Probabilistic Focal Search: Accelerating Bounded-Suboptimal Search via Lower-Bound Advancement

The sub‑optimal bounded‑quality search aims to find a solution whose cost does not exceed a factor w above the optimum while keeping computational effort low. The classic method, Focal Search (FS), expands nodes from a set called FOCAL, which contains states whose f‑value is no more than w × f_min. FS’s deterministic policy often keeps the minimum f constant, delaying the entry of new nodes into the focal set and consequently postponing the discovery of feasible solutions.

To address this, the authors introduce Probabilistic Focal Search (PFS). At each step, with probability p the algorithm follows FS’s guided choice; with probability 1 – p it expands the lowest‑f node available in OPEN. This second option pushes the lower bound f_min upward, enlarging FOCAL and allowing potentially useful nodes to enter earlier. Balancing heuristic guidance with the advancement of the lower bound reduces the number of expansions needed when f_min stalls.

Experiments compare PFS to FS on classic benchmarks such as the N‑puzzle, pancake sorting, and the traveling salesman problem, as well as an “anytime” variant evaluated on generalized covering TSP. Results show up to a 90 % reduction in expanded nodes in cases where the f_min plateau is long; in domains where FS already progresses quickly, the improvement is smaller. A further experiment applies the same probabilistic scheme to Dynamic Potential Search, yielding Probabilistic Dynamic Potential Search (PDPS), whose performance also depends on the domain and the w factor.

This study is significant because it demonstrates that controlled randomness can accelerate searches that would otherwise become trapped in bottlenecks, offering a potentially useful tool for optimizing planning and problem‑solving algorithms in AI.

Read the original article on arXiv cs.AI

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