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Improved Dominance Filtering for Unions and Minkowski Sums of Pareto Sets

Authors Konstantinos Karathanasis , Spyros Kontogiannis , Christos Zaroliagis

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Data structures design and analysis
Keywords
  • Multi-Objective Optimization
  • Multi-Dimensional Data Structures
  • Pareto Sets
  • Algorithm Engineering

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Abstract

A key task in multi-objective optimization is to compute the Pareto frontier (a.k.a. Pareto subset) P of a given d-dimensional objective space F; that is, a maximal subset P ⊆ F such that every element in P is non-dominated (i.e., it is better in at least one criterion, against any other point) within F. This process, called dominance-filtering, often involves handling objective spaces derived from either the union or the Minkowski sum of two given partial objective spaces which are Pareto sets themselves, and constitutes a major bottleneck in several multi-objective optimization techniques. In this work, we introduce three new data structures, ND^{+}-trees, QND^{+}-trees and TND^{+}-trees, which are designed for efficiently indexing non-dominated objective vectors and performing dominance-checks. We also devise three new algorithms that efficiently filter out dominated objective vectors from the union or the Minkowski sum of two Pareto sets. An extensive experimental evaluation on both synthetically generated and real-world data sets reveals that our new algorithms outperform state-of-art techniques for dominance-filtering of unions and Minkowski sums of Pareto sets, and scale well w.r.t. the number of d ≥ 3 criteria and the sets' sizes.

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Konstantinos Karathanasis, Spyros Kontogiannis, and Christos Zaroliagis. Improved Dominance Filtering for Unions and Minkowski Sums of Pareto Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.59

Author Details

Konstantinos Karathanasis
  • Department of Computer Engineering and Informatics, University of Patras, Greece
  • PIKEI New Technologies, Patras, Greece
Spyros Kontogiannis
  • Department of Computer Engineering and Informatics, University of Patras, Greece
  • Computer Technology Institute and Press "Diophantus", Patras, Greece
Christos Zaroliagis
  • Department of Computer Engineering and Informatics, University of Patras, Greece
  • Computer Technology Institute and Press "Diophantus", Patras, Greece

Funding

This work was partially supported by the EU I3 Instrument under GA No 101115116 (project AMBITIOUS) and by the University of Patras under GA No 83770 (programme "MEDICUS").

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