Abstract
2-opt, 3-opt or \(k-\)opt heuristics are classical local search algorithms for traveling salesman problems (TSP) in combinatorial optimization area. This paper introduces a judicious decision making methodology of offloading which part of the \(k-\)opt heuristic works in parallel on Graphics Processing Unit (GPU) while which part remains sequential, called “multiple \(k-\)opt evaluation, multiple \(k-\)opt moves”, in order to simultaneously execute, without interference, massive 2-/3-opt moves that are globally found on the same TSP tour or the same Euclidean space for many edges, as well as keep high performance for GPU massive \(k-\)opt evaluation. We prove the methodology is judicious and valuable because of our originally proposed sequential non-interacted 2-/3-exchange set partition algorithm taking linear time complexity and a new TSP tour representation, array of ordered coordinates-index, in order unveil how to use GPU on-chip shared memory to achieve the same goal as using doubly linked list and array of ordered coordinates for parallel \(k-\)opt implementation. We test this methodology on 22 national TSP instances with up to 71009 cities and with brute initial tour solution. Average maximum 997 non-interacted 2-opt moves are found and executed on the same tour of ch71009.tsp instance in one iteration of our proposed method. Experimental comparisons show that our proposed methodology gets huge acceleration over both classical sequential and a possible current fastest state-of-the-art GPU parallel 2-opt implementation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958)
Garey, M.R., Johnson, D.S.: A Guide to the Theory of NP-Completeness, p. 70. WH Freemann, New York (1979)
Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Manag. Sci. 40(10), 1276–1290 (1994)
Glover, F.: Tabu search–part i. ORSA J. Comput. 1(3), 190–206 (1989)
Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: a case study in local optimization. Local Search Comb. Optim. 1, 215–310 (1997)
Karp, R.M.: Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane. Math. Oper. Res. 2(3), 209–224 (1977)
Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Euro. J. Oper. Res. 59(2), 231–247 (1992)
Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44(10), 2245–2269 (1965)
Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. Handbook of Metaheuristics, pp. 320–353. Springer, Boston (2003). https://doi.org/10.1007/0-306-48056-5_11
Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)
Mulder, S.A., Wunsch, D.C.: Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks. Neural Netw. 16(5), 827–832 (2003)
Qiao, W., Créput, J.: Massive parallel self-organizing map and 2-opt on GPU to large scale TSP. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2017. LNCS, vol. 10305, pp. 471–482. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59153-7_41
Qiao, W.B., Créput, J.C.: Parallel 2-opt local search on GPU. World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 11(3), 281–285 (2017)
Reinelt, G.: Tsplib–a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)
Rios, E., Ochi, L.S., Boeres, C., Coelho, V.N., Coelho, I.M., Farias, R.: Exploring parallel multi-GPU local search strategies in a metaheuristic framework. J. Parallel Distrib. Comput. 111, 39–55 (2018)
Rocki, K., Suda, R.: Accelerating 2-opt and 3-opt local search using GPU in the travelling salesman problem. In: High Performance Computing and Simulation, pp. 489–495. IEEE (2012)
Rocki, K., Suda, R.: High performance GPU accelerated local optimization in TSP. In: 2013 IEEE 27th International Parallel and Distributed Processing Symposium Workshops & Ph.D. forum (IPDPSW), pp. 1788–1796. IEEE (2013)
Verhoeven, M., Aarts, E.H., Swinkels, P.: A parallel 2-opt algorithm for the traveling salesman problem. Future Gener. Comput. Syst. 11(2), 175–182 (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Qiao, WB., Créput, JC. (2019). Massive 2-opt and 3-opt Moves with High Performance GPU Local Search to Large-Scale Traveling Salesman Problem. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-05348-2_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05347-5
Online ISBN: 978-3-030-05348-2
eBook Packages: Computer ScienceComputer Science (R0)