Strengthening Potential Heuristics with Mutexes and Disambiguations

Self Cite

Symbolic search using binary decision diagrams is a state-of-the-art technique for cost-optimal planning. Heuristic search in this context has been problematic as even a very informative heuristic can be detrimental in case it induces difficult-to-represent state partitionings. It was recently shown that operator-potential heuristics can address this issue in forward search by computing a numeric potential for each operator corresponding to the change of the heuristic value induced by that operator. Forward search is, however, not the best known variant of symbolic search. Here we investigate the integration with backward and bi-directional search instead. We prove that forward search (distance-to-goal) operator-potential heuristics can be turned into backward search (distance-to-initial-state) heuristics elegantly in this context, by summing the backward search path operator-potentials with the initial state goal-distance estimate. We run exhaustive experiments on IPC benchmarks, showing that significant performance improvements can be obtained over symbolic forward search and other state-of-the-art techniques.

Section: Background On Potential Andmentioning

confidence: 99%

“…Theorem 3. (Fišer, Horčík, and Komenda 2020) Let Π = V, O, I, G denote a planning task with facts F , and let P denote a potential function, and let D denote a disambiguation map. If…”

Section: Background On Potential Andmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

See 3 more Smart Citations

Operator-Potentials in Symbolic Search: From Forward to Bi-directional Search

Fišer

Torralba

Hoffmann

2022

Self Cite

Endomorphisms of Lifted Planning Problems

Horčı́k

Fišer

2021

Self Cite

Classical planning tasks are usually modelled in the PDDL which is a schematic language based on first-order logic. Nevertheless, most of the current planners turn this first-order representation into a propositional one via the grounding process. It is well known that the grounding process may cause an exponential blowup. Therefore it is important to detect which grounded atoms are redundant in a sense that they are not necessary for finding a plan and therefore the grounding process does not need to generate them. This is usually done by a relaxed reachability analysis, which can be improved by employing structural symmetries. Symmetries are bijective self-maps preserving the structure of the PDDL task. In this paper, we introduce a new method which is based on self-maps preserving the structure but which need not be bijective. We call these maps PDDL endomorphisms and we show that they can be used for pruning of redundant objects even if they appear in a reachable atom. We formulate the computation of endomorphisms as a constraint satisfaction problem (CSP) that can be solved by an off-the-shelf CSP solver.

Detecting Unsolvability Based on Separating Functions

Christen

Eriksson

Pommerening

et al. 2022

While the unsolvability IPC sparked a multitude of planners proficient in detecting unsolvable planning tasks, there are gaps where concise unsolvability arguments are known but no existing planner can capture them without prohibitive computational effort. One such example is the sliding tiles puzzle, where solvability can be decided in polynomial time with a parity argument. We introduce separating functions, which can prove that one state is unreachable from another, and show under what conditions a potential function over any nonzero ring is a separating function. We prove that we can compactly encode these conditions for potential functions over features that are pairs, and show in which cases we can efficiently synthesize functions satisfying these conditions. We experimentally evaluate a domain-independent algorithm that successfully synthesizes such separating functions from PDDL representations of the sliding tiles puzzle, the Lights Out puzzle, and Peg Solitaire.