A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem

The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not b...

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Bibliographic Details
Published in:Journal of global optimization Vol. 31; no. 1; pp. 1 - 16
Main Author: Jorge, Jesús M.
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.01.2005
Subjects:
Algorithms
Hypotheses
Linear programming
Optimization
Optimization algorithms
Studies
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported. [PUBLICATION ABSTRACT]
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-003-3784-7