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Combining an ε-Constraint Method with the Pareto Global Constraint

Authors Manuel Combarro Simón , Pierre Talbot , Pascal Bouvry

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Subject Classification

ACM Subject Classification
  • Applied computing → Multi-criterion optimization and decision-making
  • Theory of computation → Constraint and logic programming
  • Theory of computation → Mathematical optimization
Keywords
  • Multi-objective combinatorial optimization
  • constraint programming
  • Pareto global constraint
  • ε-constraint method
  • SAUGMECON

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Abstract

Many real-life problems involve multiple conflicting objectives; hence, the decision maker is provided with a set of trade-off solutions, the Pareto front. While many methods to compute Pareto fronts have been proposed in the mathematical programming literature, comparatively few approaches are available for constraint programming (CP). One of the main state-of-the-art algorithms in CP is a branch-and-bound method that uses a Pareto global constraint, denoted here as MOBAB-CP. In this work, we adapt the SAUGMECON algorithm, a well-known and efficient ε-constraint method, in a CP solver. We also propose a new algorithm that combines SAUGMECON with the Pareto global constraint. Experimental results show that the proposed algorithm consistently achieves better results than our CP implementation of SAUGMECON and is competitive with MOBAB-CP, outperforming it on several of the studied problems.

Cite As Get BibTex

Manuel Combarro Simón, Pierre Talbot, and Pascal Bouvry. Combining an ε-Constraint Method with the Pareto Global Constraint. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.14

Author Details

Manuel Combarro Simón
  • University of Luxembourg, Esch-sur-Alzette, Luxembourg
  • Interdisciplinary Centre for Security, Reliability and Trust (SnT), Esch-sur-Alzette, Luxembourg
Pierre Talbot
  • University of Luxembourg, Esch-sur-Alzette, Luxembourg
Pascal Bouvry
  • University of Luxembourg, Esch-sur-Alzette, Luxembourg

Funding

  • Combarro Simón, Manuel: This work is partially funded by the Luxembourg National Research Fund (FNR) - ASTRAL Project, ref. 17043604, and by the joint research programme UL/SnT-ILNAS on Technical Standardization for Trustworthy ICT, Aerospace, and Construction.

Acknowledgements

The experiments presented in this paper were carried out using the HPC facilities of the University of Luxembourg [Sebastien Varrette et al., 2022].

Supplementary Materials

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