The coolest path problem
Frank M, Fügenschuh AR, Herty M, Schewe L (2010)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2010
Journal
Publisher: American Institute of Mathematical Sciences (AIMS)
Book Volume: 5
Pages Range: 143-162
Journal Issue: 1
Abstract
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. © American Institute of Mathematical Sciences.
Authors with CRIS profile
Armin-René Fügenschuh
Economics - Discrete Optimization - Mathematics (EDOM)
Lars Schewe
Economics - Discrete Optimization - Mathematics (EDOM)
Involved external institutions
Germany (DE)How to cite
APA:
Frank, M., Fügenschuh, A.-R., Herty, M., & Schewe, L. (2010). The coolest path problem. Networks and Heterogeneous Media, 5(1), 143-162. https://dx.doi.org/10.3934/nhm.2010.5.143
MLA:
Frank, Martin, et al. "The coolest path problem." Networks and Heterogeneous Media 5.1 (2010): 143-162.
BibTeX: Download