Finding Sets of Pareto Sets in Real-World Scenarios -- A Multitask Multiobjective Perspective

2026-04-03

AI Summary

This study addresses the challenge of efficiently generating and managing Pareto-optimal solution sets (SOS) in heterogeneous multi-task environments. It proposes an evolutionary multi-task optimization framework to construct compact, task-specific SOS repositories for real-world applications such as engineering design, inventory management, and hyperparameter optimization. The work introduces a novel similarity metric between Pareto sets and, for the first time, systematically validates the cross-domain applicability of SOS. Through visualization and objective space analysis, it reveals dynamic patterns in solution set performance across diverse task contexts. Experimental results demonstrate that the proposed approach effectively captures inter-task differences in solution sets and significantly enhances decision-making support across varying scenarios.

Abstract

Recently, evolutionary multitasking has been employed to generate a ``set of Pareto sets" (SOS) for machine learning models, addressing diverse task settings across heterogeneous environments. This involves creating a repository of compact, specialized solution models that are collectively tailored to each specific task setting and environment, enabling users to select the most suitable model based on particular specifications and preferences. In this paper, we further demonstrate the versatility and applicability of the SOS concept across diverse domains, focusing on three real-world problems: engineering design problems, inventory management problems, and hyperparameter optimization problems. Additionally, as evolutionary multitasking has proven effective in generating the SOS, we investigate the performance of current evolutionary multitasking methods on these real-world problems. Subsequently, we present visualizations of the generated SOS in both decision and objective spaces, complemented by the development of a measurement to gauge the similarity between different Pareto sets corresponding to diverse tasks. Finally, we show that by systematically examining the shifts in Pareto optimal designs across different task settings though the SOS solutions, users can gain deeper understandings on the dynamic interplay between design solutions and their performance in different settings or contexts.

Problem

• Pareto sets
• multitask optimization
• real-world applications
• evolutionary multitasking
• multiobjective optimization

Innovation

• Set of Pareto Sets
• evolutionary multitasking
• multiobjective optimization
• Pareto set similarity
• real-world applications