The Minimal Seed Set Problem

We present a simple and efficient algorithm to solve delete-free planning problems optimally and calculate the h+ heuristic. The algorithm efficiently computes a minimum-cost hitting set for a complete set of disjunctive action landmarks generated on the fly. Unlike other recent approaches, the landmarks it generates are guaranteed to be set-inclusion minimal. In almost all delete-relaxed IPC domains, this leads to a significant coverage and runtime improvement.

Section: Results and Conclusionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Minimal Landmarks for Optimal Delete-Free Planning

Haslum

Slaney

Thiébaux

2012

“…All models also use some of the preprocessing methods presented in (Imai and Fukunaga 2015). These methods are 1) finding fact landmarks (Gefen and Brafman 2011) and adding them to the goal conditions; 2) doing action relevance analysis and removing non-relevant actions; and 3) dominated action elimination. The implementation of these methods was part of the base HSP* package.…”

Section: Resultsmentioning

confidence: 99%

“…That is because there exist delete-free planning tasks that are of interest for the planning community. Examples are the minimal seed-set problem (Gefen and Brafman 2011), and the problem of determining join orders in relational database query plan generation (Robinson, McIlraith, and Toman 2014).…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation and Informative Estimation of h+ by Integer and Linear Programming

Rankooh¹,

Rintanen²

2022

We investigate modeling cost optimal delete-free STRIPS Planning by Integer/Linear Programming (IP/LP). We introduce two IP models and their LP relaxations based on a recently formulated representation of relaxed plans, named causal relaxed plan representation. The new models are produced by enforcing acyclicity in so-called causal relation graphs using vertex elimination and time labeling methods. We empirically show that while the vertex elimination based method outperforms the time labeling based method and all previously introduced domain independent methods for computing the exact values of h+, the time labeling based LP model is faster to solve compared to its vertex elimination based alternative, making it more suitable for using as heuristic function for optimal planning. We also theoretically analyze the admissible heuristic functions obtained by solving our LP models, and prove that the vertex elimination based heuristic is at least as informative as the time labeling based heuristic. Moreover, our empirical analysis shows that our vertex elimination based heuristic, which is a novel admissible estimation of h+, often has information complementary to that of the LM-cut heuristic.

“…Thus, any method that effectively solves delete-free planning problems has immediate use in standard planning. Finally, a number of interesting, naturally delete-free planning problems (Gefen and Brafman 2011;Gallo et al 1993) cannot be solved by standard planning techniques.…”

Section: Introductionmentioning

confidence: 99%

Pruning Methods for Optimal Delete-Free Planning

Gefen

Brafman

2012

Self Cite

Delete-free planning underlies many popular relaxation (h+) based heuristics used in state-of-the-art planners; it provides a simpler setting for exploring new pruning methods and other ideas; and a number of interesting recent planning domains are naturally delete-free. In this paper we explore new pruning methods for planning in delete-free planning domains. First, we observe that optimal delete-free plans can be composed from contiguous sub-plans that focus on one fact landmark at a time. Thus, instead of attempting to achieve the goal, the planner can focus on more easily achievable landmarks at each stage. Then, we suggest a number of complementary pruning techniques that are made more powerful with this observation. To carry out these pruning techniques efficiently, we make heavy use of an And/Or graph depicting the planning problem. We empirically evaluate these ideas using the FD framework, and show that they lead to clear improvements.