Skip to main content
SpringerLink
Log in

Multi-objective algorithm based on tissue P system for solving tri-objective optimization problems

  • Special Issue
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

This paper presents a multi-objective algorithm based on tissue P system (MO TPS for short) for solving the tri-objective vehicles routing problem with time windows (VRPTW). Unlike most of the work where just the accuracy or extensibility of the solution is the core, the proposed algorithm focuses on searching the boundaries of solution sets and ensuring the solutions have better extensibility and uniformly distributed. In MO TPS, the cells of the tissue P system are divided into two groups. The first group, consisting of only one cell, aims at approaching to the Pareto front by the NSGA-II while second group, consisting of six cells, focuses on searching boundaries by the artificial bee colony algorithm with different prioritization rules. The main ideas of the MO TPS are to utilize the evolution of two groups of cells with different functions in the tissue P system for searching the boundaries of solution sets, obtaining solution sets which are uniformly distributed and have better extensibility and approaching to the Pareto front on the premise of preserving the elite boundaries. 56 Solomon benchmarks are utilized to test algorithm performance. Experimental results show that on the premise of ensuring accuracy, the proposed approach outperforms compared algorithms in terms of three metrics.

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

Similar content being viewed by others

References

  1. Abualigah L, Diabat A et al (2021) The arithmetic optimization algorithm[J]. Comput Methods Appl Mech Eng 376–113609:113609

    MathSciNet  MATH  Google Scholar 

  2. Abualigah L, Diabat A (2021) Advances in sine cosine algorithm: a comprehensive survey. Artif Intell Rev. 2567–2608

  3. Abualigah L, Diabat A (2020) A comprehensive survey of the Grasshopper optimization algorithm: results, variants, and applications[J]. Neural Comput Appl. 15533–15556

  4. Abualigah L, Diabat A et al (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    MathSciNet  MATH  Google Scholar 

  5. Meng W, Ke L, Kwong S (2018) Learning to decompose: a paradigm for decomposition-based multiobjective optimization. IEEE Trans Evol Comput 23(3):376

    Google Scholar 

  6. Dbe K, Hussein R, Roy PC, Toscano G (2019) A taxonomy for metamodeling frameworks for evolutionary multiobjective optimization. IEEE Trans Evol Comput 23(1):14–116

    Google Scholar 

  7. Medhane DV, Sangaiah AK (2017) Search space-based multi-objective optimization evolutionary algorithm. Comput Electr Eng 58:126–143

    Google Scholar 

  8. Huang H (2018) A hybrid multiobjective particle swarm optimization algorithm based on R2 indicator. IEEE Access 6(99):14710–14721

    Google Scholar 

  9. Wy J, Kim BI, Kim S (2013) The rollon-rolloff waste collection vehicle routing problem with time windows. Eur J Op Res

  10. Bhusiri N, Qureshi AG, Taniguchi E (2014) The tradeoff between fixed vehicle costs and time-dependent arrival penalties in a routing problem. Transp Res E Logis Transp Rev 62:1–22

    Google Scholar 

  11. Amorim P, Almada-Lobo B (2014) The impact of food perishability issues in the vehicle routing problem. Comput Ind Eng 67(2):223–233

    Google Scholar 

  12. Melián-Batista B, De SA, Angelbello F (2014) A bi-objective vehicle routing problem with time windows: a real case in Tenerife. Appl Soft Comput J 17:140–152

    Google Scholar 

  13. Eksioglu B, Vural AV, Reisman A (2009) The vehicle routing problem: a taxonomic review. Comput Ind Eng 57(4):472–1483

    Google Scholar 

  14. Layani R, Khemakhem M, Semet F (2015) Rich vehicle routing problems: from a taxonomy to a definition. Eur J Op Res 241(1):1–14

    MathSciNet  MATH  Google Scholar 

  15. Montoya JR, Franco JL, Isaza SN, Jimenez HF, Herazo N (2015) A literature review on the vehicle routing problem with multiple depots. Comput Ind Eng 79(1):115–129

    Google Scholar 

  16. Dorling K, Heinrichs J, Messier G, Magierowski S (2016) Vehicle routing problems for drone delivery. IEEE Trans Syst Man Cybern Syst 1–16

  17. Paun G, Rozenberg G, Salomaa A (2010) The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford

    MATH  Google Scholar 

  18. Pan L, Carlos M (2005) Solving multidimensional 0–1 knapsack problem by P systems with input and active membranes. J Parallel Distrib Comput 65(12):1578–1584

    MATH  Google Scholar 

  19. Pan L, Daniel DP, Marip J (2011) Computation of Ramsey numbers by P systems with active membranes. Int J Found Comput Sci 22(1):29–58

    MathSciNet  MATH  Google Scholar 

  20. Martin C, Pazos J, Paun G, Rodriguez A (2002) A New Class of Symbolic Abstract Neural Nets: Tissue P Systems. Springer, Berlin, Heidelberg

    MATH  Google Scholar 

  21. Paun G, Perez-Jimenez MJ, Riscos-Nunez A (2008) Tissue P systems with cell division. Int J Comput Commun Control 3(3):295

    Google Scholar 

  22. Pan L, Paun G (2010) Spiking neural P systems: an improved normal form. Theor Comput Sci 411(6):906–918

    MathSciNet  MATH  Google Scholar 

  23. Pan L, Paun G, Perez-Jimenez MJ (2011) Spiking neural P systems with neuron division and budding. Sci China Inform Sci 54(8):1596–1607

    MathSciNet  MATH  Google Scholar 

  24. Wu T, Zhang Z, Paun G, Pan L (2016) Cell-like spiking neural P systems. Theor Comput Sci 623:180–189

    MathSciNet  MATH  Google Scholar 

  25. Wu T, Pan L, Yu Q, Tan KC (2020) Numerical spiking neural P systems. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3005538

    Article  Google Scholar 

  26. Wu T, Zhang L, Pan L (2020) Spiking neural P systems with target indications. Theor Comput Sci. https://doi.org/10.1061/j.tcs.2020.07.016

    Article  MATH  Google Scholar 

  27. Wu T, Paun A, Zhang Z, Pan L (2018) Spiking neural P systems with polarizations. IEEE Trans Neural Netw Learn Syst 29(8):3349–3360

    MathSciNet  Google Scholar 

  28. Wang HF, Zhou K, Zhang GX, Paul P, Duan YY, Qi HQ (2020) Application of weighted spiking neural P systems with rules on synapses for breaking RSA encryption. Int J Unconven Comput 15(1–2):37–58

    Google Scholar 

  29. NishidaTY (2005) Membrane algorithm: an approximate algorithm for NP-complete optimization problems exploiting P-systems. In: Proceedings of the 6th international workshop on membrane computing (WMC ’05),pp. 26-43, Vienna, Austria

  30. Paun G (2000) Computing with membranes. J Comput Syst Sci 61(1):108–143

    MathSciNet  MATH  Google Scholar 

  31. Martin C, Pazos J, Paun G (2003) Tissue P systems. Theor Comput Sci 61(1):295–326

    MathSciNet  MATH  Google Scholar 

  32. Zhang G, GHeorghe M, Pan L, Perez-Jimenez MJ (2014) Evolutionary membrane computing: a comprehensive survey and new results. Inform Sences 279:528–551

    Google Scholar 

  33. Wang X, Zhang G, Junbo Z, Haina R, Floentin I, Raluca L (2015) A modified membrane-inspired algorithm based on particle swarm optimization for mobile robot path planning. Int J Comput Commun Control 10(5):732–745

    Google Scholar 

  34. Huang L, He X, Wang N, Yi X (2007) P systems based multi-objective optimization algorithm. Prog Nat Sci Mater Int 17(4):458–465

    MathSciNet  MATH  Google Scholar 

  35. Zhang G, Gheorghe M, Wu CZ (2008) A quantum-inspired evolutionary algorithm based on P systems for knapsack problem. Fundamenta Inform 87(1):93–116

    MathSciNet  MATH  Google Scholar 

  36. Zhang G, Liu C, GheorgheM (2010)Diversity and convergence analysis of membrane algorithms. In: Proceedings of the 5th IEEE International Conferen ce on Bio-Inspired Computing: Theories and Applications, pp. 596-603

  37. Zhang G, Cheng J, Gheorghe M, Meng Q (2013) A hybrid approach based on differential evolution and tissue membrane systems for solving constrained manufacturing parameter optimization problems. Appl Soft Comput J 13(3):1528–1542

    Google Scholar 

  38. He J, Xiao J (2014) An adaptive membrane algorithm for solving combinatorial optimization problems. Acta Math Sci 5:1377–1394

    MathSciNet  MATH  Google Scholar 

  39. Han M, Liu C, Xing J (2014) An evolutionary membrane algorithm for global numerical optimization problems. Inform Sci 276:219–241

    MathSciNet  Google Scholar 

  40. He J, Zhang K (2015) A hybrid distribution algorithm based on membrane computing for solving the multiobjective multiple traveling salesman problem. Fundamenta Inform 136(3):199–208

    MathSciNet  MATH  Google Scholar 

  41. Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Op Res 35(2):254–265

    MathSciNet  MATH  Google Scholar 

  42. Orellana-Martín D, Valencia-Cabrera L, Riscos-Núñez A (2019) Minimal cooperation as a way to achieve the efficiency in cell-like membrane systems. J Membr Comput 1:85–92

    MathSciNet  MATH  Google Scholar 

  43. Ullrich Christian A (2013) Integrated machine scheduling and vehicle routing with time windows. Eur J Op Res 227(1):152–165

    MathSciNet  MATH  Google Scholar 

  44. Yu S, Ding C, Zhu K (2011) A hybrid GA-TS algorithm for open vehicle routing optimization of coal mines material. Exp Syst Appl 38:10568–10573

    Google Scholar 

  45. Ombuki B, Ross B, Hanshar F (2006) Multi-objective genetic algorithm for vehicle routing problem with time windows. Appl Intell 24:17–30

    Google Scholar 

  46. Tan KC, Chew YH, Lee LH (2006) A hybrid multiobjective evolutionary algorithmfor solving vehicle routing problem with time windows. Comput Optim Appl 34(1):115–151

    MathSciNet  MATH  Google Scholar 

  47. Ghoseiri K, Ghannadpour F (2010) Multi-objective vehicle routing problem withtime windows using goal programming and genetic algorithm. Appl Soft Comput 4:115–151

    Google Scholar 

  48. Hong SC, Park YB (1999) A heuristic for bi-objective vehicle routing with time window constraints. Int J Prod Econ 62(3):249–258

    Google Scholar 

  49. Zakaria N (2014) Partially optimized cyclic shift crossover for multi-objective genetic algorithms for the multi-objective vehicle routing problem with time-windows. In: 2014 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM), pp. 106–115

  50. Andreas K, Savvas P, Christoforos C (2014) Adaptive evolutionary algorithm for a multi-objective VRP. Int J Eng Intell Syst 22

  51. Niu Y, He J, Wang Z, Xiao J (2014) A P-based hybrid evolutionary algorithm for vehicle routing problem with time windows. Math Prob Eng 1–11

  52. Dong W, Zhou K, Qi H, Zhang J (2018) A tissue P system based evolutionary algorithm for multi-objective VRPTW. Swarm Evolut Comput 39:310–322

    Google Scholar 

  53. Huang L, Suh IH, Abraham H (2011) Dynamic multi-objective optimization based on membrane computing for control of time-varying unstable plants. Inform Sci 181(18):2370–2391

    Google Scholar 

  54. Cheng J, Zhang G, Zeng X (2011) A novel membrane algorithm based on differential evolution for numerical optimization. Int J Unconvent Comput 7(3):159–183

    Google Scholar 

  55. Zhang G, Liu C, Gheorghe M (2010) Diversity and convergence analysis of membrane algorithms. In: Fifth international conference on bio-inspired computing: theories applications, pp. 596-603

  56. Zhang G, Gheorghe M, Jixiang C, Dynamic behavior analysis of membrane algorithms. MATCH Communications in Mathematical and in Computer hemistry (in press)

  57. Martin C, Paun G, PAzos J (2003) Tissue P systems. Theor Comput Sci 296:295–326

    MathSciNet  MATH  Google Scholar 

  58. Eiben AE, Smit SK (2011) Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evolut Comput 1(1):19–31

    Google Scholar 

  59. Zhang W, Lin L, Gen M (2012) Hybrid multiobjective evolutionary algorithm with fast sampling strategy-based global search and route sequence difference based local search for VRPTW. Proc Comput Ence 14(4):96–101

    Google Scholar 

  60. Davis L (1985) Applying adaptive algorithms to epistatic domains. In: Proceedings of the international joint conference on Arti\(\text{\textregistered} \)cial intelligence, pp. 156–166

  61. Gen M, Runwei C (1997) Genetic algorithms and engineering design. Wiley, Hoboken

    Google Scholar 

  62. Zhang H, Zhang Q, Ma L (2019) A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows. Inform Sci

  63. Shu H, Zhou K, He Z, Hu X (2019) Two-Stage multi-objective evolutionary algorithm based on classified population for the tri-objective VRPTW. Int J Unconvent Comput

  64. Sivaramkumar V, Thansekhar MR, Saravanan R (2018) Demonstrating the importance of using total time balance instead of route balance on a multi-objective vehicle routing problem with time windows. The Int J Adv Manuf Technol,1287–1306

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, 430023, China

    Zhixin He, Kang Zhou, Hang Shu & Xinyu Lyu

  2. School of Food Science and Engineering, Wuhan Polytechnic University, Wuhan, 430023, China

    Xuan Chen

Authors
  1. Zhixin He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hang Shu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xinyu Lyu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kang Zhou.

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

He, Z., Zhou, K., Shu, H. et al. Multi-objective algorithm based on tissue P system for solving tri-objective optimization problems. Evol. Intel. 16, 1–16 (2023). https://doi.org/10.1007/s12065-021-00658-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-021-00658-y

Keywords

Search

Navigation