Exhaustive Search, Heuristics, and Metaheuristics: A Unified Framework for N-Queens
Bibliographic record
Abstract
The N-Queens problem is a classical constraint satisfaction challenge in artificial intelligence, where the task is to place N queens on an N × N chessboard such that no two queens threaten each other. While conceptually simple, the exponential growth of possible configurations makes it a benchmark problem for evaluating optimization strategies. This paper presents a comprehensive comparative analysis of four algorithmic approaches—Depth-First Search (DFS), Hill Climbing, Simulated Annealing, and Genetic Algorithms—implemented from scratch and evaluated under a unified framework. Each algorithm was tested on board sizes from N = 10 to N = 100, with performance assessed in terms of success rate, execution time, memory usage, and robustness under randomized initial states. Results show that DFS reliably solves small boards but becomes impractical beyond N = 30. Hill Climbing scales moderately but frequently converges to local optima. Genetic Algorithms exhibit inconsistent performance, requiring careful parameter tuning to avoid premature convergence. Simulated Annealing consistently outperformed other methods, achieving robust and scalable results across all board sizes with low memory overhead. The study’s novelty lies in its standardized benchmarking environment, detailed tracking of both successes and failures, and visual logging of solutions. These findings emphasize the strengths of metaheuristic methods—particularly Simulated Annealing—for large-scale constraint satisfaction and provide practical insights for designing hybrid or parallel approaches.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".