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Applied Intelligence

, Volume 49, Issue 2, pp 661–688 | Cite as

Parallel heuristic local search algorithm on OTIS hyper hexa-cell and OTIS mesh of trees optoelectronic architectures

  • Aryaf Al-Adwan
  • Ahmad Sharieh
  • Basel A. MahafzahEmail author
Article
  • 46 Downloads

Abstract

Heuristic local search algorithms have achieved good results in tackling combinatorial optimization problems, such as Travelling Salesman Problem (TSP). One of the well-known local search algorithms is the 2-opt algorithm. As a local search algorithm, 2-opt has achieved approximate optimal solutions for TSP within a reasonable time, especially for small data instances. However, solving large data instances of TSP using 2-opt requires extensive computation and considerable CPU time. Therefore, this paper presents a parallel version of the 2-opt algorithm, exploiting the features of Optical Transpose Interconnection System (OTIS) in solving the TSP. In this paper, we present the Parallel Repetitive 2-Opt (PRTO) algorithm for solving symmetric TSP on OTIS Hyper Hexa-Cell (OTIS-HHC) and OTIS Mesh of Trees (OTIS-MOT) optoelectronic architectures. We assess the performance of our algorithm analytically in terms of parallel time complexity, speedup, efficiency, cost, and communication cost on both optoelectronic architectures. Furthermore, a set of simulation experiments is conducted on various instances from the standard TSP library. The simulation results confirm that our algorithm is efficient regarding speedup and efficiency. For instance, the PRTO algorithm achieves a speedup of 32.9 for 6880 cities over OTIS-HHC with 36 processors. Moreover, the superiority of PRTO algorithm is shown through solving the TSP on OTIS-HHC and OTIS-MOT; its performance has been compared with the performance of the Parallel Repetitive Nearest Neighbor (PRNN) algorithm in terms of speedup, efficiency, and solution quality. For example, as a best case, the PRTO algorithm has shown 34 times improved speedup over the PRNN algorithm.

Keywords

Local search algorithm 2-opt algorithm Repetitive nearest neighbor algorithm Travelling salesman problem Interconnection network Optoelectronic architecture 

Notes

Acknowledgments

The authors would like to express their deep gratitude to the anonymous referees for their valuable comments and suggestions, which enhanced this research manuscript.

References

  1. 1.
    Cormen T, Leiserson C, Rivest R, Stein C (2001) Introduction to algorithms. MIT Press, LondonzbMATHGoogle Scholar
  2. 2.
    Deb S, Fong S, Tian Z, Wong RK, Mohammed S, Fiaidhi J (2016) Finding approximate solutions of NP-hard optimization and TSP problems using elephant search algorithm. J Supercomput 72(10):3960–3992CrossRefGoogle Scholar
  3. 3.
    Okano H, Misono S, Iwano K (1999) New TSP construction heuristics and their relationships to the 2-opt. J Heuristics 5(1):71–88CrossRefzbMATHGoogle Scholar
  4. 4.
    Pandiri V, Singh A (2016) Swarm intelligence approaches for multidepot salesmen problems with load balancing. Appl Intell 44:849–861CrossRefGoogle Scholar
  5. 5.
    Mollajafari M, Shahhoseini HS (2016) An efficient ACO-based algorithm for scheduling tasks onto dynamically reconfigurable hardware using TSP-likened construction graph. App Intell 45:695–712CrossRefGoogle Scholar
  6. 6.
    Matai R, Singh SP, Mittal ML (2010) Traveling salesman problem: An overview of applications, formulations, and solution approaches. In: Traveling salesman problem, theory and applications, pp 1–24Google Scholar
  7. 7.
    Da Silva FJM, Pérez JMS, Pulido JAG, Rodríguez MAV (2010) AlineaGA–a genetic algorithm with local search optimization for multiple sequence alignment. Appl Intell 32:164–172CrossRefGoogle Scholar
  8. 8.
    Johnson DS, McGeoch LA (1997) The Traveling salesman problem: a case study in local optimization. Local Search in Combinatorial Optimization. Wiley, London, pp 215–310zbMATHGoogle Scholar
  9. 9.
    Reinelt G (1994) The traveling salesman: computational solutions for TSP applications. Lecture Notes in Computer Science, vol 840. Springer, Berlin, pp 73–97Google Scholar
  10. 10.
    Karp RM (1977) Probabilistic analysis of partitioning algorithms for the traveling-salesman in the plane. Math Oper Res 2(3):209–224MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Allwright JRA, Carpenter DB (1989) A distributed implementation of simulated annealing for the travelling salesman problem. Parallel Comput 10(3):335–338MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Verhoeven MG, Aarts EH, Swinkels PC (1995) A parallel 2-opt algorithm for the traveling salesman problem. Futur Gener Comput Syst 11(2):175–182CrossRefGoogle Scholar
  13. 13.
    Reinelt G (1991) TSPLIB: A traveling salesman problem library. ORSA J Comput 3(4):376–384CrossRefzbMATHGoogle Scholar
  14. 14.
    Rocki K, Suda R (2013) High performance GPU accelerated local optimization in TSP. In: 2013 IEEE 27th international symposium on parallel and distributed processing workshops and PhD forum. Boston, Massachusetts, pp 1788–1796Google Scholar
  15. 15.
    O’Neil MA, Burtscher M (2015) Rethinking the parallelization of random-restart hill climbing: a case study in optimizing a 2-opt TSP solver for GPU execution. In: Proceedings of the 8th workshop on general purpose processing using GPUs, pp 99–108Google Scholar
  16. 16.
    Zhou Y, He F, Qiu Y (2016) Optimization of parallel iterated local search algorithms on graphics processing unit. J Supercomput 72(6):2394–2416CrossRefGoogle Scholar
  17. 17.
    Qiao WB, Créput JC (2017) Parallel 2-opt local search on GPU. Int J Electric Comput Energetic Electron Commun Eng 11(3):291–295Google Scholar
  18. 18.
    Marsden G, Marchand P, Harvey P, Esener S (1993) Optical transpose interconnection system architectures. Opt Lett 18(13):1083–1085CrossRefGoogle Scholar
  19. 19.
    Rajasekaran S, Reif J (2008) Handbook of parallel computing models algorithms and applications. CRC Press, USAzbMATHGoogle Scholar
  20. 20.
    Mahafzah B, Sleit A, Hamad N, Ahmad E, Abu-Kabeer T (2012) The OTIS hyper hexa-cell optoelectronic architecture. Computing 94(5):411–432MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Jana P, Mallick D (2010) OTIS-MOT: an efficient interconnection network for parallel processing. J Supercomput 59(2):920– 940CrossRefGoogle Scholar
  22. 22.
    Wang C-F, Sahni S (1998) Basic operations on the OTIS-mesh optoelectronic computer. IEEE Trans Parallel Distributed Syst 9(12):1226–1236CrossRefGoogle Scholar
  23. 23.
    Mahafzah B, Tahboub R, Tahboub O (2010) Performance evaluation of broadcast and global combine operations in all-port wormhole-routed OTIS-mesh interconnection networks. Clust Comput 13(1):87–110CrossRefGoogle Scholar
  24. 24.
    Osterloh A (2000) Sorting on the OTIS-mesh. In: Proceedings of the 14th international parallel and distributed processing symposium (IPDPS’00), pp 269–274Google Scholar
  25. 25.
    Mahafzah B, Jaradat B (2008) The load balancing problem in OTIS-hypercube interconnection networks. J Supercomput 46(3):276–297CrossRefGoogle Scholar
  26. 26.
    Zhao C, Xiao W, Parhami B (2009) Load-balancing on swapped or OTIS networks. J Parallel Distributed Comput 69(4):389–399CrossRefGoogle Scholar
  27. 27.
    Hashemi-Najafabadi H, Sarbazi-Azad H (2007) Mathematical performance modelling of adaptive wormhole routing in optoelectronic hypercubes. J Parallel Distributed Comput 67(9):967–980CrossRefzbMATHGoogle Scholar
  28. 28.
    Akhtar A, Lucas K (2014) Routing and sorting on OTIS-hyper hexa-cell. Int J of Eng Comput Sci 7(3):7388–7393Google Scholar
  29. 29.
    Akhtar A, Lucas K (2014) Comparison of communication algorithms on OTIS-HHC and OTIS-ring parallel architectures. Int J Eng Comput Sci 3(10):8741–8745Google Scholar
  30. 30.
    Mallick DK, Jana PK (2008) Parallel prefix on mesh of trees and OTIS mesh of trees. In: Proceedings of the international conference on parallel and distributed processing techniques and applications, pp 359–364Google Scholar
  31. 31.
    Lucas KT, Jana PK (2010) Sorting and routing on OTIS-mesh of trees. Parallel Process Lett 20(2):145–154MathSciNetCrossRefGoogle Scholar
  32. 32.
    Al-Adwan A, Mahafzah B, Sharieh A (2018) Solving traveling salesman problem using parallel repetitive nearest neighbor algorithm on OTIS-hypercube and OTIS-mesh optoelectronic architectures. J Supercomput 74(1):1–36CrossRefGoogle Scholar
  33. 33.
    Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing. Addison Wesley, USAzbMATHGoogle Scholar
  34. 34.
    Hennessy JL (2011) Computer architecture: a quantitative approach. Morgan Kaufmann, San FranciscozbMATHGoogle Scholar
  35. 35.
    Kaminow I, Li T, Willner A (2010) Optical fiber telecommunications VB: systems and networks. Academic Press, CaliforniaGoogle Scholar
  36. 36.
    Ansari AQ, Katiyar S (2015) Comparison and analysis of solving travelling salesman problem using GA, ACO and hybrid of ACO with GA and CS. In: 2015 IEEE workshop on computational intelligence: theories, applications and future directions (WCI), pp 1–5Google Scholar
  37. 37.
    Johnson DS, Aragon CR, McGeoch LA, Schevon C (1989) Optimization by simulated annealing: an experimental evaluation: Part I, graph partitioning. Oper Res 37(6):865–892CrossRefzbMATHGoogle Scholar
  38. 38.
    Weidong G et al (2015) Parallel performance of an ant colony optimization algorithm for TSP. In: 2015 8th international conference on intelligent computation technology and automation (ICICTA) Nanchang, China. IEEEGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.King Abdullah II School for Information Technology, Computer Science DepartmentThe University of JordanAmmanJordan

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