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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Schaible, S., Shi, J.: Fractional programming: The sum-of-ratios case. Optim. Methods Softw. 18, 219–229 (2003)
Kuno, T.: A branch-and-bound algorithm for maximizing the sum of several linear ratios. J. Glob. Optim. 22, 155–174 (2002)
Benson, H.: A simplicial branch and bound duality-bounds algorithm for the linear sum of ratios problem. J. Optim. Theor. Appl. 112, 1–29 (2007)
Costa, J.: A Branch & Cut technique to solve a weighted-sum of linear ratios. Pac. J. Optim. 6(1), 21–38 (2010)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE international joint conference on, neural networks, pp. 1942–1948 (1995)
Charnes, A., Cooper, W.: Programming with linear fractional functions. Naval Res. Logistics Q. 9, 181–186 (1962)
Wu, W.-Y., Sheu, R.-L., Birbil, S.: Solving the sum-of-ratios problem by a stochastic search algorithm. J. Glob. Optim. 42, 91–109 (2008)
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".
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Costa, J.P., Alves, M.J. (2014). The Linear Sum-of-Ratios Optimization Problem: A PSO-Based Algorithm. In: Helber, S., et al. Operations Research Proceedings 2012. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-00795-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-00795-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00794-6
Online ISBN: 978-3-319-00795-3
eBook Packages: Business and EconomicsBusiness and Management (R0)