Evaluation and Comparison of Brute-Force Search and Constrained Optimization Algorithms to Solve the N-Queens Problem

Abstract

AbstractThe N-Queens problem is relevant in Artificial Intelligence (AI); the solution methodology has been used in different computational intelligent approaches. Max Bezzel proposed the problem in 1848 for eight queens in 8 \(\times\) 8 chessboard. After that, the formulation was modified to an N-Queens problem in a chessboard. There are several ways of posing the problem and algorithms to solve it. We describe two commonly used mathematical models that handle the position of queens and restrictions. The first and easiest way is to find one combination that satisfies the solution. The second model uses a more compact notation to represent the queen’s potions. This generic problem has been solved with many different algorithms. However, there is no comparison of the performance among the methods. In this work, a comparison of performance for different problem sizes is presented. We tested the Backtracking, Branch and Bound, and Linear Programming algorithms for a different number of queens, reaching 17. In addition, we present statistical comparative experimental results of the different methods.