108445 20230519145518.0 doi 10.1016/j.cor.2020.105124 sideral 122239 ART-2021-122239 eng Blanco, V. On the multisource hyperplanes location problem to fitting set of points 2021 Access copy available to the general public Unrestricted In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact Mixed Integer Linear (or Non Linear) programming formulation is presented for the problem and also an extended set partitioning formulation with a huge number of variables is derived. We develop a column generation procedure embedded within a branch-and-price algorithm for solving the problem by adequately performing its preprocessing, pricing and branching. We also analyze geometrically the optimal solutions of the problem, deriving properties which are exploited to generate initial solutions for the proposed algorithms. Finally, the results of an extensive computational experience are reported. The issue of scalability is also addressed showing theoretical upper bounds on the errors assumed by replacing the original datasets by aggregated versions. info:eu-repo/grantAgreement/ES/FEDER/CEI-3-FQM331 info:eu-repo/grantAgreement/ES/FEDER/US-1256951 info:eu-repo/grantAgreement/ES/MEC-FEDER/MTM2016-74983-C02-01 info:eu-repo/grantAgreement/ES/MEC-FEDER/MTM2016-74983-C02-02 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 5.159 2021 OPERATIONS RESEARCH & MANAGEMENT SCIENCE 20 / 87 = 0.23 2021 Q1 T1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS 35 / 112 = 0.312 2021 Q2 T1 ENGINEERING, INDUSTRIAL 19 / 50 = 0.38 2021 Q2 T2 1.855 2021 Management Science and Operations Research 2021 Q1 Computer Science (miscellaneous) 2021 Q1 8.3 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Japón, A. Ponce, D. Puerto, J. 128 (2021), 105124 [15 pp] Comput. oper. res. Computers and Operations Research 0305-0548 514329 http://zaguan.unizar.es/record/108445/files/texto_completo.pdf Postprint 926986 http://zaguan.unizar.es/record/108445/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:108445 articulos driver 2023-05-18-15:19:59 ARTICLE