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

• Published in: European journal of operational research Vol. 207; no. 3; pp. 1497 - 1505
• Main Authors: Nikulin, Yury, Mäkelä, Marko M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.12.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: 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
• DOI: 10.1016/j.ejor.2010.06.042

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.