The Cyclic Min-Max Sitting Arrangement (CMMSA) is a graph layout optimization problem where the vertices of an input signed graph must be assigned to those of a cyclic host graph in a one-to-one correspondence. The input graph contains weighted edges, \(+1\) or \(-1\) , representing positive and negative relationships between the vertices. For each vertex, a penalty occurs when an adjacent vertex connected by a negative-labeled edge is positioned closer in the cycle than any other adjacent vertex connected by a positive-labeled edge. The goal is to minimize the maximum number of such penalties occurring at any single vertex. This paper presents a comprehensive study based on the Variable Neighborhood Search (VNS) methodology for solving the CMMSA. Building upon successful applications of VNS in related problems, we analyze multiple algorithmic variants and strategies. Specifically, our investigation focuses on Variable Formulation Search (VFS), which defines multiple formulations for the problem, allowing it to further explore the solution space. We propose a total of four alternative formulations specially suited for this problem. The use of VFS within the VNS methodology outperforms the use of a default VNS schema, obtaining a better solution in 19 out of 20 instances considered in the study. The findings not only highlight the efficacy of the proposed approach but also provide a foundation for future research on the CMMSA and related graph layout optimization problems.