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.
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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.
Exhaustive search (brute-force enumeration of all possible placements) is the worst approach:
Goal: Eliminate tiles that cannot contribute to a good solution.
Remove tiles that are:
Before: 100 tiles in consideration
After pruning: 20-30 candidate tiles
This alone can reduce search space by 70-90%.
Goal: Find tiles that offer exceptional value for your objective.
Score each remaining tile by:
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)
Goal: Find placements that capture as many high-value spots as possible.
For problems with a "center" constraint (e.g., all placements within range of a central point):
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
Prune early, prune aggressively - Every tile removed saves exponential work later
High-value tiles cluster - Good placements tend to be near other good placements (adjacency bonuses compound)
Anchors constrain the search - Once you fix an anchor, many other decisions follow logically
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
Constraint propagation - When you place one item, update what's valid for remaining items immediately
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