Grouping Strategies on Two-Phase Methods for Bi-objective Combinatorial Optimization

Fuente: arXiv
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Main Authors: Mota, Felipe O., Paquete, Luís, Vanderpooten, Daniel
Format: Preprint
Published: 2025
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author Mota, Felipe O.
Paquete, Luís
Vanderpooten, Daniel
author_facet Mota, Felipe O.
Paquete, Luís
Vanderpooten, Daniel
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_06869
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Grouping Strategies on Two-Phase Methods for Bi-objective Combinatorial Optimization
Mota, Felipe O.
Paquete, Luís
Vanderpooten, Daniel
Data Structures and Algorithms
Discrete Mathematics
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.
title Grouping Strategies on Two-Phase Methods for Bi-objective Combinatorial Optimization
topic Data Structures and Algorithms
Discrete Mathematics
url https://arxiv.org/abs/2504.06869