The coolest path problem

We introduce the coolest path problem, which is a mixture of two problems from distinct mathematical fields: The shortest path problem from combinatorial optimization and 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 demonstrate that it can be formulated and solved as a linear mixed-integer program.


  • TU Kaiserslautern
  • TU Darmstadt


  • Hausdorff Institute for Mathematics, Bonn, Germany

Related talks

  • The Coolest Path Problem, Seminar Nichtlineare Optimierung und Inverse Probleme, WIAS, Berlin, Germany, 2.11.2010.
  • The Coolest Path Problem, 23rd European Conference on Operational Research EURO 2009, Bonn, Germany, 8.7.2009.

Related publications

  • Martin Frank, Armin Fügenschuh, Michael Herty, Lars Schewe, MIP-PDE: Solving Discrete-Continuous Nonlinear Optimal Control Problems with Linear Mixed-Integer Programming Techniques , Hausdorff Research Institute for Mathematics, Bonn, 2011.
  • Martin Frank, Armin Fügenschuh, Michael Herty, Lars Schewe, The Coolest Path Problem , Networks and Heterogeneous Media, Vol. 5, No. 1, pp. 143 – 162, 2010.
  • Martin Frank, Armin Fügenschuh, Michael Herty, Lars Schewe, The Coolest Path Problem , ZIB Technical Report ZR-0937,2009.

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