8 Queens Puzzle · مساله هشت وزیر

حل مسئله ۸ وزیر توسط الگوریتم ژنتیک

Place eight queens on a chessboard so that none attacks another. A classic constraint problem — and a small, honest place to practice evolutionary search. Each board is a chromosome; the number of attacking pairs is its cost; selection, crossover, and mutation push the population toward a configuration whose fitness reaches zero.

The fitness function counts conflicts — any two queens sharing a row, column, or diagonal:

(defn fitness [chromosome]
  (let [N (count chromosome)]
    (reduce +
      (for [i (range N) j (range N) :when (> j i)]
        (let [q1 (get chromosome i) q2 (get chromosome j)]
          (if (or (= q1 q2) (corow? q1 q2) (cocolumn? q1 q2) (codiagonal? q1 q2))
            1 0))))))

Selection is fitness-proportional; crossover splices two boards at a random node; mutation nudges a single queen. The main loop iterates generations until it finds a zero-conflict board, stalls in a local minimum, or times out after 500 generations.

This was written in December 2015 at Amirkabir University of Technology (Tehran Polytechnic) — the first entry in what was then a Jekyll weblog. It is kept here unedited in spirit. The full source, comments and all, lives on GitHub.

github.com/zorvan/N-Queens