NDLI: Criteria and dimension reduction of linear multiple criteria optimization problems

Content Provider	Springer Nature Link
Author	Thoai, Nguyen V.
Copyright Year	2011
Abstract	Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential) objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions. Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria. This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple objective optimization.
Starting Page	499
Ending Page	508
Page Count	10
File Format	PDF
ISSN	09255001
Journal	Journal of Global Optimization
Volume Number	52
Issue Number	3
e-ISSN	15732916
Language	English
Publisher	Springer US
Publisher Date	2011-08-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multicriteria optimization Optimization over the efficient set Utility function programs Criteria reduction Dimension reduction Global optimization Operations Research/Decision Theory Computer Science Optimization Real Functions
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

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