Using Alternative Suboptimality Bounds in Heuristic Search

Abstract

Most bounded suboptimal algorithms in the search literature have been developed so as to be epsilon-admissible. This means that the solutions found by these algorithms are guaranteed to be no more than a factor of (1 + ε) greater than optimal. However, this is not the only possible form of suboptimality bounding. For example, another possible suboptimality guarantee is that of additive bounding, which requires that the cost of the solution found is no more than the cost of the optimal solution plus a constant gamma.In this work, we consider the problem of developing algorithms so as to satisfy a given, and arbitrary, suboptimality requirement. To do so, we develop a theoretical framework which can be used to construct algorithms for a large class of possible suboptimality paradigms. We then use the framework to develop additively bounded algorithms, and show that in practice these new algorithms effectively trade-off additive solution suboptimality for runtime.

Dynamic Potential Search — A New Bounded Suboptimal Search

“…A large number of BSS algorithms have been proposed over the years (see a nice survey by Thayer and Ruml, 2011). Virtually all of these algorithms can be viewed as implementations of a general search framework that is sometimes called Focal Search (Pearl and Kim 1982;Ebendt and Drechsler 2009;Valenzano et al 2013). 2 Focal Search is a special case of best-first search that maintains two sets of nodes.…”

Searching with a Corrupted Heuristic

“…Theorem 2 (Valenzano et al (2013)) IDA* using the g + h evaluation function will find a solution with a cost of at most…”

Avoiding Re-Expansions in Suboptimal Best-First Search

“…This priority function is defined for B γ (x) = x+γ, where γ is a given constant (Valenzano et al 2013). We recommend setting K = max{h(start), γ + 1}.…”