On the multisource hyperplanes location problem to fitting set of points

•Multifacility location of hyperplanes.•Mixed integer programming formulations.•Set partitioning formulation.•Branch and Price algorithm. 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 pr...

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Bibliographic Details
Published in:Computers & operations research Vol. 128; p. 105124
Main Authors: Blanco, V., Japón, A., Ponce, D., Puerto, J.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2021
Subjects:
Column generation
Hyperplanes location
Mixed Integer Non Linear programming
Column generation
90B85
90C30
90C11
Hyperplanes location
52C35
Mixed Integer Non Linear programming
ISSN:0305-0548, 1873-765X
Online Access:Get full text
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Summary:•Multifacility location of hyperplanes.•Mixed integer programming formulations.•Set partitioning formulation.•Branch and Price algorithm. 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.
ISSN:0305-0548
1873-765X
DOI:10.1016/j.cor.2020.105124