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On the calculation of stability radius for multi-objective combinatorial optimization problems by inverse optimization |
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| Authors: | Julien Roland Yves De Smet José Rui Figueira |
| Institution: | 1. CoDE-SMG, Service de Mathématiques de la Gestion, Ecole Polytechnique de Bruxelles, Université Libre de Bruxelles, Boulevard du Triomphe CP 210-01, 1050, Brussels, Belgium 2. CEG-IST, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001, Lisboa, Portugal 3. LORIA Laboratory, Nancy, France |
| Abstract: | This paper deals with stability analysis in multi-objective combinatorial optimization problems. The stability radius of an efficient solution is defined as the maximal adjustment of the problem parameters such that this solution remains efficient. An algorithm based on inverse optimization is proposed to compute it. The adjustment is limited to the coefficients of the objective functions and measured by the Chebyshev norm. This approach is applied to randomly generated instances of the bi-objective knapsack problem and computational results are reported. Several illustrative examples are analyzed. |
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