求解飞行方块谜题的基于类的启发式选择
Class-Based Heuristic Selection for Solving the Flying Block Puzzle
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- Faculty of Computer Engineering（计算机工程学院）
- University of Tehran（德黑兰大学）
- K. N. Toosi University of Technology（霍加·纳绥尔·丁·图西大学）
- Department of Electrical and Computer Engineering（电气与计算机工程学院）
- University of Kurdistan（库尔德斯坦大学）
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中文总结 AI 辅助
针对启发式搜索在空间规划中的性能问题，提出CBHA*算法，在146个飞行方块谜题基准实例上大幅提升成功率、减少节点扩展，为高效空间规划提供了可推广的自适应启发式机制。
中文摘要 AI 辅助
启发式搜索是自主系统规划的基础，涵盖仓库物流到机器人导航等领域，但通用启发式方法无法利用约束空间域的结构限制，导致在更难实例上的搜索性能急剧下降。我们通过两栏飞行方块谜题研究该问题，这是一个严格的NP完全空间规划微观世界，其瓶颈几何结构与多智能体路径查找、自动驾驶车辆导航和方块重定位系统中遇到的间隙尺寸约束相匹配。我们提出了基于类的启发式A*（CBHA*）算法，该算法整合了通用移动约束以在空闲单元稀缺时捕获最小位移成本，将状态空间正式划分为七个互斥类的运动学分类法，其可容许启发式基于空闲率和目标方块几何，以及类条件打破平局机制，可在深度优先和垂直距离排序之间动态切换以克服f值平台。在146个基准实例上，CBHA*的成功率达93.4%，而深度优先A*为64%、标准A*为39%、广度优先搜索（BFS）为17%；与标准A*相比，节点扩展减少了87.98%，平均有效分支因子约为3，证明类触发的自适应启发式是高效空间规划的合理机制，可在结构上推广到物理约束系统。
英文摘要
Heuristic search underlies planning in autonomous systems ranging from warehouse logistics to robotic navigation, yet generic heuristics fail to exploit the structural constraints that govern constrained spatial domains, causing search performance to degrade catastrophically on harder instances. We study this problem through the two-column Flying Block Puzzle, a rigorously NP-complete spatial planning microworld whose bottleneck geometry mirrors clearance-to-size constraints encountered in multi-agent path finding, autonomous vehicle navigation, and block relocation systems. We introduce the Class-Based Heuristic A* (CBHA*) algorithm, which integrates a General Move Constraint to capture minimum displacement costs when vacant units are scarce, a formal kinematic taxonomy partitioning the state space into seven mutually exclusive classes with provably admissible heuristics based on vacancy ratio and goal-piece geometry, and a class-conditional tie-breaking mechanism that dynamically switches between depth-priority and vertical-distance ordering to overcome f-value plateaus. Over 146 benchmark instances, CBHA* achieves a 93.4% success rate against 64% for Depth-Prioritized A*, 39% for Standard A*, and 17% for BFS, while reducing node expansions by 87.98% relative to Standard A* and sustaining an average effective branching factor of approximately 3, demonstrating that class-triggered adaptive heuristics constitute a principled mechanism for efficient spatial planning that generalizes structurally to physical constraint systems.
