Skill: wu-uk/civ6-adjacency-optimizer-map-optimization-strategy (version 0.1.0)

--- name: map-optimization-strategy description: Strategy for solving constraint optimization problems on spatial maps. Use when you need to place items on a grid/map to maximize some objective while satisfying constraints. --- # 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 For problems with a "center" constraint (e.g., all placements within range of a central point): - The anchor IS the center - try different center positions - For each center, the reachable high-value tiles are fixed - Optimize placement within each center's reach ## Algorithm Skeleton ```python def optimize_placements(map_tiles, constraints, num_placements): # Phase 1: Prune candidates = [t for t in map_tiles if is_valid_tile(t, constraints)] # Phase 2: Score and rank scored = [(tile, score_tile(tile, candidates)) for tile in candidates] scored.sort(key=lambda x: -x[1]) # Descending by score high_value = scored[:top_k] # Phase 3: Anchor search best_solution = None best_score = 0 for anchor in get_anchor_candidates(high_value, constraints): solution = greedy_expand(anchor, candidates, num_placements, constraints) solution = local_search(solution, candidates, constraints) if solution.score > best_score: best_solution = solution best_score = solution.score return best_solution ``` ## Key Insights 1. **Prune early, prune aggressively** - Every tile removed saves exponential work later 2. **High-value tiles cluster** - Good placements tend to be near other good placements (adjacency bonuses compound) 3. **Anchors constrain the search** - Once you fix an anchor, many other decisions follow logically 4. **Greedy + local search is often sufficient** - You don't need the global optimum; a good local optimum found quickly beats a perfect solution found slowly 5. **Constraint propagation** - When you place one item, update what's valid for remaining items immediately ## Common Pitfalls - **Ignoring interactions** - Placing item A may change the value of placing item B (adjacency effects, mutual exclusion) - **Over-optimizing one metric** - Balance intrinsic value with flexibility for remaining placements - **Forgetting to validate** - Always verify final solution satisfies ALL constraints


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