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Finding representations for an unconstrained bi-objective combinatorial optimization problem

Abstract

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.

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Acknowledgements

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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Correspondence to Luís Paquete.

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Jesus, A.D., Paquete, L. & Figueira, J.R. Finding representations for an unconstrained bi-objective combinatorial optimization problem. Optim Lett 12, 321–334 (2018). https://doi.org/10.1007/s11590-017-1129-6

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Keywords

  • Multiobjective combinatorial optimization
  • Representation problem
  • Dynamic programming