Discrete Bat Algorithm for Traveling Salesman Problem

In this paper, we present discrete bat algorithm (DBA) for solving the Traveling Salesman Problem (TSP). In this improved bat algorithm, on the one hand, the subtraction operator of location and location, the multiplication operator of real number and location, and the addition operator of velocity and location are redefined, on the other hand, the initial population are generated by Nearest Neighbor tour construction heuristic, and 2-opt edge-exchange algorithm is introduced to perform the local search. We test series of numerical instances by using 33 benchmark instances with sizes ranging from 55 to 318 nodes from the TSPLIB, and compare DBA with Chen and Chien's method (2011), Marinakis et al.'s method (2005), and Marinakis et al.'s method (2005). The experimental results show that the percentage deviations of DBA are better than that of the three methods and within satisfaction.

[1]  Shyi-Ming Chen,et al.  Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques , 2011, Expert Syst. Appl..

[2]  Alfonsas Misevičius,et al.  USING ITERATED TABU SEARCH FOR THE TRAVELING SALESMAN PROBLEM , 2015 .

[3]  Gary G. Yen,et al.  A hybrid evolutionary algorithm for traveling salesman problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[4]  Leandro Nunes de Castro,et al.  A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem , 2009, Inf. Sci..

[5]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[6]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[7]  Mary E. Kurz Heuristics for the Traveling Salesman Problem , 2011 .

[8]  Panos M. Pardalos,et al.  Expanding Neighborhood GRASP for the Traveling Salesman Problem , 2005, Comput. Optim. Appl..

[9]  Maria Teresinha Arns Steiner,et al.  A new approach to solve the traveling salesman problem , 2007, Neurocomputing.

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

[11]  Novruz Allahverdi,et al.  Development a new mutation operator to solve the Traveling Salesman Problem by aid of Genetic Algorithms , 2011, Expert Syst. Appl..

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

[13]  Christian Steczkó Nilsson,et al.  Heuristics for the Traveling Salesman Problem , 2003 .

[14]  Christian Blum,et al.  Evolutionary Computation in Combinatorial Optimization , 2015, Lecture Notes in Computer Science.

[15]  Marco César Goldbarg,et al.  Particle Swarm for the Traveling Salesman Problem , 2006, EvoCOP.

[16]  Kai Zhao,et al.  Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search , 2011, Appl. Soft Comput..