A1 Refereed original research article in a scientific journal
On accuracy, robustness and tolerances in vector Boolean optimization
Authors: Nikulin Y, Karelkina O, Mäkelä MM
Publisher: ELSEVIER SCIENCE BV
Publication year: 2013
Journal: European Journal of Operational Research
Journal name in source: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Journal acronym: EUR J OPER RES
Number in series: 3
Volume: 224
Issue: 3
First page : 449
Last page: 457
Number of pages: 9
ISSN: 0377-2217
DOI: https://doi.org/10.1016/j.ejor.2012.09.018
Abstract
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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