Population-Based Search Method Using Uncertainty-related Pareto Front for Robust Multi-objective Optimization

TL;DR

This paper identifies drawbacks of convergence-centric robustness in RMOP and introduces the Uncertainty-related Pareto Front (UPF) as a population-focused framework that balances convergence guarantees with robustness under decision-variable noise. It formalizes USP as worst-case robust benchmarks at confidence α and defines UPF as the non-dominated set of USPs, transforming robust optimization into a UPF-driven search. Building on this, the authors propose RMOEA-UPF, an archive-centric MOEA that iteratively updates an elite archive via USP-based robustness-convergence assessments and constructs a final robust solution set through niche-based diversity control. Extensive experiments on nine benchmarks and a greenhouse control case demonstrate superior robustness-convergence performance (via mGD and IGD) and practical applicability, with analyses of parameter effects on UPF quality. Overall, UPF offers a principled foundation for efficient, generalizable robust optimization under uncertainty, and RMOEA-UPF demonstrates its effectiveness in both synthetic and real-world settings.

Abstract

Traditional robust multi-objective optimization methods typically prioritize convergence while treating robustness as a secondary consideration. This approach can yield solutions that are not genuinely robust optimal under noise-affected scenarios. Furthermore, compared to population-based search methods, determining the robust optimal solution by evaluating the robustness of a single convergence-optimal solution is also inefficient. To address these two limitations,we propose a novel Uncertainty-related Pareto Front (UPF) framework that balances robustness and convergence as equal priorities. Unlike traditional Pareto Front, the UPF explicitly accounts for decision variable with noise perturbation by quantifying their effects on both convergence guarantees and robustness preservation equally within a theoretically grounded and general framework. Building upon UPF, we propose RMOEA-UPF--a population-based search robust multi-objective optimization algorithm. This method enables efficient search optimization by calculating and optimizing the UPF during the evolutionary process.Experiments on nine benchmark problems and a real-world application demonstrate that RMOEA-UPF consistently delivers high-quality results. Our method's consistent top-ranking performance indicates a more general and reliable approach for solving complex, uncertain multi-objective optimization problems. Code is available at: https://github.com/WenxiangJiang-me/RMOEA-UPF.

Figures (19)

• Figure 1: Greenhouse Microclimate Optimization Control System
• Figure 2: Diagram of traditional robust multi-objective optimization problems.
• Figure 3: Diagram of robustness comparison
• Figure 4: Diagram of UPF
• Figure 5: Main framework of RMOEA-UPF

Theorems & Definitions (2)

• Definition 1
• Definition 2