概率焦点搜索：通过下界推进加速有界次优搜索

中文摘要 AI 辅助

有界次优搜索旨在以最优解的 $w$ 倍因子内寻找解，同时减少搜索工作量。焦点搜索（FS）在FOCAL集合内使用启发式引导，FOCAL是在阈值 $w f_{\min}$ 下符合条件的边界节点集合，但其确定性策略可能在多次扩展中使 $f_{\min}$ 保持不变。我们提出了概率焦点搜索（PFS），它以概率 $p$ 遵循FS引导的选择，并以概率 $1-p$ 扩展一个最小 $f$ 值的OPEN节点。后一种分支鼓励下界推进，从而扩大FOCAL集合并接纳可能通向可行解的节点。通过平衡引导与下界推进，该机制在进度受限于FOCAL延迟接纳时，可以减少找到有界解的时间。作为二次迁移实验，我们将相同的调度器应用于动态势搜索，得到概率动态势搜索（PDPS）。我们在N-Puzzle、煎饼排序和旅行商问题（TSP）上将PFS与FS进行基准比较，并在广义覆盖旅行商问题（GCTSP）上评估其任意时间扩展，使用了多个 $w$ 和 $p$ 值。在这些基准测试中，最大的收益出现在长的 $f_{\min}$ 平台期延迟了有用的FOCAL接纳时；在这种情况下，概率因子可以将节点扩展减少约90%或更多（例如，在N-Puzzle和TSP上）。对于任意时间算法家族，任意时间概率焦点搜索（APFS）在GCTSP上的任意时间方法评估中优于所有测试算法。我们还观察到，当确定性搜索已经高效推进时（例如，煎饼排序），收益较小，这表明概率因子在FOCAL接纳是搜索瓶颈时最为有用。PDPS迁移表明，该机制也能迁移到势引导，但其常见成功效果仍依赖于领域和界限。

英文摘要

Bounded-suboptimal search seeks a solution within a factor $w$ of optimal while reducing search effort. Focal Search (FS) uses heuristic guidance within FOCAL, the frontier nodes eligible under the threshold $w f_{\min}$, but its deterministic policy may leave $f_{\min}$ unchanged for many expansions. We introduce Probabilistic Focal Search (PFS), which follows the FS guided choice with probability $p$ and expands a minimum-$f$ OPEN node with probability $1-p$. The latter branch encourages the lower bound to advance, enlarging FOCAL and admitting nodes that may lead to feasible solutions. By balancing guidance and lower-bound advancement, this mechanism can reduce time to a bounded solution when progress is limited by delayed FOCAL admission. As a secondary transfer experiment, we apply the same scheduler to Dynamic Potential Search, yielding Probabilistic Dynamic Potential Search (PDPS). We benchmark PFS against FS on N-Puzzle, Pancake Sorting, and the Traveling Salesperson Problem (TSP), and evaluate its anytime extension on the Generalized Covering TSP (GCTSP), using multiple $w$ and $p$ values. Across these benchmarks, the largest gains occur when long $f_{\min}$ plateaus delay useful FOCAL admissions; in such settings, the probabilistic factor may reduce node expansions by about 90\% or more (e.g., on N-Puzzle and TSP). For the anytime algorithm family, Anytime Probabilistic Focal Search (APFS) outperforms all tested algorithms in evaluating anytime methods on GCTSP. We also observe that the benefit is smaller when the deterministic search already advances efficiently (e.g., Pancake Sorting), indicating that the probabilistic factor is most useful when FOCAL admission is a search bottleneck. The PDPS transfer shows that the mechanism also transfers to potential guidance, although its common-success effects remain domain- and bound-dependent.

发表机构

• National Economics University（国民经济大学）
• University of Warwick（华威大学）
• Hanoi University of Science and Technology（河内理工大学）

机构由 AI 辅助整理，请以论文原文为准。