Optimal-Generation Variants of EPEA*

Abstract

It is known that A* is optimal with respect to the expanded nodes (Dechter and Pearl 1985) (D&P). The exact meaning of this optimality varies depending on the class of algorithms and instances over which A* is claimed to be optimal. A* does not provide any optimality guarantees with respect to the generated nodes. However, such guarantees may be critical for optimally solving instances of domains with a large branching factor. In this paper, we introduce two new variants of the recently introduced Enhanced Partial Expansion A* algorithm (EPEA*) (Felner et al. 2012). We leverage the results of D&P to show that these variants possess optimality with respect to the generated nodes in much the same sense as A* possesses optimality with respect to the expanded nodes. The results in this paper are theoretical. A study of the practical performance of the new variants is beyond the scope of this paper.

Search-Based Optimal Solvers for the Multi-Agent Pathfinding Problem: Summary and Challenges

“…The SIC heuristic can be calculated lazily on the fly (Silver 2005) or can be fully computed in a pre-processing phase (Standley 2010;Sharon et al 2013). More-informed heuristics by using forms of pattern-databases (Goldenberg et al 2013; had limited effectiveness due to the large overhead of creating these PDBs for each instance-specific goal state.…”

“…To guarantee optimality A* must expand all states with f = g + h < C * as well as some states with f = C * . Nodes generated by A* with f > C * are denoted as surplus nodes (Goldenberg et al 2014). They will never be expanded as they are not needed to find an optimal solution.…”

“…The number of generated nodes is the number of expanded nodes times the branching factor b. Thus, in MAPF, where b is exponential in k, the number of surplus nodes is potentially huge, and avoiding generating them can yield a substantial speedup (Goldenberg et al 2014;. Next, we describe existing techniques that attempt to avoid generating surplus nodes for MAPF.…”

“…An OSF for MAPF using h SIC can be efficiently built as the effect on the f -value of moving a single agent in a given direction can be easily computed. For more details see (Goldenberg et al 2014).…”

Position Paper: Using Early Goal Test in A*

“…Indeed, many of the early bidirectional search algorithms (see (Holte et al 2017) for a survey) and certainly all the recent ones (Barker and Korf 2015;Holte et al 2017;Chen et al 2017;Shaham et al 2017) (Thayer and Ruml 2011;Hansen and Zhou 2007), others leave it vague (Likhachev et al 2008) or describe late goal test (Gilon, Felner, and Stern 2016;Thayer and Ruml 2008;Ebendt and Drechsler 2009) In some cases there will be no practical difference between A*-LATE and A*-EARLY. In such cases, when the goal is generated for the first time it is through the optimal path (with f (goal) = C * ) directly from a parent which also has f = C * (cases with this last attribute are called pathological (Dechter and Pearl 1985;Goldenberg et al 2013)). In such cases, both A*-LATE and A*-EARLY will halt right after the generation of the first goal because at this time f min = C * and surplus nodes will never be generated.…”