地做出关于时间和资源的决定。*拟议的研究计划挑战了推理的挑战，即做什么，什么时候做，以及使用什么资源。提出的三个研究主题是在数学规划包含一套问题解决技术和理论基础的假设下统一起来的，这些技术和理论基础可以与人工智能规划相结合来解决这些挑战。*主题1将寻求统一和扩展现有的混合整数线性规划(MILP)方法来解决有时间和资源的人工智能规划问题，并开发基于约束整数规划(CIP)的新的规划技术。*主题2将专注于A*搜索的基本人工智能技术，并开发它以三种方式解决有资源和时间的规划问题：专注于解决简单的调度问题；使用LP松弛来计算A*启发式；并发展A*搜索、动态规划和多值决策图之间的关系。*主题3将采用原则性方法将问题分解应用于AI规划问题，重点关注懒惰约束生成和列生成的数学编程模式。*本研究计划专注于解决需要时间和资源推理的AI规划问题的基本进展。为了让这项研究扎根，该项目将与一个外部资助的协作机器人项目并行进行，该项目将把机器人安置在长期疗养院。此应用程序体现了我们在此计划中应对的挑战。虽然它与这里提出的是分开的，但机器人规划应用程序将作为灵感和试验台。**

Many of the day-to-day activities of people and organizations require planning and scheduling: deciding what actions to do to achieve a set of goals and deciding when actions should be done and with what resources. A daily commute might consist of deciding the latest time one can leave home to arrive in time for an important meeting while taking into account different ways to travel (bike, car, public transit), the time each one will take, and the interaction with other goals (e.g., if I drive I won't be able to have a drink with colleagues after work). As another example, a company such as Amazon must use labour, warehouse space, trucks, and fuel to coordinate the reception, storage, order-taking, packing, and delivery of goods. ****Artificial Intelligence planning has made substantial strides over the past 15 years, primarily addressing the problem of what actions to take. In contrast, the most successful technology to deal with choices about the timing and resource choices for actions arises from the mathematical programming and constraint programming disciplines. As AI planning technology is being increasingly used for real-world applications, it must increasingly make decisions about time and resources.***The proposed research program attacks the challenges of reasoning about what to do, when to do it, and what resources to use. Three proposed research themes are unified under the hypothesis that mathematical programming encompasses a suite of problem solving techniques and theoretical foundations that can be extended and integrated with AI planning to address these challenges.***Theme 1 will seek to unify and extend existing mixed integer linear programming (MILP) approaches to solving the AI planning problem with time and resources and to develop new planning technology based on Constraint Integer Programming (CIP).***Theme 2 will focus on the fundamental AI technique of A* search and develop it to solve planning problems with resources and time in three ways: focusing on solving simple scheduling problems; using LP relaxations to compute A* heuristics; and developing the relationship among A* search, dynamic programming, and multi-valued decision diagrams.***Theme 3 will take a principled approach to the application of problem decomposition to AI planning problems, focusing on the mathematical programming patterns of lazy constraint generation and column generation.***This research program is focused on fundamental advances in solving AI planning problems that require reasoning about time and resources. To ground the research, the program will be conducted in parallel with an externally-funded, collaborative robotics project that is placing robots in long-term care homes. This application embodies the challenges we address in this program. While it is separate from what is being proposed here, the robot planning application will serve as an inspiration and test-bed.**