Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function

The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud law enforcement, disease spread modeling, cancer astronomical observation, composition, fine art appreciation, sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach show converges solution under specific conditions. Here, we introduce distance concept prove the convergence based empirical probability. Moreover, numerical example provided easily explain theorem.