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

TL;DR

This paper introduces a unifying framework for shortest path problems with costly edge evaluations, using lazy best-first search with novel edge selectors inspired by sampling and statistical mechanics, leading to improved performance.

Contribution

It unifies existing algorithms under a lazy search framework and proposes new edge selectors that outperform previous methods in costly evaluation scenarios.

Findings

New edge selectors outperform existing algorithms

Lazy shortest path algorithms unify various approaches

Sampling-inspired selectors improve efficiency

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.