The impedance characteristics of the functionally graded core significantly influence the blast resistance capacity of the sandwich structure. Previous research works [1-2] have primarily focused on graded cores defined by thickness variations, whereas other potential grading mechanisms based on different geometric parameters remain largely unexplored. In the present work, multi-objective optimization is performed for a sandwich structure with functionally graded circular re-entrant star honeycomb [3] cores under blast loading conditions. The facings and the core of the sandwich structure are made up of 304 stainless steel and are modelled using a piecewise linear plasticity model. Several graded configurations of the auxetic core have been analysed, including length-graded, height-graded, and thickness-graded core architectures, while maintaining the total length of the unit cell as constant. Finite element analysis is conducted utilizing the LS-DYNA software suite, integrated with Python scripting capabilities. The analysis incorporates the Conventional Weapons Effects Program (CONWEP) to model the effects of a 260g TNT spherical air blast at a standoff distance of 500mm. A multi-objective optimization approach was used to determine the optimal geometric parameters for a functionally graded auxetic core, balancing energy absorption, displacement, and reaction forces. The optimization framework includes Optimal Latin Hypercube Design (OLHD) with Response Surface Method (RSM), and the non-dominated sorting genetic algorithm II (NSGA-II) is applied for parameter optimization. The findings indicate that the thickness-graded core exhibits high energy absorption (3.30%) with minimal deflection, whereas the height-graded core shows superior specific energy absorption (5.56%) as compared to the conventional re-entrant auxetic core. The reaction force at the boundary is lower for the length-graded core in comparison to the other core configurations.