Who Needs These Operators Anyway: Top Quality Planning with Operator Subset Criteria

Abstract

Top-quality planning in general and quotient top-quality planning in particular deal with producing multiple high-quality plans while allowing for their efficient generation, skipping equivalent ones. Prior work has explored one equivalence relation, considering two plans to be equivalent if their operator multi-sets are equal. This allowed omitting plans that are reorderings of previously found ones. However, the resulting sets of plans were still large, in some domains even infinite. In this paper, we consider a different relation: two plans are related if one's operator multiset is a subset of the other's. We propose novel reformulations that forbid plans that are related to the given ones. While the new relation is not transitive and thus not an equivalence relation, we can define a new subset top-quality planning problem, with finite size solution sets. We formally prove that these solutions can be obtained by exploiting the proposed reformulations. Our empirical evaluation shows that solutions to the new problem can be found for more tasks than unordered top-quality planning solutions. Further, the results shows that the solution sizes significantly decrease, making the new approach more practical, particularly in domains with redundant operators.

Unifying and Certifying Top-Quality Planning

“…We start by noticing that the definition for quotient topquality planning can be rewritten similarly to the one for subset top-quality planning, by requiring the plans of bounded by q costs missing from the solution to be in relation to the ones that are in the solution. With that, given any relation R, we extend the Definition 1 of Katz and Sohrabi (2022) as follows.…”

“…A body of research on generating plans of top quality (Katz et al 2018;Speck, Mattmüller, and Nebel 2020;Lee, Katz, and Sohrabi 2023) has recently yielded various computational problems, including unordered top-quality planning (Katz, Sohrabi, and Udrea 2020), subset top-quality planning (Katz and Sohrabi 2022), and loopless top-k planning (von Tschammer, Mattmüller, and Speck 2022). Each of these problems is defined in an ad-hoc manner, addressing specific issues, often identified by an application of interest.…”

“…We show how to certify top-quality for the unified definition, exploiting existing tools that can certify optimality (Mugdan, Christen, and Eriksson 2023). Further, for the computational problems of unordered top-quality planning and subset top-quality planning, the existing in the literature task transformations (Katz, Sohrabi, and Udrea 2020;Katz and Sohrabi 2022) can be used for efficient certification. For loopless top-quality planning no such transformation exists.…”

“…the relation defined by the subset operation over plan action multi-sets. The subset top-quality planning problem (Katz and Sohrabi 2022) is defined as follows. Given a planning task Π and a natural number q, find a set of plans P ⊆ P Π s.t.…”

On Producing Shortest Cost-Optimal Plans

“…In this paper, we consider the problem of finding a costoptimal plan that has a minimal number of actions among all cost-optimal plans, or shortest cost-optimal plan. This is for example required as a subroutine for top-quality planning (Katz, Sohrabi, and Udrea 2020;Katz and Sohrabi 2022) but also an interesting property if the plan gets presented to humans, as it is for example the case in human-in-the-loop planning or explainable AI planning where the optimality is measured with respect to the observer model (Chakraborti et al 2021).…”