规划中数字资源流模型的混合LP-RPG启发式算法
A Hybrid LP-RPG Heuristic for Modelling Numeric Resource Flows in Planning
摘要：
虽然使用度量fluents是许多实际规划问题的基础，但支持全自动规划人员使用这些fluents的算法研究仍然相对未被探索。最广泛使用的启发式算法是将度量流松弛为区间值变量-这个想法是十年前首次提出的。其他的语法依赖于提供关于流畅度的附加信息的域编码，例如容量限制或其他资源相关的注释。这些方法面临的一个特殊挑战是如何处理代表交换的度量流之间的相互作用，例如将大量原材料转化为大量加工产品，或以货币交换材料。在这些情况下，通常的度量流畅性放松往往非常差，因为它没有认识到资源一旦花费，就不再可以再次花费。我们提出了一个启发式的数字规划问题的命题放松规划图的基础上，但使用的数学程序的数字推理。我们定义了一类生产者-消费者规划问题，并演示了如何在这些数字约束可以建模在一个混合整数规划（MIP）。该MIP然后与度量松弛规划图（RPG）启发式算法相结合，产生一个集成的混合启发式算法。MIP比通常的放松更准确地跟踪资源使用，但放松了行动的顺序，而RPG则捕获了问题的因果命题方面。我们讨论了这两个组件如何相互作用，产生一个统一的启发式，并继续探索如何进一步的数字功能的规划问题可以集成到MIP。我们表明，编码命题问题的一个有限的子集，以增加MIP可以产生更准确的指导，部分利用结构，如命题地标和命题资源。我们的研究结果表明，使用这种启发式算法提高了问题的可扩展性，其中数字资源交互是找到解决方案的关键。
英文摘要：
Although the use of metric fluents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is the relaxation of metric fluents into interval-valued variables --- an idea first proposed a decade ago. Other heuristics depend on domain encodings that supply additional information about fluents, such as capacity constraints or other resource-related annotations. A particular challenge to these approaches is in handling interactions between metric fluents that represent exchange, such as the transformation of quantities of raw materials into quantities of processed goods, or trading of money for materials. The usual relaxation of metric fluents is often very poor in these situations, since it does not recognise that resources, once spent, are no longer available to be spent again. We present a heuristic for numeric planning problems building on the propositional relaxed planning graph, but using a mathematical program for numeric reasoning. We define a class of producer--consumer planning problems and demonstrate how the numeric constraints in these can be modelled in a mixed integer program (MIP). This MIP is then combined with a metric Relaxed Planning Graph (RPG) heuristic to produce an integrated hybrid heuristic. The MIP tracks resource use more accurately than the usual relaxation, but relaxes the ordering of actions, while the RPG captures the causal propositional aspects of the problem. We discuss how these two components interact to produce a single unified heuristic and go on to explore how further numeric features of planning problems can be integrated into the MIP. We show that encoding a limited subset of the propositional problem to augment the MIP can yield more accurate guidance, partly by exploiting structure such as propositional landmarks and propositional resources. Our results show that the use of this heuristic enhances scalability on problems where numeric resource interaction is key in finding a solution.
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