The Linear Sum-of-Ratios Optimization Problem: A PSO-Based Algorithm

João Paulo Costa () and Maria João Alves ()
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João Paulo Costa: Faculty of Economics University of Coimbra—INESC Coimbra
Maria João Alves: Faculty of Economics University of Coimbra—INESC Coimbra

A chapter in Operations Research Proceedings 2012, 2014, pp 43-48 from Springer

Abstract: 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 Vector (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-319-00795-3_7

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DOI: 10.1007/978-3-319-00795-3_7

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