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Obtaining an outer approximation of the efficient set of nonlinear biobjective problems

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Abstract

A new method for obtaining an outer approximation of the efficient set of nonlinear biobjective optimization problems is presented. It is based on the well known ‘constraint method’, and obtains a superset of the efficient set by computing the regions of δ-optimality of a finite number of single objective constraint problems. An actual implementation, which makes use of interval tools, shows the applicability of the method and the computational studies on a set of competitive location problems demonstrate its efficiency.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Murcia, Murcia, Spain

    José Fernández & Boglárka Tóth

Authors
  1. José Fernández
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  2. Boglárka Tóth
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Corresponding author

Correspondence to José Fernández.

Additional information

An extended version of this paper, with more comments, details, examples, and references, can be found in Fernández and Tóth [5]. This paper has been supported by the Ministry of Education and Science of Spain under the research project SEJ2005-06273/ECON, in part financed by the European Regional Development Fund (ERDF).

Boglárka Tóth—On leave from the Research Group on Artificial Intelligence of the Hungarian Academy of Sciences and the University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1., Hungary.

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Fernández, J., Tóth, B. Obtaining an outer approximation of the efficient set of nonlinear biobjective problems. J Glob Optim 38, 315–331 (2007). https://doi.org/10.1007/s10898-006-9132-y

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