<p>This article introduces the Multiobjective Single-Allocation Hub Median Problem (MO-SA-H-MP), extending the traditional Single-Allocation Hub Median Problem (SA-H-MP) to incorporate dual optimization objectives. SA-H-MP focuses on minimizing transportation costs by strategically locating hubs and central hubs within a network of demand nodes. However, MO-SA-H-MP introduces an innovative approach by simultaneously targeting the reduction of transportation costs among nodes and the overhead associated with hubs and central hubs. Unlike prior Hierarchical Hub Location Problem (HHLP) models, our formulation preserves the single-allocation constraint while explicitly modeling load-based overhead costs along with transportation cost, thus introducing a new variant of multi-objective HHLP network design. The study uses two approaches to solve MO-SA-H-MP. The first approach is based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithm for multiobjective optimization, while the second approach uses a Genetic Algorithm (GA) with a local refinement-based technique to solve each objective separately. The resultant network obtained from GA is applied to the other objective and the solutions of both approaches are compared. The NSGA-II-based approach is found to perform equivalently to the exact method in 48.32% of cases, perform better than the indirect approach of solving each objective separately in more than 81.67% of cases and have a deviation of less than 10% in 67.50% of cases from the direct approach for solving each objective separately using the Refined GA-based technique.</p>