Neuro-immune approach to solve routing problems

Routing problems constitute an important class of problems because they are hard to solve and have a wide variety of real-world applications. Two of the most well-studied routing problems are the traveling salesman problem (TSP) and the multiple traveling salesmen problem (MTSP). This paper proposes the use of a neuro-immune self-organizing network to solve both, TSP and MTSP. The algorithms are introduced and a brief review of the literature on self-organizing networks, applied separately to each of these problems, is performed. To assess the performance of the proposed algorithms, a number of tests are conducted on benchmark data, and the results are directly compared with those of similar works. The results obtained show a better performance in terms of the best solution found for many instances, and an equivalent average performance. The main advantages of the proposed approach are its network constructive architecture and the use of a single growing network to solve the MTSP.

[1]  S. X. Yang,et al.  An improved self-organizing map approach to traveling salesman problem , 2003, IEEE International Conference on Robotics, Intelligent Systems and Signal Processing, 2003. Proceedings. 2003.

[2]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[3]  Bezalel Gavish,et al.  An Optimal Solution Method for Large-Scale Multiple Traveling Salesmen Problems , 1986, Oper. Res..

[4]  Frederico Carvalho Vieira,et al.  An Efficient Approach to the Travelling Salesman Problem Using Self-Organizing Maps , 2003, Int. J. Neural Syst..

[5]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[6]  Bernard Angéniol,et al.  Self-organizing feature maps and the travelling salesman problem , 1988, Neural Networks.

[7]  Yves Crama,et al.  Local Search in Combinatorial Optimization , 2018, Artificial Neural Networks.

[8]  Leandro Nunes de Castro,et al.  A Constructive Self-Organizing Network Applied to a Discrete Optimization Problem , 2007, Seventh International Conference on Intelligent Systems Design and Applications (ISDA 2007).

[9]  Lixin Tang,et al.  A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex , 2000, Eur. J. Oper. Res..

[10]  Takao Enkawa,et al.  Competition-based neural network for the multiple travelling salesmen problem with minmax objective , 1999, Comput. Oper. Res..

[11]  Takao Enkawa,et al.  A self-organising model for the travelling salesman problem , 1997 .

[12]  William M. Springer Review of the traveling salesman problem: a computational study by Applegate, Bixby, Chvátal, and Cook (Princeton University Press) , 2009, SIGA.

[13]  Yasuo Matsuyama,et al.  Self-organizing neural networks and various euclidean traveling salesman problems , 1992, Systems and Computers in Japan.

[14]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[15]  Mahesan Niranjan,et al.  A theoretical investigation into the performance of the Hopfield model , 1990, IEEE Trans. Neural Networks.

[16]  B. John Oommen,et al.  The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem , 1999, Neural Networks.

[17]  B. Fritzke,et al.  FLEXMAP-a neural network for the traveling salesman problem with linear time and space complexity , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[18]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[19]  Jean-Yves Potvin,et al.  A Generalized K-Opt Exchange Procedure For The MTSP , 1989 .

[20]  Kate Smith-Miles,et al.  Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research , 1999, INFORMS J. Comput..

[21]  F. Azuaje Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

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

[23]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics) , 2007 .

[24]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[25]  Leandro Nunes de Castro,et al.  A Neuro-Immune Network for Solving the Traveling Salesman Problem , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[26]  Enrique Mérida Casermeiro,et al.  An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem , 2001, Neural Processing Letters.

[27]  Keld Helsgaun,et al.  An effective implementation of the Lin-Kernighan traveling salesman heuristic , 2000, Eur. J. Oper. Res..

[28]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[29]  Takao Enkawa,et al.  A self‐organizing neural network approach for multiple traveling salesman and vehicle routing problems , 1999 .

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

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

[32]  Leandro Nunes de Castro,et al.  Fundamentals of Natural Computing - Basic Concepts, Algorithms, and Applications , 2006, Chapman and Hall / CRC computer and information science series.

[33]  E. M. Cochrane,et al.  The co-adaptive neural network approach to the Euclidean Travelling Salesman Problem , 2003, Neural Networks.

[34]  Laura I. Burke,et al.  The guilty net for the traveling salesman problem , 1992, Comput. Oper. Res..

[35]  Bruce L. Golden,et al.  Solving vehicle routing problems using elastic nets , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[36]  Andrew Howard Gee,et al.  Problem solving with optimization networks , 1993 .

[37]  J. Fort Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem , 1988, Biological Cybernetics.

[38]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[39]  Yanping Bai,et al.  The incorporation of an efficient initialization method and parameter adaptation using self-organizing maps to solve the TSP , 2006, Appl. Math. Comput..

[40]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .