Activities per year
Abstract
We propose new algebraic solutions for constrained minimax singlefacility location problems in multidimensional spaces with Chebyshev distance, and in the plane with rectilinear distance. We first formulate the location problems in a standard form, and outline existing solutions. Then, the problems are represented in terms of tropical (idempotent) algebra as optimization problems to minimize nonlinear objective functions defined on vectors over an idempotent semifield, subject to linear vector inequality and equality constraints. We apply methods and techniques of tropical optimization to obtain direct, explicit solutions of the problems. The results obtained are used to derive solutions of the location problems under consideration in a closed form, which is ready for formal analysis and straightforward computation. We examine extensions of the approach to handle other problems, such as rectilinear singlefacility location in highdimensional spaces and multifacility location. To illustrate, we present numerical solutions of example location problems and provide graphical representation of these solutions.
Original language  English 

Pages  91 
State  Published  Jul 2016 
Event  20th Conference of the International Linear Algebra Society  KU Leuven, Leuven, Belgium Duration: 11 Jul 2016 → 15 Jul 2016 https://ilas2016.cs.kuleuven.be/ 
Conference
Conference  20th Conference of the International Linear Algebra Society 

Abbreviated title  ILAS2016 
Country  Belgium 
City  Leuven 
Period  11/07/16 → 15/07/16 
Internet address 
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Activities

20th Conference of the International Linear Algebra Society
Николай Кимович Кривулин (Participant)
11 Jul 2016 → 15 Jul 2016Activity: Attendance types › Participating in a conference, workshop, ...

Tropical optimization techniques for solving minimax location problems with Chebyshev and rectilinear distances
Николай Кимович Кривулин (Speaker)
12 Jul 2016Activity: Talk types › Oral presentation