Decision space robustness for multi-objective integer linear programming

Michael Stiglmayr (), José Rui Figueira (), Kathrin Klamroth (), Luís Paquete () and Britta Schulze ()
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Michael Stiglmayr: University of Wuppertal
José Rui Figueira: Universidade de Lisboa
Kathrin Klamroth: University of Wuppertal
Luís Paquete: University of Coimbra
Britta Schulze: University of Wuppertal

Annals of Operations Research, 2022, vol. 319, issue 2, No 13, 1769-1791

Abstract: Abstract In this article we introduce robustness measures in the context of multi-objective integer linear programming problems. The proposed measures are in line with the concept of decision robustness, which considers the uncertainty with respect to the implementation of a specific solution. An efficient solution is considered to be decision robust if many solutions in its neighborhood are efficient as well. This rather new area of research differs from robustness concepts dealing with imperfect knowledge of data parameters. Our approach implies a two-phase procedure, where in the first phase the set of all efficient solutions is computed, and in the second phase the neighborhood of each one of the solutions is determined. The indicators we propose are based on the knowledge of these neighborhoods. We discuss consistency properties for the indicators, present some numerical evaluations for specific problem classes and show potential fields of application.

Keywords: Multi-objective integer programming; Decision space robustness; Connectedness of efficient solutions; Representation; Decision analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-04462-w

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