Uncertainty-Aware Dual-Ranking Strategy for Offline Data-Driven Multi-Objective Optimization

Offline data-driven Multi-Objective Optimization Problems (MOPs) rely on limited data from simulations, experiments, or sensors. This scarcity leads to high epistemic uncertainty in surrogate predictions. Conventional surrogate methods such as Kriging assume Gaussian distributions, which can yield suboptimal results when the assumptions fail. To address these issues, we propose a simple yet novel dual-ranking strategy, working with a basic multi-objective evolutionary algorithm, NSGA-II, where the built-in non-dominated sorting is kept and the second rank is devised for uncertainty estimation. In the latter, we utilize the uncertainty estimates given by several surrogate models, including Quantile Regression (QR), Monte Carlo Dropout (MCD), and Bayesian Neural Networks (BNNs). Concretely, with this dual-ranking strategy, each solution's final rank is the average of its non-dominated sorting rank and a rank derived from the uncertainty-adjusted fitness function, thus reducing the risk of misguided optimization under data constraints. We evaluate our approach on benchmark and real-world MOPs, comparing it to state-of-the-art methods. The results show that our dual-ranking strategy significantly improves the performance of NSGA-II in offline settings, achieving competitive outcomes compared with traditional surrogate-based methods. This framework advances uncertainty-aware multi-objective evolutionary algorithms, offering a robust solution for data-limited, real-world applications.