AI Planning and Mathematical Programming

人员和组织的许多日常活动都需要规划和安排：决定采取哪些行动来实现一组目标，并决定何时采取行动以及使用哪些资源。每日通勤可能包括决定一个人可以离开家及时到达参加重要会议的最晚时间，同时考虑不同的出行方式（自行车、汽车、公共交通）、每种出行方式所需的时间以及与其他目标的互动（例如，如果我开车，下班后我将无法与同事喝一杯）。另一个例子，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、接单、包装和交付。 ****人工智能规划在过去 15 年中取得了长足进步，主要解决了要采取哪些行动的问题。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，它必须越来越多地做出有关时间和资源的决策。***拟议的研究计划应对推理做什么、何时做以及使用什么资源的挑战。三个提议的研究主题是统一的，假设数学规划包含一套问题解决技术和理论基础，可以扩展并与人工智能规划集成以应对这些挑战。***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，以解决具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) 的新规划技术。***主题 2 将重点关注 A* 搜索的基本人工智能技术，并开发它来解决具有资源和时间的规划问题三个方面：重点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 将采取原则性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编程模式。***该研究计划重点关注解决需要推理时间和资源的 AI 规划问题的基本进展。为了奠定研究基础，该计划将与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。该应用程序体现了我们在此计划中解决的挑战。虽然它与此处提议的内容不同，但机器人规划应用程序将作为灵感和测试平台。 **

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.**