Abstract
The Plant Propagation algorithm (PPA), has been demonstrated to work well on continuous optimization problems. In this paper, we investigate its use in discrete optimization and particularly on the well known Travelling Salesman Problem (TSP). This investigation concerns the implementation of the idea of short and long runners when searching for Hamiltonian cycles in complete graphs. The approach uses the notion of k-optimality. The performance of the algorithm on a standard list of test problems is compared to that of the Genetic Algorithm (GA), Simulated Annealing (SA), Particle Swarm Optimization (PSO) and the New Discrete Firefly Algorithm (New DFA). Computational results are included.
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Aarts, E.H., Korst, J.H., van Laarhoven, P.J.: A quantitative analysis of the simulated annealing algorithm: a case study for the traveling salesman problem. J. Stat. Phys. 50(1–2), 187–206 (1988)
Albayrak, M., Allahverdi, N.: Development a new mutation operator to solve the traveling salesman problem by aid of genetic algorithms. Expert Syst. Appl. 38(3), 1313–1320 (2011)
Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. J. ACM 45(3), 501–555 (1998). doi:10.1145/278298.278306. http://doi.acm.org/10.1145/278298.278306
Bellmore, M., Nemhauser, G.L.: The traveling salesman problem: a survey. Oper. Res. 16(3), 538–558 (1968)
Clerc, M.: Discrete particle swarm optimization, illustrated by the traveling salesman problem. In: New Optimization Techniques in Engineering, pp. 219–239. Springer (2004)
Dorigo, M.: Ant colony optimization and swarm intelligence. In: Proceedings of 5th International Workshop, ANTS 2006, Brussels, Belgium, September 4–7, 2006, vol. 4150. Springer Science & Business Media (2006)
Dorigo, M., Gambardella, L.M.: Ant colonies for the travelling salesman problem. BioSystems 43(2), 73–81 (1997)
Fister Jr., I., Yang, X.S., Fister, I., Brest, J., Fister, D.: A brief review of nature-inspired algorithms for optimization. arXiv preprint arXiv:1307.4186 (2013)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)
Glover, F., Laguna, M.: Tabu Search. Springer (1999)
Grefenstette, J., Gopal, R., Rosmaita, B., Van Gucht, D.: Genetic algorithms for the traveling salesman problem. In: Proceedings of the First International Conference on Genetic Algorithms and their Applications, pp. 160–168. Lawrence Erlbaum, New Jersey (1985)
Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. J. Soc. Ind. Appl. Math 196–210 (1962)
Helsgaun, K.: An effective implementation of k-opt moves for the lin-kernighan tsp heuristic. Ph.D. thesis, Roskilde University. Department of Computer Science (2006)
Hoffman, K.L., Padberg, M., Rinaldi, G.: Traveling salesman problem. In: Encyclopedia of Operations Research and Management Science, pp. 1573–1578. Springer (2013)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U Michigan Press (1975)
Jati, G.K., Manurung, R., Suyanto: 13–discrete firefly algorithm for traveling salesman problem: a new movement scheme. In: X.S.Y.C.X.H.G. Karamanoglu (ed.) Swarm Intelligence and Bio-Inspired Computation, pp. 295–312. Elsevier, Oxford (2013). doi:10.1016/B978-0-12-405163-8.00013-2. http://www.sciencedirect.com/science/article/pii/B9780124051638000132
Jati, G.K., Suyanto: Evolutionary Discrete Firefly Algorithm for Travelling Salesman Problem. In: Bouchachia, Abdelhamid (ed.) Adaptive and Intelligent SystemsSpringer, pp. 393–403.Springer, Berlin, Heidelberg (2011). ISBN:978-3-642-23857-4
Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: a case study in local optimization. Local Search Comb. Optim. 1, 215–310 (1997)
Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J. Global Optim. 39(3), 459–471 (2007)
Karaboga, D., Gorkemli, B.: A combinatorial artificial bee colony algorithm for traveling salesman problem. In: Innovations in Intelligent Systems and Applications (INISTA), 2011 International Symposium on, pp. 50–53. IEEE (2011)
Karaboga, D., Gorkemli, B.: A quick artificial bee colony-qabc-algorithm for optimization problems. In: Innovations in Intelligent Systems and Applications (INISTA), 2012 International Symposium on, pp. 1–5. IEEE (2012)
Kennedy, J.: Particle swarm optimization. In: Encyclopedia of Machine Learning, pp. 760–766. Springer (2010)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Land, A.H., Doig, A.G.: An automatic method of solving discrete programming problems. Econometrica: J. Econometric Soc. 497–520 (1960)
Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59(2), 231–247 (1992)
Li, L., Cheng, Y., Tan, L., Niu, B.: A discrete artificial bee colony algorithm for tsp problem. In: Bio-Inspired Computing and Applications, pp. 566–573. Springer (2012)
Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973). doi:10.1287/opre.21.2.498. http://dx.doi.org/10.1287/opre.21.2.498
Mahi, M., mer Kaan Baykan, Kodaz, H.: A new hybrid method based on particle swarm optimization, ant colony optimization and 3-opt algorithms for traveling salesman problem. Appl. Soft Comput. 30, 484–490 (2015). doi:10.1016/j.asoc.2015.01.068. http://www.sciencedirect.com/science/article/pii/S1568494615000940
Mak, K.T., Morton, A.J.: Distances between traveling salesman tours. Discrete Appl. Math. 58(3), 281–291 (1995). doi:10.1016/0166-218X(93)E0115-F. http://www.sciencedirect.com/science/article/pii/0166218X93E0115F
Malek, M., Guruswamy, M., Pandya, M., Owens, H.: Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem. Ann. Oper. Res. 21(1), 59–84 (1989)
Marinakis, Y., Marinaki, M., Dounias, G.: Honey bees mating optimization algorithm for the euclidean traveling salesman problem. Inform. Sci. 181(20), 4684–4698 (2011)
Ouaarab, A., Ahiod, B., Yang, X.S.: Improved and discrete cuckoo search for solving the travelling salesman problem. In: Cuckoo Search and Firefly Algorithm, pp. 63–84. Springer (2014)
Padberg, M., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33(1), 60–100 (1991)
Pang, W., Wang, K.P., Zhou, C.G., Dong, L.J., Liu, M., Zhang, H.Y., Wang, J.Y.: Modified particle swarm optimization based on space transformation for solving traveling salesman problem. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 2004, vol. 4, pp. 2342–2346. IEEE (2004)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Courier Corporation (1998)
Rego, C., Gamboa, D., Glover, F., Osterman, C.: Traveling salesman problem heuristics: leading methods, implementations and latest advances. Eur. J. Oper. Res. 211(3), 427–441 (2011)
Reinelt, G.: TSPLIB–A T.S.P. library. Tech. Rep. 250, Universität Augsburg, Institut für Mathematik, Augsburg (1990)
Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Springer, Berlin (1994)
Saenphon, T., Phimoltares, S., Lursinsap, C.: Combining new fast opposite gradient search with ant colony optimization for solving travelling salesman problem. Eng. Appl. Artif. Intell. 35, 324–334 (2014). doi:10.1016/j.engappai.2014.06.026. http://dx.doi.org/10.1016/j.engappai.2014.06.026
Salhi, A.: The ultimate solution approach to intractable problems. In: Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications, pp. 84–93 (2010)
Salhi, A., Fraga, E.: Nature-inspired optimisation approaches and the new plant propagation algorithm. In: Proceedings of the ICeMATH2011 pp. K2–1 to K2–8 (2011)
Salhi, A., Proll, L.: Rios Insua, D., Martin, J.: Experiences with stochastic algorithms for a class of constrained global optimisation problems. RAIRO–Oper. Res. 34, 183–197 (2000). doi:10.1051/ro:2000110
Salhi, A., Rodríguez, J.A.V.: Tailoring hyper-heuristics to specific instances of a scheduling problem using affinity and competence functions. Memetic Comput. 6(2), 77–84 (2014)
Salhi, A., Töreyen, Ö.: A game theory-based multi-agent system for expensive optimisation problems. In: Computational Intelligence in Optimization, pp. 211–232. Springer (2010)
Shi, X.H., Liang, Y.C., Lee, H.P., Lu, C., Wang, Q.: Particle swarm optimization-based algorithms for tsp and generalized tsp. Inform. Process. Lett. 103(5), 169–176 (2007)
Song, X., Li, B., Yang, H.: Improved ant colony algorithm and its applications in tsp. In: Sixth International Conference on Intelligent Systems Design and Applications, 2006. ISDA’06, vol. 2, pp. 1145–1148. IEEE (2006)
Sulaiman, M., Salhi, A.: A Seed-based plant propagation algorithm: the feeding station model. Sci World J (2015)
Sulaiman, M., Salhi, A., Fraga, E.S.: The Plant Propagation Algorithm: Modifications and Implementation. ArXiv e-prints (2014)
Sulaiman, M., Salhi, A., Selamoglu, B.I., Kirikchi, O.B.: A plant propagation algorithm for constrained engineering optimisation problems. Mathematical Problems in Engineering 627416, 10 pp (2014). doi:10.1155/2014/627416
Supowit, K.J., Plaisted, D.A., Reingold, E.M.: Heuristics for weighted perfect matching. In: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 398–419. ACM (1980)
Supowit, K.J., Reingold, E.M., Plaisted, D.A.: The travelling salesman problem and minimum matching in the unit square. SIAM J. Comput. 12(1), 144–156 (1983)
Tsai, H.K., Yang, J.M., Tsai, Y.F., Kao, C.Y.: An evolutionary algorithm for large traveling salesman problems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(4), 1718–1729 (2004)
Yagiura, M., Ibaraki, T.: On metaheuristic algorithms for combinatorial optimization problems. Syst. Comput. Jpn 32(3), 33–55 (2001)
Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspir. Comput. 2(2), 78–84 (2010)
Yang, X.S.: Nature-inspired Metaheuristic Algorithms, 2nd edn. (2010)
Yang, X.S.: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74. Springer (2010)
Yang, X.S., Deb, S.: Cuckoo search via lévy flights. In: World Congress on Nature & Biologically Inspired Computing, 2009. NaBIC 2009. pp. 210–214. IEEE (2009)
Yang, X.S., Cui, Z., Xiao, R., Gandomi, A.H., Karamanoglu, M.: Swarm Intelligence and Bio-inspired Computation: Theory and Applications. Newnes (2013)
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Selamoğlu, B.İ., Salhi, A. (2016). The Plant Propagation Algorithm for Discrete Optimisation: The Case of the Travelling Salesman Problem. In: Yang, XS. (eds) Nature-Inspired Computation in Engineering. Studies in Computational Intelligence, vol 637. Springer, Cham. https://doi.org/10.1007/978-3-319-30235-5_3
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