NBS is a non-parametric bidirectional search algorithm proven to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

Making plans that depend on external events can be tricky. For example, an agent considering a partial plan that involves taking a bus must recognize that this partial plan is only viable if completed and selected for execution in time for the agent to arrive at the bus stop. This setting raises the thorny problem of allocating the agent’s planning effort across multiple open search nodes, each of which has an expiration time and an expected completion effort in addition to the usual estimated plan cost. This paper formalizes this metareasoning problem, studies its theoretical properties, and presents several algorithms for solving it. Our theoretical results include a surprising connection to job scheduling, as well as to deliberation scheduling in time-dependent planning. Our empirical results indicate that our algorithms are effective in practice. This work advances our understanding of how heuristic search planners might address realistic problem settings.

We address the problem of situated temporal planning, in which an agent's plan can depend on scheduled exogenous events, and thus it becomes important to take the passage of time into account during the planning process. Previous work on situated temporal planning has proposed simple pruning strategies, as well as complex schemes for a simplified version of the associated metareasoning problem. Although even the simplified version of the metareasoning problem is NP-hard, we provide a pseudo-polynomial time optimal solution to the case with known deadlines. We leverage intuitions emerging from this case to provide a fast greedy scheme that significantly improves upon previous schemes even for the case of unknown deadlines. Finally, we show how this new method can be applied inside a practical situated temporal planner. An empirical evaluation suggests that the new planner provides state-of-the-art results on problems where external deadlines play a significant role.

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms.

In the Multi-Agent Meeting problem (MAM), the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Heuristic Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding an optimal meeting location for multiple agents. Several admissible heuristics are proposed, and experiments demonstrate the benefits of MM*.