Traveling Salesman Problem (TSP) is one of the
most widely studied real world problems of finding the shortest (minimum cost)
possible route that visits each node in a given set of nodes (cities) once and then
returns to origin city. The optimization of cuboid areas has potential samples that
can be adapted to real world. Cuboid surfaces of buildings, rooms, furniture etc.
can be given as examples. Many optimization algorithms have been used in solution
of optimization problems at present. Among them, meta-heuristic algorithms come
first. In this study, ant colony optimization, one of meta-heuristic methods, is
applied to solve Euclidian TSP consisting of nine different sized sets of nodes
randomly placed on a cuboid surface. The performance of this method is shown in
Arora, S. (1996) Polynomial Time Approximation Schemes for Euclidean TSP and Other Geometric Problems. Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, Burlington, 14-16 October 1996, 2-11.
Shinozawa, K., Uchiyama, T. and Shimohara, K. (1991) An Approach for Solving Dynamic TSPs Using Neural Networks. Proceedings of the IEEE International Joint Conference on Neural Networks, 3, 2450-2454.
Colorni, A., Dorigo, M. and Maniezzo, V. (1991) Distributed Optimization by Ant Colonies. In: Varela, F. and Bourgine, P., Eds., Proceedings of the European Conference on Artificial Life, ECAL’91, Paris, Elsevier Publishing, Amsterdam, 134-142.
Colorni, A., Dorigo, M. and Maniezzo, V. (1992) An Investigation of Some Properties of an Ant Algorithm. In: Maenner, R. and Manderick, B., Eds., Proceedings of the Second Conference on Parallel Problem Solving from Na- ture, Brussels, PPSN II, North-Holland, Amsterdam, 509- 520.
Johnson, D.S. and McGeoch, L.A. (1997) The Traveling Salesman Problem: A Case Study in Local Optimization. In: Aarts, E.H.L. and Lenstra, J.K., Eds., Local Search in Combinatorial Optimization, John Wiley & Sons, New York, 215-310.
Marinakis, Y., Migdalas, A. and Pardalos, P.M. (2005) A Hybrid Genetic-GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem. Journal of Combinatorial Optimization, 10, 311-326.