Abstract
In this paper, we present an improved and discrete version of the Cuckoo Search (CS) algorithm to solve the famous traveling salesman problem (TSP), an NP-hard combinatorial optimisation problem. CS is a metaheuristic search algorithm which was recently developed by Xin-She Yang and Suash Deb in 2009, inspired by the breeding behaviour of cuckoos. This new algorithm has proved to be very effective in solving continuous optimisation problems. We now extend and improve CS by reconstructing its population and introducing a new category of cuckoos so that it can solve combinatorial problems as well as continuous problems. The performance of the proposed discrete cuckoo search (DCS) is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that DCS is superior to some other metaheuristics.
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References
Abdel-Kader RF (2011) Fuzzy particle swarm optimization with simulated annealing and neighbourhood information communication for solving TSP. Int J Adv Comput Sci Appl 2(5):15–21
Arora S (1998) Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J ACM (JACM) 45(5):753–782
Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surveys (CSUR) 35(3):268–308
Bonomi E, Lutton JL (1984) The n-city travelling salesman problem: statistical mechanics and the metropolis algorithm. SIAM Rev 26(4):551–568
Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in dobe ju/’hoansi foraging patterns. Hum Ecol 35(1):129–138
Chen SM, Chien CY (2011) Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst Appl 38(12):14439–14450
Croes GA (1958) A method for solving traveling-salesman problems. Oper Res 6(6):791–812
Dorigo M, Gambardella LM et al (1997) Ant colonies for the travelling salesman problem. BioSystems 43(2):73–82
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845
Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336
Gandomi AH, Talatahari S, Yang XS, Deb S (2012) Design optimization of truss structures using cuckoo search algorithm. Struct Des Tall Special Build. doi:10.1002/tal.1033
Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35
Geem ZW, Kim JH et al (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68
Glover F, Kochenberger GA (2003) Handbook of metaheuristics. Springer, New York
Gutin G, Punnen AP (2002) The traveling salesman problem and its variations, vol 12. Springer, New York
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Neural networks, 1995. Proceedings, IEEE international conference on, IEEE, vol4, pp 1942–1948
Larranaga P, Kuijpers CMH, Murga RH, Inza I, Dizdarevic S (1999) Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif Intell Rev 13(2):129–170
Lawler EL, Lenstra JK, Kan AR, Shmoys DB (1985) The traveling salesman problem: a guided tour of combinatorial optimization, vol 3. Wiley, New York
Lenstra JK, Rinnooy Kan AHG (1975) Some simple applications of the travelling salesman problem. Oper Res Q 26(5): 717–733
Malek M, Guruswamy M, Pandya M, Owens H (1989) Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem. Ann Oper Res 21(1):59–84
Martin O, Otto SW, Felten EW (1991) Large-step markov chains for the traveling salesman problem. Complex Syst 5(3):299–326
Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. In: Data mining, systems analysis, and optimization in biomedicine(AIP conference proceedings, vol 953), American Institute of Physics, 2 Huntington Quadrangle, Suite 1 NO 1, Melville, NY, 11747-4502, USA, vol 953, pp 162–173
Payne RB, Sorenson MD (2005) The cuckoos, vol 15. Oxford University Press, USA
Reinelt G (1991) Tsplib—a traveling salesman problem library. ORSA J Comput 3(4):376–384
Reinelt G (1994) The traveling salesman: computational solutions for TSP applications, vol 15. Springer, New York
Shah-Hosseini H (2009) The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. Int J Bio-Inspired Comput 1(1):71–79
Shi XH, Liang YC, Lee HP, Lu C, Wang QX (2007) Particle swarm optimization-based algorithms for tsp and generalized tsp. Inf Process Lett 103(5):169–176
Shlesinger MF, Zaslavsky GM, Frisch U (1995) Lévy flights and related topics in physics:(Nice, 27–30 June 1994). Springer, New York
Taillard ED, Gambardella LM, Gendreau M, Potvin JY (2001) Adaptive memory programming: a unified view of metaheuristics. Eur J Oper Res 135(1):1–16
Teodorovic D, Lucic P, Markovic G, Orco MD (2006) Bee colony optimization: principles and applications. In: Neural network applications in electrical engineering, 2006. NEUREL 2006. 8th Seminar on, IEEE, pp 151–156
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. Evol Comput IEEE Trans 1(1):67–82
Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and application, SAGA 2009. Lecture notes in computer sciences, vol 5792, pp 169–178
Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010), pp 65–74
Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: Nature & biologically inspired computing, 2009. NaBIC 2009. World congress on, IEEE, pp 210–214
Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Modell Numer Optim 1(4):330–343
Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483
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Ouaarab, A., Ahiod, B. & Yang, XS. Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput & Applic 24, 1659–1669 (2014). https://doi.org/10.1007/s00521-013-1402-2
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DOI: https://doi.org/10.1007/s00521-013-1402-2