Optimization Letters

, Volume 12, Issue 2, pp 321–334 | Cite as

Finding representations for an unconstrained bi-objective combinatorial optimization problem

  • Alexandre D. Jesus
  • Luís Paquete
  • José Rui Figueira
Original Paper


Typically, multi-objective optimization problems give rise to a large number of optimal solutions. However, this information can be overwhelming to a decision maker. This article introduces a technique to find a representative subset of optimal solutions, of a given bounded cardinality for an unconstrained bi-objective combinatorial optimization problem in terms of \(\epsilon \)-indicator. This technique extends the Nemhauser–Ullman algorithm for the knapsack problem and allows to find a representative subset in a single run. We present a discussion on the representation quality achieved by this technique, both from a theoretical and numerical perspective, with respect to an optimal representation.


Multiobjective combinatorial optimization Representation problem Dynamic programming 



This work was partially supported by the European Regional Development Fund (FEDER), through the COMPETE 2020—Operational Program for Competitiveness and Internationalization (POCI).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Alexandre D. Jesus
    • 1
  • Luís Paquete
    • 1
  • José Rui Figueira
    • 2
  1. 1.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.CEG-IST, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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