🎨 Designing Heuristic Functions
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# 🎨 Designing Heuristic Functions ## 1. 🎯 Learning Objectives - Design heuristics by problem relaxation - Use pattern databases for 8-puzzle/15-puzzle - Explain admissible vs informed trade-off ## 2.
🎨 Designing Heuristic Functions
1. 🎯 Learning Objectives
- Design heuristics by problem relaxation
- Use pattern databases for 8-puzzle/15-puzzle
- Explain admissible vs informed trade-off
2. 📖 Core Content
3.1 Relaxation
Remove constraints from problem → easier problem → optimal cost is admissible heuristic. 8-puzzle relaxations:
- Relax "slide tile" to "move tile to any adjacent square" → Manhattan
- Relax "tile cannot occupy same square" → Hamming
- Relax both → 0 (trivial, useless)
3.2 Pattern Databases
Store optimal cost-to-goal for a subset of tiles (pattern). Use as heuristic for full problem. Example: 15-puzzle with 7-tile pattern database: precompute distances for all 7-tile configurations (~16M entries = ~64 MB).
3.3 Heuristic Quality
- More informed ≠ better if computation cost outweighs pruning savings
- Dominance: h₁ dominates h₂ if h₁(N) ≥ h₂(N) for all N
- Effective branching factor: b* = N^{1/d} where N = nodes expanded, d = solution depth Join Discord PreviousBest First SearchNextHeuristic Functions