Recently, a Euclidean heuristic (EH) has been proposed for A* search. EH exploits manifold learning methods to construct an embedding of the state space graph, and derives an admissible heuristic distance between two states from the Euclidean distance between their respective embedded points. EH has shown good performance and memory efficiency in comparison to other existing heuristics such as differential heuristics. However, its potential has not been fully explored. In this paper, we propose a number of techniques that can significantly improve the quality of EH. We propose a goal-oriented manifold learning scheme that optimizes the Euclidean distance to goals in the embedding while maintaining admissibility and consistency. We also propose a state heuristic enhancement technique to reduce the gap between heuristic and true distances. The enhanced heuristic is admissible but no longer consistent. We then employ a modified search algorithm, known as B' algorithm, that achieves optimality with inconsistent heuristics using consistency check and propagation. We demonstrate the effectiveness of the above techniques and report un-matched reduction in search costs across several non-trivial benchmark search problems.

An important problem in AI is to construct high-quality heuristics for optimal search. Recently, the Euclidean heuristic (EH) has been proposed, which embeds a state space graph into a Euclidean space and uses Euclidean distances as approximations for the graph distances. The embedding process leverages recent research results from manifold learning, a subfield in machine learning, and guarantees that the heuristic is provably admissible and consistent. EH has shown good performance and memory efficiency in comparison to other existing heuristics. Our recent works have further improved the scalability and quality of EH. In this short paper, we present our latest progress on applying EH to problems in planning formalisms, which provide richer semantics than the simple state-space graph model. In particular, we improve EH by exploiting the landmark structure derived from the SAS+ planning formalism.

Search is a major technique for planning. It amounts to exploring a state space of planning domains typically modeled as a directed graph. However, prohibitively large sizes of the search space make search expensive. Developing better heuristic functions has been the main technique for improving search efficiency. Nevertheless, recent studies have shown that improving heuristics alone has certain fundamental limits on improving search efficiency. Recently, a new direction of research called partial order based reduction (POR) has been proposed as an alternative to improving heuristics. POR has shown promise in speeding up searches. POR has been extensively studied in model checking research and is a key enabling technique for scalability of model checking systems. Although the POR theory has been extensively studied in model checking, it has never been developed systematically for planning before. In addition, the conditions for POR in the model checking theory are abstract and not directly applicable in planning. Previous works on POR algorithms for planning did not establish the connection between these algorithms and existing theory in model checking. In this paper, we develop a theory for POR in planning. The new theory we develop connects the stubborn set theory in model checking and POR methods in planning. We show that previous POR algorithms in planning can be explained by the new theory. Based on the new theory, we propose a new, stronger POR algorithm. Experimental results on various planning domains show further search cost reduction using the new algorithm.