Operations Research Proceedings 2012 pp 43-48 | Cite as
The Linear Sum-of-Ratios Optimization Problem: A PSO-Based Algorithm
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Abstract
Problems modeled as a sum-of-ratios arise naturally when several rates (objectives) have to be optimized simultaneously. The linear sum-of-ratios problem is also used for computing nondominated solutions in multiobjective linear fractional programming problems when the weighted-sum is applied to the objective functions. We previously developed a Branch & Cut algorithm for computing solutions, considering a pre-defined error, for this kind of problems. The algorithm has a good performance for problems of medium dimensions (less than roughly ten ratios), even considering a very small pre-defined error. In this text we propose a combination of particle swarm optimization (PSO) techniques with the Branch & Cut algorithm in order to improve the performance of the computations for problems of higher dimensions. We present computational results for problems with up to twenty five ratios.
Keywords
Multiobjective Linear Fractional Programming Problems Medium Properties Search Region Electromagnetism-like Mechanism (EM) Shift VectorNotes
Acknowledgments
This work has been partially supported by FCT under project grant PEst-C/EEI/UI0308/2011 and by QREN, project EMSURE. We would also like to recognize the support of the “40th Anniversary of Faculty of Economics of University of Coimbra".
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