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

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 o...

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Veröffentlicht in:European journal of operational research Jg. 207; H. 3; S. 1497 - 1505
Hauptverfasser: Nikulin, Yury, Mäkelä, Marko M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 16.12.2010
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
Accuracy
Applied sciences
Boolean
Boolean algebra
Combinatorial analysis
Condorcet optimality
Condorcet optimality Pareto optimality Stability and accuracy Multicriteria optimization
Cost function
Decision theory. Utility theory
Exact sciences and technology
Flows in networks. Combinatorial problems
Linear programming
Mathematical analysis
Mathematical programming
Multicriteria optimization
Multiple criteria decision making
Norms
Operational research and scientific management
Operational research. Management science
Optimization
Parameter optimization
Pareto optimality
Pareto optimum
Perturbation methods
Stability
Stability and accuracy
Studies
Pareto optimality
Condorcet optimality
Multicriteria optimization
Stability and accuracy
Condorcet effect
Boolean programming
Pareto optimum
Multicriteria analysis
Multiobjective programming
Linear programming
Initial cost
Combinatorial optimization
Social decision
Lexicography
Voting
Quality control
Cost function
Optimality principle
ISSN:0377-2217, 1872-6860
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Zusammenfassung: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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.06.042