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

TL;DR

This paper explores the use of evolutionary multitasking to generate sets of Pareto optimal solutions across diverse real-world problems, enhancing understanding and decision-making in multiobjective scenarios.

Contribution

It demonstrates the application of the SOS concept in engineering, inventory, and hyperparameter optimization problems, and evaluates current multitasking methods on these tasks.

Findings

Visualizations of SOS in decision and objective spaces.

A new measurement for Pareto set similarity.

Insights into Pareto solution shifts across tasks.

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.