Skip to main content

A New Optimized Approach to Resolve a Combinatorial Problem: CoronaVirus Optimization Algorithm and Self-organizing Maps

  • Conference paper
  • First Online:
Digital Technologies and Applications (ICDTA 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 211))

Included in the following conference series:

Abstract

The optimization provides resolutions to complex combinatorial problems that generally deal within large data size and expensive operating processes. Metaheuristics target the promoting of new applied algorithms to resolve NP-Hard problems in order to improve resolutions requiring enhanced search strategies. Travelling Salesman Problem (TSP) is a common combinatorial problem, applied on several benchmark networks, namely the transportation networks and the routing vehicle problem in order to establish new intelligent computing methods as well as, to prove studies on their performances and efficiencies. Collective intelligence has proven satisfactory resolutions wherewith metaheuristics, although their algorithms complexity. The aim of this work is to solve the Euclidean TSP, classified as a NP-hard problem by means of Self-Organizing Maps (SOM) which is a Kohonen-type network. The resolution is also computed corresponding to a new bio-inspired evolutionary strategy so-called coronavirus optimization algorithm combined with SOM algorithm. The present approach is combining an unsupervised learning strategy within the new coronavirus optimization algorithm to replicate iteratively new infected individuals and to generate diversification on the search space. This new hybrid method presents a good approximative resolutions, proved by applying tests for TSPLIB instances wherein the exact optimum is defined corresponding to each TSP data. However, the present resolutions are complex specifically for large scale by means of increasing the size of input data or size parameters.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bovet DP, Clementi A, Crescenzi P, Silvestri R (1996) Parallel approximation of optimization problems. In: Ferreira A, Pardalos PM (eds) Solving combinatorial optimization problems in parallel. LNCS, vol 1054, pp 248–274. Springer, Berlin

    Google Scholar 

  2. Lüling R, Monien B, Reinefeld A, Tschöke S (1996) Mapping tree-structured combinatorial optimization problems onto parallel computers. In: Ferreira A, Pardalos PM (eds) Solving combinatorial optimization problems in parallel. LNCS, vol. 1054. Springer, Berlin, Heidelberg

    Google Scholar 

  3. Laursen PS (1996) Parallel heuristic search – introductions and a new approach. In: Ferreira A, Pardalos PM (eds) Solving combinatorial optimization problems in parallel, LNCS, vol 1054. Springer, Berlin, Heidelberg, pp 248–274

    Chapter  Google Scholar 

  4. Akhand MAH, Ayon SI, Shahriyar SA, Siddique N, Adeli H (2020) Discrete spider monkey optimization for TSP. Appl Soft Comput vol 86, p 105887

    Google Scholar 

  5. Clementi A, Rolim JDP, Urland E (1996) Randomized parallel algorithms. In: Ferreira A, Pardalos PM (eds) Solving combinatorial optimization problems in parallel. LNCS, vol 1054. Springer, Heidelberg

    Google Scholar 

  6. Bouzidi A, Riffi ME (2019) Improved CSO to solve the TSP. In: Ezziyyani M (eds) AI2SD Conference 2018. Advances in Intelligent Systems and Computing, vol 714. Springer, Singapore

    Google Scholar 

  7. Othman A, Haimoudi E, Mouhssine R, Ezziyyani M (2019) An effective parallel approach to solve multiple TSP. In: Ezziyyani M (eds) AI2SD Conference 2018. Advances in Intelligent Systems and Computing, vol 714. Springer

    Google Scholar 

  8. Ferreira A, Pardalos PM (1996) SCOOP: Solving combinatorial optimization problems in parallel. In: Ferreira A, Pardalos PM (eds) Solving combinatorial optimization problems in parallel. LNCS, vol 1054. Springer, Berlin

    Google Scholar 

  9. Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689–691

    Article  Google Scholar 

  10. Wang J, Ersoy OK, He M, Wang F (2016) Multi-offspring genetic algorithm and its application to TSP. Appl Soft Comput 30:484–490

    Google Scholar 

  11. Ezugwu AES, Adewumi A, Frîncu M (2017) Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem. Expert Syst Appl 77:189–210

    Article  Google Scholar 

  12. Choong SS, Wong LP, Lim CP (2019) An artificial bee colony algorithm with a modified choice function for the traveling salesman problem. Swarm Evol Comput 44:22–635

    Article  Google Scholar 

  13. Chen WL, Dai SG (2006) Survey of algorithms for traveling salesman problem. J Chuzhou Univ 8(3):1–6

    Google Scholar 

  14. Guo JY (2006) An overview of traveling salesman problem. Pop Sci Technol 8:229–230

    Google Scholar 

  15. Lahjouji A, Tajani C, Krkri I, Fakhouri H (2019) Immune based genetic algorithm to solve a combinatorial optimization problem: Application to traveling salesman problem. In: Ezziyyani M (eds) AI2SD Conference 2018, Advances in intelligent systems and computing, vol 915. Springer

    Google Scholar 

  16. Ismail MA, Daryl E, Kathryn K (2020) A novel design of differential evolution for solving discrete TSP. Swarm Evol Comput 52:100607

    Article  Google Scholar 

  17. Hoffman KL, Padberg M, Rinaldi G (2013) Traveling salesman problem. In: Gass S I, Fu MC (eds) Encyclopedia of operations research and management science. Springer, Boston

    Google Scholar 

  18. Gilmore PC, Gomory RE (1964) A solvable case of the traveling salesman problem. Proc Natl Acad Sci 51:178–181

    Article  MathSciNet  Google Scholar 

  19. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows. Prentice-Hall

    Google Scholar 

  20. Bazaraa MS, Jarvis JJ, Sherali HD (1990) Linear programming and network flows. Wiley, New York

    MATH  Google Scholar 

  21. Koprinkova HP, Mladenov V, Kasabov NK (2015) Artificial neural networks. Springer Series in Bio-/Neuroinformatics

    Google Scholar 

  22. Trick M (2008) Oper Res Lett 36(2):276–277

    Article  Google Scholar 

  23. Khourdifi Y, Bahaj M (2020) Analyzing social media opinions using hybrid machine learning model based on artificial neural network optimized by particle swarm optimization. In: Ezziyyani M (eds) AI2SD Conference 2019. Advances in Intelligent Systems and Computing, vol 714. Springer, Singapore

    Google Scholar 

  24. Kohonen T (1990) The self-organizing map. Proc IEEE 78(9):1464–1480

    Article  Google Scholar 

  25. Kohonen T (2001) Self-organizing maps. Springer , Heidelberg

    Book  Google Scholar 

  26. Somhom S, Modares A, Enkawa T (1997) A self-organising model for TSP problem. J Oper Res Soc 48(9):919–928

    Article  Google Scholar 

  27. Kohonen T, Kaski S, Lagus K, Salojarvi J, Honkela J, Paatero V, Saarela A (2000) Self organization of a massive document collection. IEEE Trans Neural Netw 11(3):574–585

    Article  Google Scholar 

  28. Moukhafi M, Yassini KE, Bri S, Oufaska K (2019) Artificial neural network optimized by genetic algorithm for intrusion detection system. In: Ezziyyani M (eds) AI2SD Conference 2018. Advances in Intelligent Systems and Computing, vol 714. Springer, Singapore

    Google Scholar 

  29. Yanping B, Wendong Z, Zhen J (2006) A new self-organizing maps strategy for solving TSP. Chaos Solitons Fractals 28(4):1082–1089

    Article  MathSciNet  Google Scholar 

  30. Jan F, Miroslav K, Vojtěch V, Libor P (2011) An application of the self-organizing map in the non-euclidean TSP. Neurocomputing 74(5):671–679

    Article  Google Scholar 

  31. Créput JC, Koukam A (2009) A memetic neural network for the euclidean TSP. Neurocomputing 72(4–6):1250–1264

    Article  Google Scholar 

  32. Tinós R (2020) Artificial neural network based crossover for evolutionary algorithms. Appl Soft Comput 95:106512

    Article  Google Scholar 

  33. Martínez-Álvarez F, Asencio-Cortés G, Torres JF, Gutiérrez-Avilés D, Melgar-García L, Pérez-Chacón R, Rubio-Escudero C, Riquelme JC, Troncoso A (2020) Coronavirus optimization algorithm: a bioinspired metaheuristic based on the COVID-19 propagation model. Big data 8(4):308–322

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

EL Majdoubi, O., Abdoun, F., Abdoun, O. (2021). A New Optimized Approach to Resolve a Combinatorial Problem: CoronaVirus Optimization Algorithm and Self-organizing Maps. In: Motahhir, S., Bossoufi, B. (eds) Digital Technologies and Applications. ICDTA 2021. Lecture Notes in Networks and Systems, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-030-73882-2_86

Download citation

Publish with us

Policies and ethics