TY - JOUR
T1 - A linear ordering problem with weighted rank
AU - Vieira, Manuel V. C.
N1 - Funding Information:
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).
Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/3
Y1 - 2024/3
N2 - 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.
AB - 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.
KW - Aggregation of individual preferences
KW - Linear ordering problem
KW - Memetic algorithm
UR - http://www.scopus.com/inward/record.url?scp=85185832947&partnerID=8YFLogxK
U2 - 10.1007/s10878-024-01109-x
DO - 10.1007/s10878-024-01109-x
M3 - Article
AN - SCOPUS:85185832947
SN - 1382-6905
VL - 47
JO - Journal Of Combinatorial Optimization
JF - Journal Of Combinatorial Optimization
IS - 2
M1 - 13
ER -