A Unifying Formalism for Shortest Path Problems with Expensive Edge Evaluations via Lazy Best-First Search over Paths with Edge Selectors

Abstract

While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function dominates algorithm running time. Inspired by approaches in robotic motion planning, we define and investigate the Lazy Shortest Path class of algorithms which is differentiated by the choice of an edge selector function. We show that several algorithms in the literature are equivalent to this lazy algorithm for appropriate choice of this selector. Further, we propose various novel selectors inspired by sampling and statistical mechanics, and find that these selectors outperform existing algorithms on a set of example problems.

PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning

“…The remaining algorithms (Focused, Binding, and Adaptive) use the shared pseudocode OPTIMISTIC, which takes in a meta-parameter procedure PROCESS-STREAMS that implements each algorithm. The key principle behind our algorithms is to lazily explore candidate plans before checking their validity (Dellin and Srinivasa 2016). In order to apply laziness to PDDLStream, we plan using optimistic objects that represent hypothetical stream outputs before evaluating actual stream outputs.…”

The Provable Virtue of Laziness in Motion Planning

“…We are especially interested in the LazySP class of algorithms, introduced by Dellin and Srinivasa (2016). Any algorithm in the class LazySP is determined by an edge selector, which, informally, decides which edge to query on a given s-t path.…”

“…Our results suggest that LAZYSP is an excellent proxy for the optimal policy in the probabilistic setting, in that with, say, the forward edge selector, it is computationally efficient and provides satisfying guarantees. This is backed up by the empirical evaluation presented by Dellin and Srinivasa (2016). One may ask, though, whether the optimal policy itself can be computed.…”

“…Thus, path planning on G differs from traditional search algorithms such as Dijkstra (1959) or A* (Hart, Nilsson, and Raphael 1968), where the graph is typically implicit and large, but edge evaluation is trivial compared to search. Indeed, much recent work in motion planning focuses on evaluating the edges of G lazily, that is, assuming that the edges do not intersect with the obstacles O (Bohlin and Kavraki 2000;Hauser 2015;Dellin and Srinivasa 2016;Salzman and Halperin 2015;Choudhury et al 2017;Mandalika, Salzman, and Srinivasa 2018).…”

“…In a recent paper, Dellin and Srinivasa (2016) present a unifying formalism for shortest-path problems where edge evaluation dominates the running time of the algorithm. Specifically, they define and investigate a class of algorithms termed Lazy Shortest Path (LazySP), which run any shortestpath algorithm on G followed by evaluating the edges along that shortest path.…”