Abstract
This paper introduces an integer linear program for a variant of the linear ordering problem. This considers, besides the pairwise preferences in the objective function as the linear ordering problem, positional preferences (weighted rank) in the objective. The objective function is mathematically supported, as the full integer linear program is motivated by the instant run-off voting method to aggregate individual preferences. The paper describes two meta-heuristics, iterated local search and Memetic algorithms to deal with large instances which are hard to solve to optimality. These results are compared with the objective value of the linear relaxation. The instances used are the ones available from the LOP library, and new real instances with preferences given by juries.
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Acknowledgements
This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications).
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Appendix A
Appendix A
A large table with the results for Eurovision song contest is shown in this appendix to not disaggregate the text of this paper (Table 10).
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Vieira, M.V.C. A linear ordering problem with weighted rank. J Comb Optim 47, 13 (2024). https://doi.org/10.1007/s10878-024-01109-x
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DOI: https://doi.org/10.1007/s10878-024-01109-x