Despite the widespread success of pattern database (PDB) heuristics in classical planning, to date there has been no application of PDBs to planning with numeric variables. In this paper we attempt to close this gap. We address optimal numeric planning involving conditions characterized by linear expressions and actions that modify numeric variables by constant quantities. Building upon prior research, we present an adaptation of PDB heuristics to numeric planning, introducing several approaches to deal with the unbounded nature of numeric variable projections. These approaches aim to restrict the initially infinite projections, thereby bounding the number of states and ultimately constraining the resulting PDBs. We show that the PDB heuristics obtained with our approach can provide strong guidance for the search.

In bidirectional heuristic search, the meeting-in-the-middle property (MMP) and the theory of must-expand pairs (MEP) have driven significant recent developments in search efficiency. However, these methodologies typically terminate the search based on minimal priority metrics in the forward and backward open lists, requiring exploration of all potentially better solutions and potentially incurring substantial computational burden. In this paper, we investigate the reasons that contribute to the potential inefficiency in MM , and introduce a tighter termination condition that enables earlier termination without exhaustive exploration while still ensuring both MMP and optimality. This results in a highly efficient bidirectional search algorithm. Experimental comparisons demonstrate that our algorithm outperforms MM in terms of running time by at least two orders of magnitude and is on par or better compared to A*, highlighting its potential in a wide range of applications.

The Multi-Agent Warehouse Rearrangement (MAWR) problem calls for computing agents plans such that they collectively rearrange a warehouse environment from a given layout which species the location of every movable obstacle in the environment, to a goal layout. It is a natural variant of the well-studied Multi-Agent Path Finding (MAPF) and Multi-Agent Pickup and Delivery (MAPD) problems, which have numerous applications in warehouse automation. Similar to MAPF and MAPD, the problem is computationally hard and existing methods forgo any optimality guarantees while computing solutions to the problem. In contrast, in this work we present the first fully-coupled search-based makespan-optimal approach for solving the MAWR problem. This is done by shifting the algorithmic viewpoint from being agent centric to obstacle centric: Common MAPF and MAPD algorithms are agent-centric wherein tasks are assigned to agents, and the agents’ paths are planned to fulfill these tasks. In contrast, the approach we present here is obstacle-centric: Our algorithm iterates between two phases: Ph1 planning optimal paths for the movable obstacles using an adaptation of the celebrated CBS MAPF algorithm and Ph2 attempting to realize the movable obstacles paths using a network-flow algorithm. We prove that our approach guarantees minimal-makespan solutions and empirically demonstrate that it achieves better plans than state-of-the-art approaches for MAWR.

The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking these factors into consideration can potentially lead to a performance boost in relevant applications. Recently, a generalized framework for weighted directed graphs was suggested, where edge-weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. We build on this framework to introduce the problem of finding the tightest admissible shortest path (TASP); a path with the tightest suboptimality bound on the optimal cost. This is a generalization of the shortest path problem to bounded uncertainty, where edge-weight uncertainty can be traded for computational cost. We present a complete algorithm for solving TASP, with guarantees on solution quality. Empirical evaluation supports the effectiveness of this approach.

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises several generalized variants of the shortest path problem. We introduce the problem of finding a path with the tightest lower-bound on the optimal cost. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. In this paper we present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises a generalized shortest path problem that optimizes different aspects of path cost and its uncertainty. We describe in high-level a complete anytime algorithm for the generalized problem and discuss possible future extensions.