A branch & cut algorithm for the windy general routing problem and special cases

In this paper, we present an exact algorithm for the Windy General Routing Problem. This problem generalizes many important Arc Routing Problems and also has some interesting real-life applications. The Branch & Cut method presented here is based on a cutting-plane algorithm that identifies violated inequalities of several classes of facet-inducing inequalities for the corresponding polyhedron. The whole procedure has been tested over different sets of instances and is capable of solving to optimality large-size instances of several routing problems defined on undirected, mixed, and windy graphs. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 49(4), 245–257 2007

[1]  Jack Edmonds,et al.  Matching, Euler tours and the Chinese postman , 1973, Math. Program..

[2]  Christos H. Papadimitriou,et al.  On the complexity of edge traversing , 1976, J. ACM.

[3]  E. Minieka.  The Chinese Postman Problem for Mixed Networks , 1979 .

[4]  Peter Brucker.  The Chinese Postman Problem for Mixed Graphs , 1980, WG.

[5]  M. R. Rao,et al.  Odd Minimum Cut-Sets and b-Matchings , 1982, Math. Oper. Res..

[6]  Meigu Guan,et al.  On the windy postman problem , 1984, Discret. Appl. Math..

[7]  B. Fleischmann.  A cutting plane procedure for the travelling salesman problem on road networks , 1985 .

[8]  Gérard Cornuéjols,et al.  The traveling salesman problem on a graph and some related integer polyhedra , 1985, Math. Program..

[9]  Ángel Corberán,et al.  An algorithm for the Rural Postman problem on a directed graph , 1986 .

[10]  M. Padberg,et al.  Addendum: Optimization of a 532-city symmetric traveling salesman problem by branch and cut , 1990 .

[11]  Giovanni Rinaldi,et al.  The symmetric traveling salesman polytope and its graphical relaxation: Composition of valid inequalities , 1991, Math. Program..

[12]  Martin Grötschel,et al.  A cutting plane algorithm for the windy postman problem , 1992, Math. Program..

[13]  Á. Corberán,et al.  A polyhedral approach to the rural postman problem , 1994 .

[14]  Michel Gendreau,et al.  Arc Routing Problems, Part II: The Rural Postman Problem , 1995, Oper. Res..

[15]  Wen Lea Pearn,et al.  Algorithms for the rural postman problem , 1995, Comput. Oper. Res..

[16]  Giovanni Rinaldi,et al.  The Graphical Asymmetric Traveling Salesman Polyhedron: Symmetric Inequalities , 1996, SIAM J. Discret. Math..

[17]  Adam N. Letchford.  New inequalities for the General Routing Problem , 1997 .

[18]  Ángel Corberán,et al.  The general routing problem polyhedron: Facets from the RPP and GTSP polyhedra , 1998, Eur. J. Oper. Res..

[19]  Gilbert Laporte,et al.  Improvement Procedures for the Undirected Rural Postman Problem , 1999, INFORMS J. Comput..

[20]  José Manuel Pastor,et al.  A climbing autonomous robot for inspection applications in 3D complex environments , 2000, Robotica.

[21]  M. Dror.  Arc Routing : Theory, Solutions and Applications , 2000 .

[22]  Ángel Corberán,et al.  A cutting plane algorithm for the General Routing Problem , 2001, Math. Program..

[23]  Ángel Corberán,et al.  The mixed general routing polyhedron , 2003, Math. Program..

[24]  Ángel Corberán,et al.  New heuristic algorithms for the windy rural postman problem , 2005, Comput. Oper. Res..

[25]  Ángel Corberán,et al.  New Results on the Mixed General Routing Problem , 2005, Oper. Res..

[26]  Ángel Corberán,et al.  Zigzag inequalities: a new class of facet-inducing inequalities for Arc Routing Problems , 2006, Math. Program..

[27]  Ángel Corberán,et al.  A comparison of two different formulations for arc routing problems on mixed graphs , 2006, Comput. Oper. Res..

[28]  Daniele Vigo,et al.  Lower bounds and heuristics for the Windy Rural Postman Problem , 2007, Eur. J. Oper. Res..

[29]  Ángel Corberán,et al.  The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra , 2008, SIAM J. Discret. Math..