Multi-Objective Optimization of Approximate Functionals via Implicit Interdependency Modeling

Accurate and transferable exchange-correlation (XC) functionals are central to the predictive power of density functional theory (DFT). However, conventional parameter optimization of XC functionals is typically performed using single-objective or stepwise strategies, which may lead to imbalanced performance across chemically diverse systems. This work introduces a multi-objective optimization framework, termed EBI4MO (explicit-by-implicit for multi-objectives), that enables simultaneous and consistent optimization with respect to multiple performance criteria. EBI4MO constructs a hierarchy of implicit functions that couple interdependent parameter groups across objectives, allowing sequential yet interlinked parameter updates. As a demonstration, EBI4MO is applied to optimize the parameters in hybrid XC functionals with dispersion corrections, using the GMTKN55 benchmark database. Two objectives are considered: minimizing the overall prediction error and achieving uniform improvement relative to B3LYP-D3(BJ), a widely used and balanced functional. The resulting functionals demonstrate consistent and balanced performance across all benchmark subsets, outperforming functionals optimized via conventional single-objective or stepwise methods. These results highlight the effectiveness and generality of EBI4MO, offering a new strategy for functional development and broader multi-objective optimization problems in computational chemistry.