A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On accuracy, robustness and tolerances in vector Boolean optimization
Tekijät: Nikulin Y, Karelkina O, Mäkelä MM
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2013
Journal: European Journal of Operational Research
Tietokannassa oleva lehden nimi: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Lehden akronyymi: EUR J OPER RES
Numero sarjassa: 3
Vuosikerta: 224
Numero: 3
Aloitussivu: 449
Lopetussivu: 457
Sivujen määrä: 9
ISSN: 0377-2217
DOI: https://doi.org/10.1016/j.ejor.2012.09.018
Tiivistelmä
A Boolean programming problem with a finite number of alternatives where initial coefficients (costs) of linear payoff functions are subject to perturbations is considered. We define robust solution as a feasible solution which for a given set of realizations of uncertain parameters guarantees the minimum value of the worst-case relative regret among all feasible solutions. For the Pareto optimality principle, an appropriate definition of the worst-case relative regret is specified. It is shown that this definition is closely related to the concept of accuracy function being recently intensively studied in the literature. We also present the concept of robustness tolerances of a single cost vector. The tolerance is defined as the maximum level of perturbation of the cost vector which does not destroy the solution robustness. We present formulae allowing the calculation of the robustness tolerance obtained for some initial costs. The results are illustrated with several numerical examples. (c) 2012 Elsevier B.V. All rights reserved.
A Boolean programming problem with a finite number of alternatives where initial coefficients (costs) of linear payoff functions are subject to perturbations is considered. We define robust solution as a feasible solution which for a given set of realizations of uncertain parameters guarantees the minimum value of the worst-case relative regret among all feasible solutions. For the Pareto optimality principle, an appropriate definition of the worst-case relative regret is specified. It is shown that this definition is closely related to the concept of accuracy function being recently intensively studied in the literature. We also present the concept of robustness tolerances of a single cost vector. The tolerance is defined as the maximum level of perturbation of the cost vector which does not destroy the solution robustness. We present formulae allowing the calculation of the robustness tolerance obtained for some initial costs. The results are illustrated with several numerical examples. (c) 2012 Elsevier B.V. All rights reserved.
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