Memory-based heuristics are a popular and effective class of admissible heuristic functions. However, corruptions to memory they use may cause these heuristics to become inadmissible. Corruption can be caused by the physical environment due to radiation and network errors, or it can be introduced voluntarily in order to decrease energy consumption. We introduce memory error correction schemes that do not require additional memory and exploit knowledge about the behavior of consistent heuristics. This is in contrast with error correcting code approaches which can limit the amount of corruption but at the cost of additional energy and memory consumption. Search algorithms using our methods are guaranteed to find a solution if one exists and its suboptimality is bounded. Moreover, our methods are resilient to any number of memory errors that may occur. An experimental evaluation is also provided to demonstrate the applicability of our approach.

The agent operates in a real-time setting by interleaving local planning, learning and move execution. In this paper we propose a simple parametric algorithm that combines weighting with learning from multiple neighbors. Doing so breaks heuristic admissibility but allows the agent to escape heuristic depressions more quickly. We prove completeness of the algorithm and empirically compare it to several competitors more than twenty years apart. In a large-scale evaluation the new algorithm found better solutions than the recent algorithms, despite not learning additional information that they do. Finally, we study robustness of the algorithms to noise in the heuristic function -- a desirable property in a physical implementation of real-time heuristic search. The new algorithm outperforms its contemporaries.

The sleep sets technique is a path-dependent pruning method for state space search. In the past, the combination of sleep sets with graph search algorithms that perform duplicate elimination has often shown to be error-prone. In this paper, we provide the theoretical basis for the integration of sleep sets with common search algorithms in AI that perform duplicate elimination. Specifically, we investigate approaches to safely integrate sleep sets with optimal (best-first) search algorithms. Based on this theory, we provide an initial step towards integrating sleep sets within A* and additional state pruning techniques like strong stubborn sets. Our experiments show slight, yet consistent improvements on the number of generated search nodes across a large number of standard domains from the international planning competitions.

In this paper we study the k goal search problem (kGS), which is the problem of solving k shortest path problems that share the same start state. Two fundamental heuristic search approaches are analyzed: searching for the k goals one at a time, or searching for all k goals together in a single pass. Key theoretical properties are established and a preliminary experimental evaluation is performed.

The efficiency of heuristic search depends dramatically on the quality of the heuristic function. For an optimal heuristic search, heuristics that estimate cost-to-goal better typically lead to faster searches. For a sub-optimal heuristic search such as weighted A*, the search speed depends more on the correlation between the heuristic and the true cost-to-goal. In this extended abstract, we discuss our preliminary work on computing heuristic functions that exploit this fact. In particular, we introduce a many-to-one mapping from an original search space to a conservative abstract space.

Admissible heuristics are essential for optimal planning in the context of search algorithms like A*, and they can also be used in the context of suboptimal planning in order to find quality-bounded solutions. In satisfacing planning, on the other hand, admissible heuristics are not exploited by the best-first search algorithms of existing planners even when a time window is available for improving the first solution found. For example, in the well-know planner LAMA, better solutions within such a time window are sought by restarting a Weighted-A* search guided by inadmissible heuristics, each time a better solution is found. In this paper, we investigate the use of admissible heuristics in the context of LAMA for pruning nodes that cannot lead to better solutions. The revised search of LAMA is experimentally evaluated using two alternative admissible heuristics for pruning and three types of problems: planning with soft goals, planning with action costs, and planning with both action costs and soft goals. Soft goals are compiled into hard goals following the approach of Keyder and Geffner. The empirical results show that the use of admissible heuristics in LAMA can be of great help to improve the planner performance.

The pancake puzzle is a standard benchmark domain used to test search algorithms, and the gap heuristic is the state-of-the-art heuristic function most often used in such tests. In this work, we analyze the accuracy of this heuristic and identify ways to enhance it. We begin by showing that in the worst-case, the amount that the gap heuristic underestimates the optimal cost of a pancake puzzle state can be linear in the number of pancakes in the stack. However, empirical analysis suggests that it is extremely rare that the gap heuristic underestimates the optimal cost by more than two. We then identify several simple methods that can be used to generate large sets of problems on which the gap heuristic underestimates the optimal cost by a larger amount than it typically does on random permutations. In doing so, we provide new pancake puzzle test sets that can be used to evaluate how search algorithms behave when the heuristic is inaccurate. We also formally characterize states according to the size of the heuristic plateaus around them. This characterization allows us to efficiently compute a two-step look ahead of the gap heuristic on any state, which we can use alongside a state's dual to further improve heuristic accuracy. These enhancements substantially improve the performance of an IDA*-based pancake problem solver on both the existing benchmarks and the new ones proposed in this paper.

Symmetry-based state space pruning techniques have proved to greatly improve heuristic search based classical planners. Similarly, abstraction heuristics in general and pattern databases in particular are key ingredients of such planners. However, only little work has dealt with how the abstraction heuristics behave under symmetries. In this work, we investigate the symmetry properties of the popular canonical pattern databases heuristic. Exploiting structural symmetries, we strengthen the canonical pattern databases by adding symmetric pattern databases, making the resulting heuristic invariant under structural symmetry, thus making it especially attractive for symmetry-based pruning search methods. Further, we prove that this heuristic is at least as informative as using symmetric lookups over the original heuristic. An experimental evaluation confirms these theoretical results.

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f-value is below the optimal solution cost and no state whose f-value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behaviour of greedy best-first search (gbfs) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a gbfs algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are not expanded under any gbfs tie-breaking strategy. For the remaining states, we show that some are expanded by all gbfs searches, while others are expanded only if certain conditions are met.

Heuristic search is one of the most successful approaches to classical planning, finding solution paths in large state spaces. A major focus has been the development of domain-independent heuristic functions. One recent method are partial delete relaxation heuristics, improving over the standard delete relaxation heuristic through imposing a set C of conjunctions to be treated as atomic. Practical methods for selecting C are based on counter-example guided abstraction refinement, where iteratively a relaxed plan is checked for conflicts and new atomic conjunctions are introduced to address these. However, in each refinement step, the choice of possible new conjunctions is huge. The literature so far offers merely one simple strategy to make that choice. Here we fill that gap, considering a sizable space of basic ranking strategies as well as combinations thereof. We furthermore devise ranking strategies for conjunction-forgetting, where the ranking pertains to the current conjunctions and thus statistics over their usefulness can be maintained. Our experiments show that ranking strategies do make a large difference in performance, and that our new strategies can be useful.