Skip to main content
SpringerLink
Log in

Travelling salesman problem in tissue P systems with costs

  • Regular Paper
  • Published:
Journal of Membrane Computing Aims and scope Submit manuscript

Abstract

We define tissue P systems with costs assigning execution costs to the synapses that are used to transport the objects between cells. We use the Priced-Timed Maude rewriting engine to provide an implementation of tissue P systems with costs. The implementation allows us to analyze and verify some behavioural aspects of tissue P systems with costs. We illustrate an application of these tissue P systems with costs by providing a solution to the Travelling Salesman Problem.

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

Similar content being viewed by others

Notes

  1. The implementation is available at

    https://profs.info.uaic.ro/~bogdan.aman/CostTissuePS/costPS.ptm.

References

  1. Agrigoroaiei, O., & Ciobanu, G. (2009). Rewriting logic specification of membrane systems with promoters and inhibitors. Electronic Notes in Theoretical Computer Science, 238, 5–22. https://doi.org/10.1016/j.entcs.2009.05.010.

    Article  MATH  Google Scholar 

  2. Aman, B., & Ciobanu, G. (2009). Turing completeness using three mobile membranes. Lecture Notes in Computer Science, 5715, 42–55. https://doi.org/10.1007/978-3-642-03745-0_12.

    Article  MathSciNet  MATH  Google Scholar 

  3. Aman, B., & Ciobanu, G. (2009). Simple, enhanced and mutual mobile membranes. Lecture Notes in Computer Science, 5750, 26–44. https://doi.org/10.1007/978-3-642-04186-0_2.

    Article  MATH  Google Scholar 

  4. Aman, B., & Ciobanu, G. (2011). Time delays in Membrane systems and Petri nets. Electronic Proceeding in Theoretical Computer Science, 57, 47–60. https://doi.org/10.4204/EPTCS.57.4.

    Article  MATH  Google Scholar 

  5. Aman, B., Ciobanu, G. (2016). Verifying P Systems with Costs by Using Priced-Timed Maude. Proceedings 14th Brainstorming Week on Membrane Computing (BWMC), Sevilla.

  6. Aman, B., & Ciobanu, G. (2020). Mobile Membranes. IEEE. Access, 8, 147439–147450. https://doi.org/10.1109/ACCESS.2020.3011803.

    Article  Google Scholar 

  7. Applegate, D. L., Bixby, R. E., Chvatal, V., & Cook, W. J. (2006). The Travelling Salesman Problem. A Computational Study: Princeton University Press. https://doi.org/10.1007/978-3-642-03741-2_31.

    Book  MATH  Google Scholar 

  8. Bendiksen, L., & Ölveczky, P. C. (2009). The Priced-Timed Maude tool. Lecture Notes in Computer Science, 5728, 443–448. https://doi.org/10.1007/978-3-642-03741-2_31.

    Article  Google Scholar 

  9. Bouhoula, A., Jouannaud, J.-P., & Meseguer, J. (2000). Specification and proof in membership equational logic. Theoretical Computer Science, 236, 35–132. https://doi.org/10.1016/S0304-3975(99)00206-6.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ciobanu, G. (2010). Semantics of P systems. In Gh. Păun, G. Rozenberg, & A. Salomaa (Eds.), The Oxford Handbook of Membrane Computing (pp. 413–436). Oxford: Oxford University Press.

    Google Scholar 

  11. Ciobanu, G., Marcus, S., & Păun, Gh. (2009). New strategies of using the rules of a P system in a maximal way: power and complexity. Romanian Journal of Information Science and Technology, 12, 157–173.

    Google Scholar 

  12. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., & Quesada, J. F. (2002). Maude: specification and programming in rewriting logic. Theoretical Computer Science, 285, 187–243. https://doi.org/10.1016/S0304-3975(01)00359-0.

    Article  MathSciNet  MATH  Google Scholar 

  13. Cook, W. J. (2012). In Pursuit of the Travelling Salesman: Mathematics at the Limits of Computation. Princeton University Press.

  14. Cooper, J., & Nicolescu, R. (2019). The Hamiltonian cycle and travelling salesman problems in cP systems. Fundamenta Informaticae, 164(2–3), 157–180. https://doi.org/10.3233/FI-2019-1760.

    Article  MathSciNet  MATH  Google Scholar 

  15. Dantzig, R., Fulkerson, R., & Johnson, S. (1954). Solution of a large-scale travelling salesman problem. Operations Research, 2, 393–410.

    MATH  Google Scholar 

  16. He, J., & Zhang, K. (2015). A hybrid distribution algorithm based on membrane computing for solving the multiobjective multiple traveling salesman problem. Fundamenta Informaticae, 136, 199–208. https://doi.org/10.3233/FI-2015-1151.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ionescu, M., Păun, Gh., & Yokomori, T. (2006). Spiking Neural P Systems. Fundamenta Informaticae, 71, 279–308.

  18. Karp, R. M. (1972). Reducibility Among Combinatorial Problems. Complexity of Computer Computations, Plenum,. https://doi.org/10.1007/978-3-540-68279-0_8.

    Article  MATH  Google Scholar 

  19. Leporati, A., Zandron, C., & Mauri, G. (2004). Simulating the Fredkin Gate with energy-based P systems. Journal of Universal Computer Science, 10, 600–619. https://doi.org/10.3217/jucs-010-05-0600.

    Article  MathSciNet  Google Scholar 

  20. Martín-Vide, C., Păun, Gh., Pazos, J., & Rodríguez-Patón, A. (2003). Tissue P Systems. Theoretical Computer Science, 296, 295–326. https://doi.org/10.1016/S0304-3975(02)00659-X.

  21. Meseguer, J. (1992). Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science, 96, 73–155. https://doi.org/10.1016/0304-3975(92)90182-F.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Milner. Operational and Algebraic Semantics of Concurrent Processes. Handbook of Theoretical Computer Science B, 1201–1242, Elsevier (1990). https://doi.org/10.1016/b978-0-444-88074-1.50024-x.

  23. Papadimitriou, C. H. (1977). The Euclidean travelling salesman problem is NP-complete. Theoretical Computer Science, 4, 237–244. https://doi.org/10.1016/0304-3975(77)90012-3.

    Article  MathSciNet  MATH  Google Scholar 

  24. Păun, Gh. (2002). Membrane Computing: An Introduction. Berlin: Springer. https://doi.org/10.1007/978-3-642-56196-2.

    Book  MATH  Google Scholar 

  25. Păun, Gh., Rozenberg, G., & Salomaa, A. (Eds.). (2010). The Oxford Handbook of Membrane Computing. Oxford University Press.

  26. Song, B., Hu, Y., Adorna, H. N., & Xu, F. (2018). A quick survey of tissue-like P systems. Romanian Journal of Information Science and Technology, 21, 310–321.

    Google Scholar 

  27. Song, X., & Wang, J. (2015). An approximate algorithm combining P systems and active evolutionary algorithms for traveling salesman problems. International Journal of Computers, Communications & Control, 10, 89–99.

    Article  Google Scholar 

  28. Zhang, G., Cheng, J., & Gheorghe, M. (2011). A Membrane-inspired approximate algorithm for travelling salesman problems. Romanian Journal of Information Science and Technology, 14, 3–19.

    Google Scholar 

  29. Zhang, G., Rong, H., Neri, F., & Pérez-Jiménez, M. J. (2014). An optimization spiking neural P system for approximately solving combinatorial optimization problems. International Journal of Neural Systems, 24(5), 1440006. https://doi.org/10.1142/S0129065714400061.

    Article  Google Scholar 

  30. Zhang, H., Xiang, L., & Liu, X. (2018). A SN P system for travelling salesman problem. Lecture Notes in Computer Science, 11354, 339–346. https://doi.org/10.1007/978-3-030-15127-0_33.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Romanian Academy, Institute of Computer Science, Iasi, Romania

    Bogdan Aman & Gabriel Ciobanu

  2. Alexandru Ioan Cuza University, Iasi, Romania

    Bogdan Aman & Gabriel Ciobanu

Authors
  1. Bogdan Aman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gabriel Ciobanu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabriel Ciobanu.

Ethics declarations

Conflict of interest

The authors declare they have no financial interests and no conflicts of interest.

Additional information

Publisher's Note

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

This work was presented at the Int’l Conference on Membrane Computing (ICMC20).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aman, B., Ciobanu, G. Travelling salesman problem in tissue P systems with costs. J Membr Comput 3, 97–104 (2021). https://doi.org/10.1007/s41965-021-00077-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41965-021-00077-z

Keywords

Search

Navigation