8th Cologne/Twente Workshop on Graphs and Combinatorial Optimization (CTW 2009)

We present two approaches for the Euclidean TSP which compute high quality tours for large instances. Both approaches are based on pseudo backbones consisting of all common edges of good tours. The first approach starts with some pre-computed good tours. Using this approach we found record tours for seven VLSI instances. The second approach is window based and constructs from scratch very good tours of huge TSP instances, e. g., the World TSP.

[1]  Egon Balas,et al.  Optimizing over the split closure , 2008, Math. Program..

[2]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[3]  Matteo Fischetti,et al.  Optimizing over the first Chvátal closure , 2005, Math. Program..

[4]  Arie M. C. A. Koster,et al.  Combinatorial Optimization on Graphs of Bounded Treewidth , 2008, Comput. J..

[5]  Alberto Caprara,et al.  On the separation of split cuts and related inequalities , 2003, Math. Program..

[6]  Majid Sarrafzadeh,et al.  On the Sum Coloring Problem on Interval Graphs , 1999, Algorithmica.

[7]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[8]  Hans L. Bodlaender,et al.  A Tourist Guide through Treewidth , 1993, Acta Cybern..

[9]  James Renegar,et al.  On the Computational Complexity of Approximating Solutions for Real Algebraic Formulae , 1992, SIAM J. Comput..

[10]  Gérard Cornuéjols,et al.  Polyhedral study of the capacitated vehicle routing problem , 1993, Math. Program..

[11]  Martin Grötschel,et al.  The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[12]  Patrice Marcotte,et al.  Bilevel programming: A survey , 2005, 4OR.

[13]  Tibor Szkaliczki,et al.  Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is NP-Complete , 1999, SIAM J. Comput..

[14]  M. Golumbic Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57) , 2004 .

[15]  Ju. V. Matijasevic,et al.  ENUMERABLE SETS ARE DIOPHANTINE , 2003 .

[16]  Mohammad R. Salavatipour,et al.  On Sum Coloring of Graphs , 2003, Discret. Appl. Math..

[17]  Giovanni Rinaldi,et al.  When is min cut with negative edges easy to solve? Easy and difficult objective functions for max cut , 2000 .

[18]  S. Dempe Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints , 2003 .

[19]  Matteo Fischetti,et al.  On the separation of disjunctive cuts , 2011, Math. Program..

[20]  Andrea Lodi,et al.  On the MIR Closure of Polyhedra , 2007, IPCO.