1157
eng
reportzib
0
2009-11-23
2009-11-23
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The Coolest Path Problem
We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.
09-37
1438-0064
1216
urn:nbn:de:0297-zib-11571
Appeared in: NETWORKS AND HETEROGENEOUS MEDIA, Volume 5, Number 1, March 2010 pp. 143–162. doi:10.3934/nhm.2010.5.143
Martin Frank
unknown unknown
Armin Fügenschuh
Michael Herty
Lars Schewe
ZIB-Report
09-37
Mathematik
Heat equation
Network models, deterministic
Integer programming
Mathematical Optimization
Fügenschuh, Armin
https://opus4.kobv.de/opus4-zib/files/1157/ZR_09_37.pdf
https://opus4.kobv.de/opus4-zib/files/1157/Data.zip