arXiv:2507.02337v1 Announce Type: cross Abstract: Understanding the behavior of numerical metaheuristic optimization algorithms is critical for advancing their development and application. Traditional visualization techniques, such as convergence plots, trajectory mapping, and fitness landscape analysis, often fall short in illustrating the structural dynamics of the search process, especially in high-dimensional or complex solution spaces. To address this, we propose a novel representation and visualization methodology that clusters solution candidates explored by the algorithm and tracks the evolution of cluster memberships across iterations, offering a dynamic and interpretable view of the search process. Additionally, we introduce two metrics - algorithm stability and algorithm similarity- to quantify the consistency of search trajectories across runs of an individual algorithm and the similarity between different algorithms, respectively. We apply this methodology to a set of ten numerical metaheuristic algorithms, revealing insights into their stability and comparative behaviors, thereby providing a deeper understanding of their search dynamics.