SKILL.md
Map-Based Constraint Optimization Strategy
A systematic approach to solving placement optimization problems on spatial maps. This applies to any problem where you must place items on a grid to maximize an objective while respecting placement constraints.
Why Exhaustive Search Fails
Exhaustive search (brute-force enumeration of all possible placements) is the worst approach:
- Combinatorial explosion: Placing N items on M valid tiles = O(M^N) combinations
- Even small maps become intractable (e.g., 50 tiles, 5 items = 312 million combinations)
- Most combinations are clearly suboptimal or invalid
The Three-Phase Strategy
Phase 1: Prune the Search Space
Goal: Eliminate tiles that cannot contribute to a good solution.
Remove tiles that are:
- Invalid for any placement - Violate hard constraints (wrong terrain, out of range, blocked)
- Dominated - Another tile is strictly better in all respects
- Isolated - Too far from other valid tiles to form useful clusters
Before: 100 tiles in consideration
After pruning: 20-30 candidate tiles
This alone can reduce search space by 70-90%.
Phase 2: Identify High-Value Spots
Goal: Find tiles that offer exceptional value for your objective.
Score each remaining tile by:
- Intrinsic value - What does this tile contribute on its own?
- Adjacency potential - What bonuses from neighboring tiles?
- Cluster potential - Can this tile anchor a high-value group?
Rank tiles and identify the top candidates. These are your priority tiles - any good solution likely includes several of them.
Example scoring:
- Tile A: +4 base, +3 adjacency potential = 7 points (HIGH)
- Tile B: +1 base, +1 adjacency potential = 2 points (LOW)