Complexity of necessary efficiency in interval linear programming and multiobjective linear programming

We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x * is called necessarily efficient if it is efficient for all instances of interval...

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Bibliographic Details
Published in:Optimization letters Vol. 6; no. 5; pp. 893 - 899
Main Author: Hladík, Milan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.06.2012
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Interval matrix
Multiobjective linear programming
Efficient solution
NP-completeness
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x * is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the case of only one objective. Provided that x * is a non-degenerate basic solution, the problem is polynomially solvable for one objective, but remains co-NP-hard in the general case. Some open problems are mentioned at the end of the paper.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-011-0315-1