A Hybrid Heuristic for Restricted 4-Dimensional TSP (r-4DTSP)
In this paper, we proposed a hybridized soft computing technique to solve a restricted 4-dimensional TSP (r-4DTSP) where different paths with various numbers of conveyances are available to travel between two cities. Here, some restrictions on paths and conveyances are imposed. The algorithm is a hybridization of genetic algorithm (GA) and swap operator-based particle swarm optimization (PSO). The initial solutions are produced by proposed GA which used as swarm in PSO. The said hybrid algorithm (GA-PSO) is tested against some test functions, and efficiency of the proposed algorithm is established. The r-4DTSPs are considered with crisp costs. The models are illustrated with some numerical data.
KeywordsHybrid algorithm GA-PSO r-4DTSP
This research article is supported by University Grant Commission of India by grant number PSW-150/14-15 (ERO).
- 1.Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The traveling salesman problem: G. E. Re Guided tour of combinatorial optimization. Wiley, New York (1985)Google Scholar
- 4.Petersen, H.L., Madsen, O.B.G.: The double travelling salesman problem with multiple stack—formulation heuristic solution approaches. Eur. J. Op. Res. 198, 339–347 (2009)Google Scholar
- 12.Ardalan, Z., Karimi, S., Poursabzi, O., Nader, B.: A novel imperialist competitive algorithm for generalized TSP. Appl. Soft Comput. xxx, XX–XX (2014)Google Scholar
- 13.Psychas, I.-D., Delimpasi, E., Marinakis, Y.: Hybrid evolutionary algorithms for the multiobjective traveling salesman problem. Expert Syst. Appl. https://doi.org/10.1016/j.eswa.2015.07.051
- 14.Kennedy, J., Eberhart, R.: Particle swarm optimization. IEEE Int. Conf. Neural Netw. 4, 1942–1948 (1995)Google Scholar
- 15.Chen, Y.L.: Particle swarm optimization survey for traveling salesman problem. Master Thesis. Department of Industrial Engineering and Management National Taipei University of Technology, July 2006Google Scholar
- 18.Wang, K., Hunang, L., Zhou, C.-G., Pang, W.: Particle swarm optimization for TSP, 2nd Intr. In: IEEE Conference on Machine Learning and Cybernetics, pp. 1583–1585 (2003)Google Scholar