where g ref (r) denotes the radial distribution function from the reference fine-grained simulation. Effective potentials derived from structure-based coarse-graining often show (thermodynamic) state dependence, e.g., temperature, composition, 50 etc, even after the optimization. Additional constraints can be introduced to the coarse-graining process to improve the transferability and representability of the structure-based CG model. In structural coarse-graining, we believe that achieving an accurate CG model can be transformed into a problem of efficient multi-objective optimization with constraints. In this section, we begin with a brief introduction to DiffSim, explaining its fundamental principles and methodologies for optimizing CG potentials. Following that, we delve into the concept of multi-objective optimization algorithms, discussing how they can be integrated into DiffSim for faithful structure-based bottom-up coarse-graining.