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.
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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".
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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
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DOI: https://doi.org/10.1007/978-3-319-00795-3_7
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