A global optimization procedure for the location of a median line in the three-dimensional space
A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that the p...
| Authors: | , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/107475 |
| Online Access: | https://hdl.handle.net/11441/107475 https://doi.org/10.1016/j.ejor.2011.05.030 |
| Access Level: | Open access |
| Keyword: | Geometric branch-and-bound methods Global optimization Line location |
| Summary: | A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that the problem becomes much harder to solve. However, a problem parameterization as well as lower bounds are suggested whereby we succeeded in solving medium-size instances in a reasonable amount of computing time. |
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