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.
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: Invalid for any placement
candidates = [t for t in map_tiles if is_valid_tile(t, constraints)]
scored = [(tile, score_tile(tile, candidates)) for tile in candidates] scored.sort(key= lambda x: -x[ 1 ])
high_value = scored[:top_k]
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 Prune early, prune aggressively