Survey of Methods of Solving TSP along with its Implementation using Dynamic Programming Approach

The Traveling salesperson problem is one of the problem in mathematics and computer science which haddrown attention as it is easy to understand and difficult to solve. In this paper, we survey the various methods/techniques available to solve traveling salesman problem and analyze it to make critical evaluation of their time complexities. An implementation of the traveling salesman problem using dynamic programming is also presented in this paper which generates optimal answer and tested with 25 cities and it executes in reasonable time.

[1]  Ailsa H. Land,et al.  An Automatic Method of Solving Discrete Programming Problems , 1960 .

[2]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[3]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[4]  Daniel J. Rosenkrantz,et al.  An Analysis of Several Heuristics for the Traveling Salesman Problem , 1977, SIAM J. Comput..

[5]  Alex Fraser,et al.  Simulation of Genetic Systems by Automatic Digital Computers I. Introduction , 1957 .

[6]  J. S. F. Barker,et al.  Simulation of Genetic Systems by Automatic Digital Computers , 1958 .

[7]  Tom Downs,et al.  Fast optimization by Demon Algorithms , 1998 .

[8]  Gregory Gutin,et al.  Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number , 2002, Discret. Appl. Math..

[9]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[10]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

[11]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

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

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

[14]  李幼升,et al.  Ph , 1989 .

[15]  As Fraser,et al.  Simulation of Genetic Systems by Automatic Digital Computers II. Effects of Linkage on Rates of Advance Under Selection , 1957 .

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

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

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

[19]  Leena Jain,et al.  Traveling Salesman Problem: A Case Study , 2012, BIOINFORMATICS 2012.

[20]  David L. Applegate,et al.  The traveling salesman problem , 2006 .

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

[22]  Vinod Chachra,et al.  Applications of graph theory algorithms , 1979 .

[23]  A. Land,et al.  An Automatic Method for Solving Discrete Programming Problems , 1960, 50 Years of Integer Programming.

[24]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[25]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .

[26]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[27]  Richard W. Eglese,et al.  Simulated annealing: A tool for operational research , 1990 .

[28]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[29]  David S. Johnson,et al.  The Traveling Salesman Problem: A Case Study in Local Optimization , 2008 .

[30]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

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

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

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

[34]  Marco Furini,et al.  International Journal of Computer and Applications , 2010 .

[35]  岡野 裕之,et al.  Study of practical solutions for combinatorial optimization problems , 2009 .