Open AccessJournal Article
Nonessential objective functions in linear multiobjective optimization problems
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TL;DR: This paper presents a new method to decide if a given linear objective function is nonessential or not, which is based on multiple criteria decision making and efficient solutions.
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Abstract: In multiobjective (vector) optimization problems, among the given objective functions there exist some, which do not influence the set of efficient solutions. These objective functions are said to be nonessential. In this paper we present a new method to decide if a given linear objective function is nonessential or not. Keywords: multiple criteria decision making, multiobjective (vector) optimization, efficient solutions, nonessential objectives.
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Citations
Criteria and dimension reduction of linear multiple criteria optimization problems
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Laurence Devillers,Tatsuya Kawahara,Roger K. Moore,Matthias Scheutz +3 more
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Many-objective optimization and hypervolume based search
Dimo Brockhoff
- 01 Jan 2009
TL;DR: This thesis tackles such many-objective optimization problems in terms of theoretical investigations to better understand why classical MOEAs have difficulties with many objectives and develops objective reduction techniques that automatically reduce the number of objectives while the Pareto dominance relation is preserved or only slightly changed.
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Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization
TL;DR: This work presents two methods for determining nonessential objective functions for multiple-criteria decision making problems using a computational implementation of a computer algebra system.
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Weakly and properly nonessential objectives in multiobjective optimization problems
TL;DR: This work characterize objective functions which do not change the set of efficient solutions (weakly efficient solutions, properly efficient solutions) and establishes relations between weakly nonessential, properly nonessential and nonessential functions.
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References
Existence of efficient solutions for vector maximization problems
TL;DR: In this article, the existence of efficient and properly efficient solutions for the vector maximization problem is examined, and conditions are derived which guarantee that the outcome of any improperly efficient point is the limit of the outcomes of some sequence of properly efficient points.
159
Nonessential objectives within network approaches for MCDM
Tomas Gal,Thomas Hanne +1 more
TL;DR: The application of network approaches for multicriteria decision making such as neural networks and an approach for combining M CDM methods (called MCDM networks) are considered and it is argued for considering redundancies such as nonessential objectives as a native feature in complex information processing.
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A Note on Size Reduction of the Objective Functions Matrix in Vector Maximum Problems
Tomas Gal
- 01 Jan 1980
TL;DR: In this article, a straightforward method is described how to determine at least a part of the deletable objective functions in vector maximum problems, where the matrix of the corresponding coefficients is reduced in size.
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•Journal Article
Changes of the set of efficient solutions by extending the number of objectives and its evaluation
TL;DR: In this article, a vector optimization problem with continuous and convex objective functions on a compact convex feasible set is considered, and the necessary and sufficient conditions for the sets of efficient solutions of these two problems to be equal are given.
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Redundant objective functions in linear vector maximum problems and their determination
Tomas Gal,Heiner Leberling +1 more
TL;DR: A method for determining all the relative and absolute redundant objectives, based on this theory, is given and Illustrative examples demonstrate the procedure.