Planning graph as the basis for deriving heuristics for plan synthesis by state space and CSP search

Abstract

Most recent strides in scaling up planning have centered around two competing themesdisjunctive planners, exemplified by Graphplan, and heuristic state search planners, exemplified by UNPOP, HSP and HSP-r. In this paper, we present a novel approach for successfully harnessing the advantages of the two competing paradigms to develop planners that are significantly more powerful than either of the approaches. Specifically, we show that the polynomial-time planning graph structure that the Graphplan builds provides a rich substrate for deriving a family of highly effective heuristics for guiding state space search as well as CSP style search. The main leverage provided by the planning graph structure is a systematic and graded way to take subgoal interactions into account in designing state space heuristics. For state space search, we develop several families of heuristics, some aimed at search speed and others at optimality of solutions, and analyze many approaches for improving the cost-quality tradeoffs offered by these heuristics. Our normalized empirical comparisons show that our heuristics handily outperform the existing state space heuristics. For CSP style search, we describe a novel way of using the planning graph structure to derive highly effective variable and value ordering heuristics. We show that these heuristics can be used to improve Graphplan's own backward search significantly. To demonstrate the effectiveness of our approach vis a vis the state-of-the-art in plan synthesis, we present AltAlt, a planner literally cobbled together from the implementations of Graphplan and state search style planners using our theory. We evaluate AltAlt on the suite of problems used in the recent AIPS-2000 planning competition. The results place AltAlt in the top tier of the competition planners-outperforming both Graphplan based and heuristic search based planners.  2001 Published by Elsevier Science B.V.

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“…Therefore, the precise ordering of actions/propositions is only relevant at the last level of the graph and does not greatly reduce the search space. This demonstrates the difficulty of finding domain-independent admissible heuristics for Graphplan (Nguyen, Kambhampati, & Nigenda, 2002). Consequently, it seems more promising to focus on nonadmissible heuristics that achieve reasonable quality solutions in most domains.…”

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“…• Critical path heuristics (Haslum & Geffner, 2000;Haslum, Bonet, & Geffner, 2005) estimate the goal distance by computing lower bound estimates on the cost of achieving sets of facts of a predefined size, • Delete relaxation heuristics (Nguyen, Kambhampati, & Nigenda, 2002;Hoffmann & Nebel, 2001;Domshlak, Hoffmann, & Katz, 2015) estimate the cost of reaching a goal state by ignoring the negative effects of actions, • Abstraction heuristics (Ededlkamp, 2001;Helmert, Haslum, Hoffmann, & Nissim, 2014;Katz & Domshlak, 2008) try to collapse several states into one depending on their properties in order to reduce the size of the search space. When the abstraction is small enough it is feasible to quickly find an optimal solution for the abstracted problem that is used as a heuristics value during the search, • Landmarks heuristics (Hoffmann, Porteous, & Sebastia, 2004;Richter, Helmet, & Westphal, 2008) are based on the observation that some propositions are true at some point in every plan to reduce and decompose the search space.…”

“…h +M is admissible, but empirical evaluations (Nguyen et al, 2002) show that h +M is more informative than h + specially when subgoals are relatively independent. The procedure used to compute mutex relations starts with a large set of potential mutex pairs and then precludes those that are not actually mutex.…”

“…The set-level heuristic (Nguyen et al, 2002) computation is based on the extraction of information from a planning graph structure. Suppose a planning graph P G = P 0 , µP 0 , A 0 , µA 0 , .…”

A State-Based Regression Formulation for Domains with Sensing Actions and Incomplete Information

“…The relation between these two, formally proven in [16], shows the correctness of regression based planners; which, through use of heuristics (e.g. [4,14]), have done well in planning competitions. However, the focus of these papers has been the regression function in domains where agents have complete knowledge about the world.…”