An Efficient Heuristic Algorithm for the Traveling Salesman Problem

This paper presents a new heuristic algorithm based on combining branch and bound algorithm and a dynamic simulation model for the traveling salesman problem. The approach uses the simulation results for creating the best tours within the branch and bound tree. The most advantage of this approach lies in the learning profcedure both in simulation process and B&B algorithm. In order to test the efficiency of the proposed algorithm, several computational experiments were conducted over middle-scale and large-scale problems. As the computational results show the algorithm can be used easily in practice with reasonable accuracy and speed.

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

[2]  Heinz Mühlenbein,et al.  Parallel Genetic Algorithms in Combinatorial Optimization , 1992, Computer Science and Operations Research.

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

[4]  Satoshi Matsuda,et al.  Set-theoretic comparison of mappings of combinatorial optimization problems to hopfield neural networks , 1996, Systems and Computers in Japan.

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

[6]  M. J. Rijckaert,et al.  Heuristic for the Asymmetric Travelling Salesman Problem , 1978 .

[7]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems , 1998, JACM.

[8]  Weixiong Zhang,et al.  Depth-First Branch-and-Bound versus Local Search: A Case Study , 2000, AAAI/IAAI.

[9]  Gerald L. Thompson,et al.  Computational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems. , 1977 .

[10]  Guangzhou Zeng,et al.  Study of genetic algorithm with reinforcement learning to solve the TSP , 2009, Expert Syst. Appl..

[11]  Cheng-Yan Kao,et al.  Applying the genetic approach to simulated annealing in solving some NP-hard problems , 1993, IEEE Trans. Syst. Man Cybern..

[12]  H. L. Ong,et al.  A New Heuristic Algorithm for the Classical Symmetric Traveling Salesman Problem , 2007 .

[13]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

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

[15]  Samuel J. Raff,et al.  Routing and scheduling of vehicles and crews : The state of the art , 1983, Comput. Oper. Res..

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

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

[18]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[19]  William J. Cook,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, 50 Years of Integer Programming.

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