Improving Bidirectional Heuristic Search by Bounds Propagation

Abstract

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.

On the Differences and Similarities of fMM and GBFHS

“…However, p * is not known a priori since it depends on search tree structure and the value of C * . Finally, fMM was shown to be neither reasonable nor well-behaved (Shperberg et al 2019b).…”

“…In this paper we discuss the differences and similarities of the algorithms in terms of minimal node expansions. In addition, we show that both GBFHS and fMM can be enriched by the lower-bound propagation (lb-propagation) (Shperberg et al 2019b), creating fMM lb and GBFHS lb respectively. We show that adding lb-propagation to both algorithms never harm their performance (in terms of minimal node expansions required to solve and verify optimal solutions) and the performance even improves for many problem instances.…”

“…Bi-HS algorithms may expand nodes from both sides, potentially covering all the MEPs with fewer expansions. Shperberg et al (2019b) extended the lb notation and defined a lower-bound for nodes instead of pairs. In order to define a lower-bound to a node u, the bound lb(u, v) is applied to every node v on the opposite frontier of u, and only the minimum among these values is considered.…”

“…Example 1. Consider the problem instance that previously appeared in (Holte et al 2017;Shperberg et al 2019b) and is depicted in Figure 1. In this problem instance = 1, and the values inside nodes are h-values in the direction indicated by the arrow.…”

Meta-Level Techniques for Planning, Search, and Scheduling

“…This tradeoff induces a metareasoning problem which we briefly discussed. Finally, we also developed a method for enabling existing algorithm to benefit from the G MX structure by incorporating this information into the heuristic function (Shperberg et al 2019b).…”