Evolutionary Algorithms and Multi-Objective Minimum Spanning Trees with Limited Distinct Weight Values

2026-06-16

AI Summary

This study addresses the lack of theoretical understanding regarding the structure of the Pareto front and its impact on the runtime of evolutionary algorithms for the multi-objective minimum spanning tree problem under the practical assumption of finitely many distinct edge weights. The work provides the first systematic characterization of the Pareto front’s structural properties in this setting and, by integrating combinatorial optimization with runtime complexity theory, derives refined upper bounds on the expected running time of multi-objective evolutionary algorithms. The theoretical analysis elucidates how the discreteness of edge weights influences search difficulty, and empirical results confirm the high efficiency of these algorithms in scenarios with limited weight values, offering a novel perspective for the theoretical analysis of multi-objective combinatorial optimization.

Abstract

Evolutionary algorithms have been used for a wide range of multi-objective combinatorial optimization problems. Despite practical success, theoretical results on the runtime of evolutionary algorithms for multi-objective combinatorial problems are rather limited. One classical problem that has been investigated is the multi-objective minimum spanning tree problem for which runtime bounds have been obtained to compute all extremal corner points of the Pareto front. With this paper, we provide some more detailed insights into the structure of the Pareto front when the edge weights take on a small number of distinct values. Based on these insights, we derive new runtime results for evolutionary multi-objective algorithms and complement our theoretical results with experimental investigations.

Problem

• Evolutionary Algorithms
• Multi-Objective Optimization
• Minimum Spanning Trees
• Pareto Front
• Runtime Analysis

Innovation

• Evolutionary Algorithms
• Multi-Objective Optimization
• Minimum Spanning Tree
• Pareto Front
• Runtime Analysis