Skip to main content
SpringerLink
Log in

Parallel deterministic local search heuristic for minimum latency problem

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

Minimum latency problem (MLP) is an NP-Hard combinatorial optimization problem. Metaheuristics use perturbation and randomization to arrive at a satisfactory solution under time constraints. The current work uses deterministic local search heuristic (DLSH) to identify a satisfactory solution without setting up metaheuristic parameters. A move evaluation procedure is proposed for the swap approach which computes a move in O(1) order. Additionally, GPU-based parallel deterministic local search heuristic (PDLSH) is also proposed. PDLSH parallelizes the solution improvement phase and solves MLP for larger instances than the state-of-the-art. The DLSH and PDLSH implementations are tested on the TRP and TSPLIB standard instances. DLSH reaches new best solutions for five TSPLIB instances, namely eil51,  berlin52,  pr107,  rat195,  and pr226. The proposed PDLSH achieves a speedup of up to 179.75 for the instances of size 10–11,849 nodes compared to its sequential counterpart.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, STOC ’94, New York, NY, USA, pp. 163–171 (1994). ACM

  2. Sitters, R.: The minimum latency problem is NP-hard for weighted trees. In: Cook, W.J., Schulz, A.S. (eds.) Integer Programming and Combinatorial Optimization, pp. 230–239. Springer, Berlin (2002)

    Chapter  Google Scholar 

  3. Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM 23(3), 555–565 (1976)

    Article  MathSciNet  Google Scholar 

  4. Bianco, L., Mingozzi, A., Ricciardelli, S.: The traveling salesman problem with cumulative costs. Networks 23(2), 81–91 (1993)

    Article  MathSciNet  Google Scholar 

  5. Fischetti, M., Laporte, G., Martello, S.: The delivery man problem and cumulative matroids. Oper. Res. 41(6), 1055–1064 (1993)

    Article  MathSciNet  Google Scholar 

  6. Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, trees, and minimum latency tours. In: 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings, October 2003, pp. 36–45

  7. Tsitsiklis, J.N.: Special cases of traveling salesman and repairman problems with time windows. Networks 22(3), 263–282 (1992)

    Article  MathSciNet  Google Scholar 

  8. Méndez-Díaz, I., Zabala, P., Lucena, A.: A new formulation for the traveling deliveryman problem. Discrete Appl. Math. 156(17), 3223–3237 (2008)

    Article  MathSciNet  Google Scholar 

  9. Campbell, A.M., Vandenbussche, D., Hermann, W.: Routing for relief efforts. Transp. Sci. 42(2), 127–145 (2008)

    Article  Google Scholar 

  10. Yelmewad, P., Talawar, B.: Near optimal solution for traveling salesman problem using GPU. In: 2018 IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT), pp. 1–6, March 2018

  11. Yelmewad, P., Talawar, B.: Parallel iterative hill climbing algorithm to solve TSP on GPU. Concurr. Comput. Pract. Exp. 31(7), e4974 (2019)

    Article  Google Scholar 

  12. Abeledo, H., Fukasawa, R., Pessoa, A., Uchoa, E.: The time dependent traveling salesman problem: polyhedra and algorithm. Math. Program. Comput. 5(1), 27–55 (2013)

    Article  MathSciNet  Google Scholar 

  13. Lucena, A.: Time-dependent traveling salesman problem—the deliveryman case. Networks 20(6), 753–763 (1990)

    Article  MathSciNet  Google Scholar 

  14. Wu, B.Y.: Polynomial time algorithms for some minimum latency problems. Inf. Process. Lett. 75(5), 225–229 (2000)

    Article  MathSciNet  Google Scholar 

  15. Wu, B.Y., Huang, Z.-N., Zhan, F.-J.: Exact algorithms for the minimum latency problem. Inf. Process. Lett. 92(6), 303–309 (2004)

    Article  MathSciNet  Google Scholar 

  16. Salehipour, A., Sörensen, K., Goos, P., Bräysy, O.: Efficient GRASP+VND and GRASP+VNS metaheuristics for the traveling repairman problem. 4OR 9(2), 189–209 (2011)

    Article  MathSciNet  Google Scholar 

  17. Goemans, M., Kleinberg, J.: An improved approximation ratio for the minimum latency problem. Math. Program. 82(1), 111–124 (1998)

    MathSciNet  MATH  Google Scholar 

  18. Archer, A., Blasiak, A.: Improved approximation algorithms for the minimum latency problem via prize-collecting strolls. In: Proceedings of the Twenty-First Annual ACM–SIAM Symposium on Discrete Algorithms, SODA ’10, Philadelphia, PA, USA, pp. 429–447. Society for Industrial and Applied Mathematics (2010)

  19. Talbi, E.-G.: Metaheuristics: From Design to Implementation. Wiley, Hoboken (2009)

    Book  Google Scholar 

  20. Al-Janabi, S., Mohammad, M., Al-Sultan, A.: A new method for prediction of air pollution based on intelligent computation. Soft Comput. 24, 661–680 (2020)

    Article  Google Scholar 

  21. Al-Janabi, S., Alkaim, A.F.: A Nifty collaborative analysis to predicting a novel tool (DRFLLS) for missing values estimation. Soft Comput. 24, 555–569 (2020)

    Article  Google Scholar 

  22. Al-Janabi, S., Alkaim, A.F., Adel, Z.: An Innovative synthesis of deep learning techniques (DCapsNet and DCOM) for generation electrical renewable energy from wind energy. Soft Comput. 24, 10943–10962 (2020)

    Article  Google Scholar 

  23. Ngueveu, S.U., Prins, C., Calvo, R.W.: An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput. Oper. Res. 37(11), 1877–1885 (2010)

    Article  MathSciNet  Google Scholar 

  24. Silva, M.M., Subramanian, A., Vidal, T., Ochi, L.S.: A simple and effective metaheuristic for the minimum latency problem. Eur. J. Oper. Res. 221(3), 513–520 (2012)

    Article  Google Scholar 

  25. Dewilde, T., Cattrysse, D., Coene, S., Spieksma, F.C.R., Vansteenwegen, P.: Heuristics for the traveling repairman problem with profits. Comput. Oper. Res. 40(7), 1700–1707 (2013)

    Article  MathSciNet  Google Scholar 

  26. Afif, M., Said, Y., Atri, M.: Computer vision algorithms acceleration using graphic processors NVIDIA CUDA. Clust. Comput. (2020). https://doi.org/10.1007/s10586-020-03090-6

    Article  Google Scholar 

  27. Kim, S., Kim, D., Son, Y., Eom, H.: Towards predicting GPGPU performance for concurrent workloads in Multi-GPGPU environment. Clust. Comput. (2020). https://doi.org/10.1007/s10586-020-03105-2

    Article  Google Scholar 

  28. Carvalho, P., Cruz, R., Drummond, L.M.A., Bentes, C., Clua, E., Cataldo, E., Marzulo, L.A.J.: Kernel concurrency opportunities based on GPU benchmarks characterization. Clust. Comput. 23, 177–188 (2020)

    Article  Google Scholar 

  29. Alawneh, L., Shehab, M.A., Al-Ayyoub, M., Jararweh, Y., Al-Sharif, Z.A.: A scalable multiple pairwise protein sequence alignment acceleration using hybrid CPU–GPU approach. Clust. Comput. (2020). https://doi.org/10.1007/s10586-019-03035-8

    Article  Google Scholar 

  30. Geng, X., Zhang, H., Zhao, Z., Ma, H.: Interference-aware parallelization for deep learning workload in GPU cluster. Clust. Comput. (2020). https://doi.org/10.1007/s10586-019-03037-6

    Article  Google Scholar 

  31. NVIDIA. CUDA Programming Guide. http://docs.nvidia.com/cuda/index.html. Accessed 1 July 2020

  32. Ban, H.B., Duc, N.N.: A parallel algorithm combines genetic algorithm and ant colony algorithm for the minimum latency problem. In: Proceedings of the Fifth Symposium on Information and Communication Technology, SoICT ’14, New York, NY, USA, 2014. Association for Computing Machinery (2014)

  33. Ban, H.-B., Nguyen, D.-N.: A meta-heuristic algorithm combining between Tabu and variable neighborhood search for the minimum latency problem. Fundam. Inform. 156, 21–41 (2017)

    Article  MathSciNet  Google Scholar 

  34. Avci, M., Avci, M.G.: A GRASP with iterated local search for the traveling repairman problem with profits. Comput. Ind. Eng. 113, 323–332 (2017)

    Article  Google Scholar 

  35. 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)

    Article  Google Scholar 

  36. Araujo, R.P., Coelho, I.M., Marzulo, L.A.J.: A DVND local search implemented on a dataflow architecture for the minimum latency problem. In: 2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp. 1250–1259 (2018)

  37. Araujo, R.P., Coelho, I.M., Augusto Justen Marzulo, L.: A multi-improvement local search using dataflow and GPU to solve the minimum latency problem. Parallel Comput. (2020). https://doi.org/10.1016/j.parco.2020.102661

    Article  MathSciNet  Google Scholar 

  38. Santana, Í., Plastino, A., Rosseti, I.: Improving a state-of-the-art heuristic for the minimum latency problem with data mining. Int. Trans. Oper. Res. (2020). https://doi.org/10.1111/itor.12774

    Article  Google Scholar 

  39. Lu, Y., Hao, J.-K., Wu, Q.: Hybrid evolutionary search for the traveling repairman problem with profits. Inf. Sci. 502, 91–108 (2019)

    Article  MathSciNet  Google Scholar 

  40. Van Luong, T., Melab, N., Talbi, E.-G.: GPU computing for parallel local search metaheuristics. IEEE Trans. Comput. 62(1), 173–185 (2013)

    Article  MathSciNet  Google Scholar 

  41. Reinelt, G.: TSPLIB—a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. System Parallelization & Architecture Research @ NITK (SPARK Lab), Department of Computer Science and Engineering, National Institute of Technology Karnataka, Surathkal, Mangalore, India

    Pramod Yelmewad & Basavaraj Talawar

Authors
  1. Pramod Yelmewad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Basavaraj Talawar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pramod Yelmewad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yelmewad, P., Talawar, B. Parallel deterministic local search heuristic for minimum latency problem. Cluster Comput 24, 969–995 (2021). https://doi.org/10.1007/s10586-020-03173-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-020-03173-4

Keywords

Search

Navigation