Using the TSP Solution for Optimal Route Scheduling in Construction Management

History of the TSP is rather long. One of the first TSP-like problems was studied by Leonhard Euler in 1759 (Euler, 1759) whose interest was in solving the knight’s tour problem. An accurate solution of the knight’s tour problem would have a knight visit each of the 64 squares of a chessboard exactly once in its tour. First descriptive formulation of the TSP can be found in a famous German handbook for traveling salesman from 1832 (Voigt, 1832). The mentioned handbook handles the shortest route along 45 German cities. Taking into account the travel conditions of that time, the proposed 1832 German route might even be optimal.

[1]  Linus Schrage,et al.  Linear, Integer, and Quadratic Programming with Lindo , 1984 .

[2]  H. D. Ratliff,et al.  Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem , 1983, Oper. Res..

[3]  H. Crowder,et al.  Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality , 1980 .

[4]  Abraham P. Punnen,et al.  The traveling salesman problem and its variations , 2007 .

[5]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[6]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

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

[8]  William J. Cook,et al.  Certification of an optimal TSP tour through 85, 900 cities , 2009, Oper. Res. Lett..

[9]  P. Camerini,et al.  On improving relaxation methods by modified gradient techniques , 1975 .

[10]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[11]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

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

[13]  Daniel G. Espinoza,et al.  Computing with Domino-Parity Inequalities for the TSP , 2006 .

[14]  David Applegate,et al.  Finding Cuts in the TSP (A preliminary report) , 1995 .

[15]  George B. Dantzig,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, Oper. Res..

[16]  Martin Grötschel,et al.  Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme , 1977 .

[17]  A. Schrijver,et al.  The Traveling Salesman Problem , 2011 .

[18]  Martin Grötschel,et al.  A cutting plane algorithm for minimum perfect 2-matchings , 1987, Computing.