Minimizacija vsote obteženih razdalj v evklidski ravnini : magistrsko delo

Premru, Jože (author), Cencelj, Matija (mentor), Gabrovšek, Boštjan (co-mentor)

V magistrskem delu bo predstavljen problem iskanja točke, od katere je vsota razdalj do preostalih končno mnogo točk v evklidski ravnini minimalna. Narejen bo zgodovinski pregled reševanja danega problema. Problem bo razširjen z dodajanjem uteži na posamezno povezavo in iskanjem optimalne lokaije točke, od katere je vsota razdalj do vseh točk minimalna. Predstavljen bo numerični postopek za iskanje rešitve razširjenega problema. Izdelana bo aplikaija, s katero bo moč grafično prikazati in analizirati dani problem. Rešitev takega problema lahko služi kot izhodišče za iskanje logističnega centra pri na primer tovornem prometu, poštnih storitvah in podobno.

• Language: Slovenian
• Keywords: Webrov problem, Fermat-Webrov problem, Fermatova točka, Fermat-Torricellijeva točka, Weiszfieldov algoritem
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Publisher: [J. Premru]
• Year: 2015
• Number of pages: 56 str.
• PID: 20.500.12556/RUL-72794
• UDC: 51(043.2)
• COBISS.SI-ID: 10731337
• Publication date in RUL: 01.10.2015

Secondary language

• Language: English
• Title: Minisum of weighted distances in euclid plane

Abstract

In the master thesis the problem of finding the point from which the sum of all the distances to any number of points in the Euclidean plane is minimal, will be presented. A historical overview of solving the given problem will be made. The given problem will be expanded by adding weights to the individual connections and finding the optimal location for the point mentioned above. A numerical method for finding a solution to the expended problem will be presented. An application, which allows a graphic display and analysis of the given problem, will be made. A solution for such a problem can act as the starting point in search of the logistics center for freight transport or postal services, and the like.

• Keywords: Minisum point