Representing the Non-dominated Set of Multi-objective Network Problems by Supported Non-dominated Points

2026-07-13

AI Summary

This work addresses the challenge of efficiently generating high-quality fixed-size representations from the typically vast set of nondominated solutions in multi-objective network optimization. The authors propose using supported nondominated points—particularly extreme points—as a compact candidate set to replace the full nondominated set for subset selection. For the first time, they systematically demonstrate that supported nondominated points in capacitated network problems offer both high representational quality and computational efficiency. Experimental results show that fixed-size solution sets selected solely from this reduced candidate set achieve solution quality nearly equivalent to those selected from the complete nondominated set, while substantially reducing computational overhead.

Abstract

In multi-objective combinatorial optimization, unsupported non-dominated points typically outnumber supported points and are often significantly more challenging to compute. Recent studies show that extreme supported non-dominated points provide high-quality representations of the non-dominated set for certain binary problems. We demonstrate that this observation does not generalize to capacitated network optimization problems: representation quality decreases with increasing arc capacities, whereas supported non-dominated points consistently provide high-quality representations with respect to several quality indicators. However, supported point sets may still be too large in practical applications, where only a small, fixed number of alternatives is typically desired. Selecting fixed-size representations from the non-dominated set requires its computationally expensive generation and thus diminishes the computational advantages that representations are intended to provide. We therefore suggest the (extreme) supported points as alternative candidate sets in subset selection problems. Our numerical results show that restricting the candidate set to supported non-dominated points yields fixed-size representations of nearly the same quality as those selected from the complete non-dominated set. Overall, supported non-dominated points serve both as high-quality representations and as reasonable candidate sets for subset selection.

Problem

• multi-objective optimization
• non-dominated set
• supported points
• network optimization
• subset selection

Innovation

• supported non-dominated points
• multi-objective network optimization
• subset selection
• representation quality
• computational efficiency