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

TL;DR

This work tackles offline data-driven multi-objective optimization under surrogate uncertainty by introducing an uncertainty-aware dual-ranking strategy for NSGA-II. By computing both an original and an uncertainty-adjusted fitness, and then averaging their non-dominated ranks, the method robustly guides survival selection while accommodating multiple surrogate models (Kriging, Quantile Regression, Monte Carlo Dropout, and Bayesian Neural Networks). Extensive experiments on 14 benchmark problems show that the dual-ranking approach often matches or surpasses state-of-the-art probabilistic MOEAs, while remaining robust under data scarcity and capable of handling constrained problems. The framework offers practical value for real-world, data-limited optimization tasks and points to future work on data streams and online adaptation.

Abstract

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.

Figures (3)

• Figure 1: Example of solution ranking in a multi-objective minimization problem, showing how surrogate evaluations ($f_\text{sur}(\boldsymbol{A})$, $f_\text{sur}(\boldsymbol{B})$) may misjudge the Pareto dominance relation due to prediction uncertainty, with the dashed circle denoting the uncertainty interval.
• Figure 2: Workflow of the enhanced non-dominated-sorting-based MOEA, in which the improvement is contributed by our proposed Dual-Ranking (DR) strategy. DR is the integration of rankings coming from the surrogate model training and conventional optimization process.
• Figure 3: Pareto front obtained on DTLZ1 using surrogate-based (sur) and real (real) evaluations for all compared methods. The bar chart in the bottom-right corner summarizes the corresponding HV values, with different surrogate models indicated by different colors. The best performance based on surrogate-based and real evaluations is denoted in bold. In the legend, the first row corresponds to the plots for surrogate-based and real evaluations, while the second and third rows refer to the bar charts.