[论文解读] Taming Numbers and Durations in the Model Checking Integrated Planning System

Stefan Edelkamp|Jun 30, 2011

AI-based Problem Solving and Planning被引用 14

一句话总结

本文将模型检查集成规划系统（MIPS）扩展至处理数值状态变量、动作持续时间以及目标函数，以支持时序规划。提出一种基于PERT的线性时间调度算法，将顺序计划转换为最优并行计划，绕过了部分序调度中的NP难问题，并将该算法与启发式搜索相结合，显著提升了复杂度量规划领域中的计划质量与效率。

ABSTRACT

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization.

研究动机与目标

• 解决将数值状态变量、动作持续时间与目标函数整合进通用规划器的挑战。
• 通过引入线性时间调度算法，克服顺序计划中部分序调度的NP难问题。
• 通过为每个遇到的状态调度松弛计划，改进状态空间搜索中的启发式引导。
• 在具有复杂约束的度量与时序规划领域中，实现高效、完整且最优的规划。
• 检测并利用动态对象对称性，以减少状态空间爆炸并提升搜索性能。

提出的方法

• 将PERT（项目评估与审查技术）调度集成至规划循环中，从顺序生成的计划中计算最优并行计划。
• 应用线性时间算法计算计划的关键路径，实现在无需完整NP难部分序优化的情况下高效调度。
• 将所得并行计划长度用作精细化启发式估计，引导前向搜索以获得更短、更高效的计划。
• 实现静态分析器以实例化并简化参数化谓词，检测对称性，并最小化状态描述长度。
• 结合显式与符号化搜索技术，并采用在线与离线启发式估计，包括不可行加权启发式以提升性能。
• 集成基于哈希的置换与剪枝剪枝机制，避免在对称领域中重复探索状态。

实验结果

研究问题

• RQ1 规划器如何高效调度持续动作，以最小化计划长度并保持最优性？
• RQ2 线性时间调度算法是否能够绕过顺序计划部分序调度中的已知NP难性？
• RQ3 如何利用松弛计划的结构特性来引导启发式搜索，以提升解的质量？
• RQ4 动态对象对称性在状态空间爆炸中扮演何种角色？如何检测并加以利用？
• RQ5 显式与符号化搜索技术在多大程度上可结合使用，以扩展至复杂度量规划问题？

主要发现

• 线性时间PERT调度算法成功从顺序计划中计算出最优并行计划，避免了部分序调度中的NP难问题。
• 为每个状态调度松弛计划作为启发式估计，显著改善了搜索引导，从而产生更高质量的计划。
• 静态分析器通过检测并消除冗余或对称的事实，减少了状态描述长度，提升了可扩展性。
• 动态对象对称性检测被证明是可行且有效的，并提供了新颖的时间与空间复杂度分析。
• 该系统在国际规划竞赛中表现出色，证明了其在包含数值与持续动作的多样化领域中的有效性。
• 符号化与显式搜索技术结合启发式估计，实现了复杂度量规划问题中高效、完整且最优的规划。