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Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality "from Condorcet to Pareto"

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  • Nikulin, Yury
  • Mäkelä, Marko M.

Abstract

A multicriteria Boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality "from Condorcet to Pareto", appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an optimal alternative preserves its optimality are calculated. To illustrate the way how the stability and accuracy functions can be used as efficient tools for post-optimal analysis, an application from the voting theory is considered.

Suggested Citation

  • Nikulin, Yury & Mäkelä, Marko M., 2010. "Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality "from Condorcet to Pareto"," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1497-1505, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1497-1505
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    References listed on IDEAS

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    1. Yury Nikulin, 2009. "Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies," Annals of Operations Research, Springer, vol. 172(1), pages 25-35, November.
    2. Marek Libura & Yury Nikulin, 2006. "Stability and accuracy functions in multicriteria linear combinatorial optimization problems," Annals of Operations Research, Springer, vol. 147(1), pages 255-267, October.
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    Cited by:

    1. Elena Krugliakova & Alexey Gorin & Anna Shestakova & Vasily Klucharev, 2015. "Short-Term Plasticity in Auditory Cortical Circuit Evoked by Monetary Incentive Delay Task," HSE Working papers WP BRP 55/PSY/2015, National Research University Higher School of Economics.
    2. Nikulin, Y. & Karelkina, O. & Mäkelä, M.M., 2013. "On accuracy, robustness and tolerances in vector Boolean optimization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 449-457.
    3. Korotkov, Vladimir & Wu, Desheng, 2020. "Evaluating the quality of solutions in project portfolio selection," Omega, Elsevier, vol. 91(C).
    4. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

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