Locating a median line segment in Euclidean space: An application snapshot

U. Aytun Öztürk; Bryan A. Norman

Locating a median line segment in Euclidean space: An application snapshot

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In wind conversion systems it is possible to reduce wiring costs of connection to the grid through a bus bar. Assuming the turbines connect directly to the bus bar, which is needed for conditioning of the power provided, one can formulate a nonlinear math program that is used to find the optimal location of the bus bar. This problem reduces to the problem of locating a median line segment with unknown length in Euclidean space but with an additional term in the objective function that ensures proximity to the power grid. There are well established algorithms developed for locating median or center lines. However, location of line segments hasn't been thoroughly studied. Algorithms capable of finding a segment center with a given length for a planar point set exist. However, the median line segment location problem has not been solved to optimality to our knowledge. This work outlines an algorithm in detail that is capable of solving such a problem and demonstrates the application for a real-life problem.

Original language	English
Title of host publication	In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005
Editors	Petri Helo, Hector Cancela, Gerardo Rubino, Maria E. Urquhart
Publisher	International Centre for Innovation and Industrial Logistics (ICIIL)
Pages	153-162
Number of pages	10
ISBN (Electronic)	9974002745
State	Published - 2005
Event	7th International Conference on Industrial Logistics: In Memoriam Lilian Barros, ICIL 2005 - Montevideo, Uruguay Duration: Feb 14 2005 → Feb 18 2005

Publication series

Name	In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005

Conference

Conference	7th International Conference on Industrial Logistics: In Memoriam Lilian Barros, ICIL 2005
Country	Uruguay
City	Montevideo
Period	02/14/05 → 02/18/05

Keywords

Location theory
Optimization methods
Wind energy

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Cite this

Öztürk, U. A., & Norman, B. A. (2005). Locating a median line segment in Euclidean space: An application snapshot. In P. Helo, H. Cancela, G. Rubino, & M. E. Urquhart (Eds.), In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005 (pp. 153-162). (In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005). International Centre for Innovation and Industrial Logistics (ICIIL).

Öztürk, U. Aytun ; Norman, Bryan A. / Locating a median line segment in Euclidean space : An application snapshot. In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005. editor / Petri Helo ; Hector Cancela ; Gerardo Rubino ; Maria E. Urquhart. International Centre for Innovation and Industrial Logistics (ICIIL), 2005. pp. 153-162 (In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005).

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abstract = "In wind conversion systems it is possible to reduce wiring costs of connection to the grid through a bus bar. Assuming the turbines connect directly to the bus bar, which is needed for conditioning of the power provided, one can formulate a nonlinear math program that is used to find the optimal location of the bus bar. This problem reduces to the problem of locating a median line segment with unknown length in Euclidean space but with an additional term in the objective function that ensures proximity to the power grid. There are well established algorithms developed for locating median or center lines. However, location of line segments hasn't been thoroughly studied. Algorithms capable of finding a segment center with a given length for a planar point set exist. However, the median line segment location problem has not been solved to optimality to our knowledge. This work outlines an algorithm in detail that is capable of solving such a problem and demonstrates the application for a real-life problem.",

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Öztürk, UA & Norman, BA 2005, Locating a median line segment in Euclidean space: An application snapshot. in P Helo, H Cancela, G Rubino & ME Urquhart (eds), In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005. In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005, International Centre for Innovation and Industrial Logistics (ICIIL), pp. 153-162, 7th International Conference on Industrial Logistics: In Memoriam Lilian Barros, ICIL 2005, Montevideo, Uruguay, 02/14/05.

Locating a median line segment in Euclidean space : An application snapshot. / Öztürk, U. Aytun; Norman, Bryan A.

In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005. ed. / Petri Helo; Hector Cancela; Gerardo Rubino; Maria E. Urquhart. International Centre for Innovation and Industrial Logistics (ICIIL), 2005. p. 153-162 (In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Öztürk, U. Aytun

AU - Norman, Bryan A.

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N2 - In wind conversion systems it is possible to reduce wiring costs of connection to the grid through a bus bar. Assuming the turbines connect directly to the bus bar, which is needed for conditioning of the power provided, one can formulate a nonlinear math program that is used to find the optimal location of the bus bar. This problem reduces to the problem of locating a median line segment with unknown length in Euclidean space but with an additional term in the objective function that ensures proximity to the power grid. There are well established algorithms developed for locating median or center lines. However, location of line segments hasn't been thoroughly studied. Algorithms capable of finding a segment center with a given length for a planar point set exist. However, the median line segment location problem has not been solved to optimality to our knowledge. This work outlines an algorithm in detail that is capable of solving such a problem and demonstrates the application for a real-life problem.

AB - In wind conversion systems it is possible to reduce wiring costs of connection to the grid through a bus bar. Assuming the turbines connect directly to the bus bar, which is needed for conditioning of the power provided, one can formulate a nonlinear math program that is used to find the optimal location of the bus bar. This problem reduces to the problem of locating a median line segment with unknown length in Euclidean space but with an additional term in the objective function that ensures proximity to the power grid. There are well established algorithms developed for locating median or center lines. However, location of line segments hasn't been thoroughly studied. Algorithms capable of finding a segment center with a given length for a planar point set exist. However, the median line segment location problem has not been solved to optimality to our knowledge. This work outlines an algorithm in detail that is capable of solving such a problem and demonstrates the application for a real-life problem.

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Öztürk UA, Norman BA. Locating a median line segment in Euclidean space: An application snapshot. In Helo P, Cancela H, Rubino G, Urquhart ME, editors, In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005. International Centre for Innovation and Industrial Logistics (ICIIL). 2005. p. 153-162. (In Memoriam Lilian Barros - Proceedings of the International Conference on Industrial Logistics, ICIL 2005).