map-optimization-strategy

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:

1. Invalid for any placement - Violate hard constraints (wrong terrain, out of range, blocked)
2. Dominated - Another tile is strictly better in all respects
3. 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:

1. Intrinsic value - What does this tile contribute on its own?
2. Adjacency potential - What bonuses from neighboring tiles?
3. 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)

Phase 3: Anchor Point Search

Goal: Find placements that capture as many high-value spots as possible.

1. Select anchor candidates - Tiles that enable access to multiple high-value spots
2. Expand from anchors - Greedily add placements that maximize marginal value
3. Validate constraints - Ensure all placements satisfy requirements
4. Local search - Try swapping/moving placements to improve the solution