<h3>🔥<strong>Introduction</strong></h3>
<p>Are you ready to improve your problem-solving skills with genetic algorithms? In this article, we delve into the fascinating world of genetic algorithms, drawing parallels with natural selection in humans. We’ll tackle the famous n-queens problem and build everything from scratch using the Julia language. With its growing popularity among scientific communities, you won’t want to miss this opportunity to learn more about Julia and how it can enhance your work. As my first written work, I’d love to hear your thoughts — so don’t hesitate to share your feedback with me!</p>
<h3>⁉️<strong>What is the n-Queens problem?</strong></h3>
<p>The problem statement goes as follows:</p>
<blockquote>
<p>Given n queens placed on an n*n chessboard, the challenge is to position these queens in such a way that no queen can attack another.</p>
</blockquote>
<p>It should be noted that this problem has a solution for $$n ≠ 2$$ and $n ≠ 3$. One of the most popular cases is the 8-queens problem, where n = 8. For this case, we can see that we have C(8 * 8, 8) = C(64, 8) = 4.426.165.368 possibilities, as we choose 8 positions out of 64 which is the number of squares on the board. Trying all of these possibilities can take an eternity. We can reduce the number of possibilities with some tricks, such as fixing one queen per row, which brings us to 8⁸ = 16.777.216 possibilities (8 choices of columns for each row), or fixing a permutation for these columns (i.e. we cannot choose 2 columns with the same number), which will bring us to 8! = 40.320. Although this is smaller than the number of base possibilities, trying all of these possibilities can be very costly, especially since we know we are just in the case n=8 which is a small number. For n=8, the problem does not have a unique solution, but 92 solutions.</p>


Conquer the n-queens puzzle with a genetic algorithm in Julia!