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组目标，决定何时采取行动，使用什么资源。每天的通勤可能包括决定一个人最晚可以离开家的时间，以便及时到达一个重要的会议，同时考虑不同的旅行方式（自行车，汽车，公共交通），每种方式所需的时间，以及与其他目标的互动（例如，如果我开车，我就不能下班后和同事喝一杯了）。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、存储、接受订单、包装和交付。****人工智能规划在过去15年中取得了实质性进展，主要解决了采取什么行动的问题。相比之下，处理行动的时间选择和资源选择的最成功的技术来自数学规划和约束规划学科。随着人工智能规划技术越来越多地用于现实世界的应用，它必须越来越多地对时间和资源做出决策。***提议的研究项目解决了推理该做什么、何时做以及使用什么资源的挑战。假设数学规划包含一套解决问题的技术和理论基础，可以扩展并与人工智能规划集成以应对这些挑战，这三个拟议的研究主题是统一的。***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，以解决时间和资源的人工智能规划问题，并基于约束整数规划（CIP）开发新的规划技术。***主题2将围绕A*搜索的基本AI技术，通过三种方式将其发展为解决资源和时间的计划问题：专注于解决简单的调度问题；利用LP松弛计算A*启发式算法；发展A*搜索、动态规划和多值决策图之间的关系。***主题3将采取原则性的方法将问题分解应用于AI规划问题，重点关注惰性约束生成和列生成的数学规划模式。***该研究项目的重点是解决需要对时间和资源进行推理的人工智能规划问题的基本进展。为了使研究落地，该项目将与一个外部资助的协作机器人项目同时进行，该项目将机器人放置在长期护理院中。这个应用程序体现了我们在这个项目中所面临的挑战。虽然它与这里提出的建议是分开的，但机器人规划应用程序将作为一个灵感和试验台

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.**