From Exact Search to Evolutionary Algorithms: Benchmarking N-Queens Solvers
Bibliographic record
Abstract
The N-Queens problem, a classical benchmark in combinatorial optimization, is widely used to evaluate algorithmic strategies across search, heuristic, and metaheuristic paradigms. This paper presents a systematic comparative study of four representative algorithms—Depth-First Search (DFS), Hill-Climbing (HC), Simulated Annealing (SA), and Genetic Algorithms (GA)—analyzed under a standardized experimental framework. Each solver was implemented in Python and tested on board sizes ranging from N = 10 to N = 200, with performance measured by success rate, runtime, memory usage, initialization robustness, and sensitivity to parameter tuning. Results indicate that DFS provides guaranteed completeness for small-scale problems but becomes intractable beyond N = 30 due to exponential runtime growth. HC offers fast approximate solutions for medium board sizes but suffers from premature convergence to local optima and sensitivity to initialization. SA consistently outperformed HC in both robustness and scalability, achieving success rates above 80% for N ≤ 100, though performance declined on very large boards. GA demonstrated the highest reliability for large-scale instances (N ≥ 100), maintaining near-100% success rates with greater computational cost and tuning complexity. These findings highlight the trade-offs between completeness, scalability, and robustness, offering actionable guidelines for selecting suitable algorithms in large-scale constraint satisfaction problems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 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 teacher head, 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".