Researchers propose Probabilistic Focal Search to accelerate bounded-suboptimal search algorithms

Researchers propose Probabilistic Focal Search (PFS), a variant of Focal Search (FS) designed to accelerate bounded-suboptimal search by probabilistically balancing heuristic guidance and lower-bound advancement. In FS, the algorithm restricts expansions to nodes in FOCAL, defined as those with cost bounded by w·f_min, where f_min is the minimum cost among expanded nodes. The deterministic policy of FS can leave f_min unchanged for many expansions, delaying useful admissions to FOCAL and increasing search effort.

PFS introduces a probabilistic policy: with probability p, it follows FS’s heuristic-guided choice, and with probability 1−p, it expands a minimum-f OPEN node to encourage advancement of the lower bound. This mechanism enlarges FOCAL and admits nodes that may lead to feasible solutions sooner, particularly in settings where long f_min plateaus stall progress.

The authors benchmark PFS against FS on N-Puzzle, Pancake Sorting, and the Traveling Salesperson Problem (TSP), and evaluate an anytime extension (Anytime Probabilistic Focal Search, APFS) on the Generalized Covering TSP (GCTSP). Across these domains, the largest gains occur when delayed FOCAL admissions limit progress; in such cases, PFS reduces node expansions by about 90% or more, for example on N-Puzzle and TSP.

The probabilistic mechanism is also transferred to Dynamic Potential Search, yielding Probabilistic Dynamic Potential Search (PDPS). While the benefits vary by domain and bound, the approach shows that probabilistic scheduling can improve search efficiency in bounded-suboptimal settings where deterministic methods stall.