A Comparative Analysis of Traveling Salesman Solutions from Geographic Information Systems

The Traveling Salesman Problem is one of the most prominent problems in combinatorial optimization, and is regularly employed in a wide variety of applications. The objective of this article is to demonstrate the extent of sub-optimality produced by Traveling Salesman solution procedures implemented in the context of Geographic Information Systems and to discuss the consequences that such solutions have for practice. Toward that end, an analysis is made of Traveling Salesman solutions from implementations in four Geographic Information System packages. These implementations are tested against the optimal solution for a range of problem sizes. Computational results are presented in the context of a school bus routing application. This analysis concludes that no Traveling Salesman implementation in GIS is likely to find the optimal solution when problems exceed 10 stops. In contrast, optimal solutions can be generated with desktop linear programming software for up to 25 cities. Moreover, one GIS implementation consistently found solutions that were closer to optimal than its competitors. This research strongly suggests that for applications with fewer than 25 stops, the use of an optimal solution procedure is advised, and that GIS implementations can benefit from the integration of more robust optimization techniques.

[1]  John E. Beasley,et al.  A tabu search algorithm for the single vehicle routing allocation problem , 2007, J. Oper. Res. Soc..

[2]  T Bektag,et al.  Solving school bus routing problems through integer programming , 2008 .

[3]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

[4]  L. Bodin.  ROUTING AND SCHEDULING OF VEHICLES AND CREWS–THE STATE OF THE ART , 1983 .

[5]  T. Bektaş.  The multiple traveling salesman problem: an overview of formulations and solution procedures , 2006 .

[6]  Gregory Gutin.  Traveling Salesman Problems , 2013 .

[7]  Michel Gendreau,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

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

[9]  David O'Sullivan,et al.  Geographical information science: agent-based models , 2008 .

[10]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[11]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[12]  Jonathan L. Gross,et al.  Introduction to Graphs , 2003, Handbook of Graph Theory.

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

[14]  Egon Balas,et al.  Report of the Session on: Branch and Bound/Implicit Enumeration , 1979 .

[15]  S. Skiena.  The Algorithm Design Manual, Second Edition , 2008 .

[16]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[17]  Manfred M. Fischer,et al.  GIS and Network Analysis , 2004 .

[18]  Lawrence Bodin,et al.  Approximate Traveling Salesman Algorithms , 1980, Oper. Res..

[19]  Richard L. Church,et al.  Geographical information systems and location science , 2002, Comput. Oper. Res..

[20]  Michel Gendreau,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Stochastic Demands and Customers , 1996, Oper. Res..

[21]  Howard J. Simkowitz,et al.  Transportation applications of geographic information systems , 1988 .

[22]  Buyang Cao,et al.  Applying GIS and OR Techniques to Solve Sears Technician-Dispatching and Home Delivery Problems , 1999, Interfaces.

[23]  Panos M. Pardalos,et al.  A Hybrid Genetic—GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem , 2005, J. Comb. Optim..

[24]  Abraham P. Punnen,et al.  The Traveling Salesman Problem: Applications, Formulations and Variations , 2007 .

[25]  Fred W. Glover,et al.  Implementation analysis of efficient heuristic algorithms for the traveling salesman problem , 2006, Comput. Oper. Res..

[26]  Gilbert Laporte,et al.  A tabu search heuristic for a routing problem arising in servicing of offshore oil and gas platforms , 2008, J. Oper. Res. Soc..

[27]  Armin Fügenschuh,et al.  Solving a school bus scheduling problem with integer programming , 2009, Eur. J. Oper. Res..

[28]  William J. Cook,et al.  Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems , 2003, Math. Program..

[29]  A J Klein.  MICROCOMPUTER-BASED VEHICLE ROUTING AND SCHEDULING: AN OVERVIEW , 1987 .

[30]  James P. Kelly,et al.  A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem , 1996, Transp. Sci..

[31]  Fred Glover,et al.  Tabu Search: A Tutorial , 1990 .

[32]  Edward P. K. Tsang,et al.  Guided local search and its application to the traveling salesman problem , 1999, Eur. J. Oper. Res..

[33]  J. Monnot,et al.  The Traveling Salesman Problem and its Variations , 2014 .

[34]  A. Ishigame,et al.  Multi‐point Tabu Search for traveling salesman problems , 2006 .

[35]  Lawrence Bodin,et al.  Microcomputer-based vehicle routing and scheduling software , 1986, Comput. Oper. Res..

[36]  Martha S. Hollis,et al.  Heuristic determination of postal delivery routes , 1985 .

[37]  Zhuo Fu,et al.  The school bus routing problem: a case study , 2002, J. Oper. Res. Soc..

[38]  Richard L. Church,et al.  Integrating Normative Location Models into GIS: Problems and Prospects with the p-median Model (94-5) - eScholarship , 1994 .

[39]  James R. Evans,et al.  Optimizing tabu list size for the traveling salesman problem , 1998, Comput. Oper. Res..

[40]  Claude-Nicolas Fiechter,et al.  A Parallel Tabu Search Algorithm for Large Traveling Salesman Problems , 1994, Discret. Appl. Math..

[41]  Hoon Jung,et al.  Integration of GIS, GPS, and optimization technologies for the effective control of parcel delivery service , 2006, Comput. Ind. Eng..

[42]  Kevin M. Curtin.  Network Analysis in Geographic Information Science: Review, Assessment, and Projections , 2007 .

[43]  Michel Gendreau,et al.  Parallel Tabu Search for Real-Time Vehicle Routing and Dispatching , 1999, Transp. Sci..

[44]  Nigel Waters,et al.  Transportation GIS: GIS-T , 2005 .

[45]  John C Sutton,et al.  The Role of GIS in Routing and Logistics , 2004 .

[46]  Lawrence Bodin,et al.  Twenty Years of Routing and Scheduling , 1990, Oper. Res..

[47]  Kevin M. Curtin,et al.  Determining Optimal Police Patrol Areas with Maximal Covering and Backup Covering Location Models , 2010 .

[48]  Jean-Yves Potvin,et al.  A tabu search heuristic for the vehicle routing problem with private fleet and common carrier , 2009, Eur. J. Oper. Res..

[49]  John Knox,et al.  Tabu search performance on the symmetric traveling salesman problem , 1994, Comput. Oper. Res..

[50]  A. Schrijver.  On the History of Combinatorial Optimization (Till 1960) , 2005 .

[51]  Gregory Gutin,et al.  The traveling salesman problem , 2006, Discret. Optim..

[52]  Alain Hertz,et al.  A Tabu Search Algorithm for the Split Delivery Vehicle Routing Problem , 2003, Transp. Sci..

[53]  Michel Gendreau,et al.  An Introduction to Tabu Search , 2003, Handbook of Metaheuristics.

[54]  Howard L Slavin.  The Role of GIS in Land Use and Transport Planning , 2004 .

[55]  Panos M. Pardalos,et al.  Expanding neighborhood search–GRASP for the probabilistic traveling salesman problem , 2008, Optim. Lett..

[56]  Hermant K. Bhargava,et al.  A web-based decision support system for waste disposal and recycling , 1997 .

[57]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

[58]  Andrew B. Whinston,et al.  Computer-Assisted School Bus Scheduling , 1972 .

[59]  Debbie A. Niemeier,et al.  GIS AND TRANSPORTATION PLANNING -- A CASE STUDY. , 1993 .

[60]  CaoBuyang,et al.  Applying GIS and Or Techniques to Solve Sears Technician-Dispatching and Home Delivery Problems , 1999 .

[61]  Shin-ichi Tanigawa,et al.  Generalized skew bisubmodularity: A characterization and a min-max theorem , 2014, Discret. Optim..

[62]  Gábor Nagy,et al.  A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries , 2008, J. Comb. Optim..

[63]  Paul H. Calamai,et al.  A multi-objective optimization approach to urban school bus routing: Formulation and solution method , 1995 .

[64]  Harvey J. Miller,et al.  Geographic Information Systems for Transportation in the 21st Century , 2015 .

[65]  Emmanouil E. Zachariadis,et al.  A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints , 2009, Eur. J. Oper. Res..

[66]  M. M. Flood.  The Traveling-Salesman Problem , 1956 .