Grouping strategies on two-phase methods for bi-objective combinatorial optimization

Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the identification of search zones that may contain other nondominated points...

Full description

Saved in:
Bibliographic Details
Published in:Computers & operations research Vol. 185; p. 107254
Main Authors: Mota, Felipe O., Paquete, Luís, Vanderpooten, Daniel
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.01.2026
Subjects:
Minimum spanning tree problem
Multi-objective combinatorial optimization
Ranking algorithms
Two-phase methods
Ranking algorithms
Two-phase methods
Minimum spanning tree problem
Multi-objective combinatorial optimization
ISSN:0305-0548
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the identification of search zones that may contain other nondominated points. The second phase focuses on exploring these search zones to locate the remaining points, which typically accounts for most of the computational cost. Ranking algorithms are frequently employed to explore each zone individually, but this approach leads to redundancies, causing multiple visits to the same solutions. To mitigate these redundancies, we propose several strategies that group adjacent zones, allowing a single run of the ranking algorithm for the entire group. Additionally, we explore an implicit grouping approach based on a new concept of coverage. Our experiments on the Bi-Objective Spanning Tree Problem demonstrate the beneficial impact of these grouping strategies when combined with coverage. •Improvement of ranking-based two-phase methods by grouping search zones.•Shortest-path formulation to compute a posteriori optimal grouping.•Extended coverage technique improves upon known results.•Dynamic grouping strategies reduce the total number of visited solutions up to 50%.
ISSN:0305-0548
DOI:10.1016/j.cor.2025.107254