Skip to main content
SpringerLink
Log in

Grasshopper optimization algorithm for multi-objective optimization problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This work proposes a new multi-objective algorithm inspired from the navigation of grass hopper swarms in nature. A mathematical model is first employed to model the interaction of individuals in the swam including attraction force, repulsion force, and comfort zone. A mechanism is then proposed to use the model in approximating the global optimum in a single-objective search space. Afterwards, an archive and target selection technique are integrated to the algorithm to estimate the Pareto optimal front for multi-objective problems. To benchmark the performance of the algorithm proposed, a set of diverse standard multi-objective test problems is utilized. The results are compared with the most well-regarded and recent algorithms in the literature of evolutionary multi-objective optimization using three performance indicators quantitatively and graphs qualitatively. The results show that the proposed algorithm is able to provide very competitive results in terms of accuracy of obtained Pareto optimal solutions and their distribution.

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

Similar content being viewed by others

Notes

  1. The source codes of MOGOA can be found at http://www.alimirjalili.com/Projects.html.

References

  1. Holland JH, Reitman JS (1977) Cognitive systems based on adaptive algorithms. ACM SIGART Bulletin, pp 49–49

  2. Tsai C-F, Eberle W, Chu C-Y (2013) Genetic algorithms in feature and instance selection. Knowl-Based Syst 39:240–247

    Article  Google Scholar 

  3. Lin M-H, Tsai J-F, Yu C-S (2012) A review of deterministic optimization methods in engineering and management. Mathematical Problems in Engineering, vol 2012

  4. Shmoys DB, Swamy C (2004) Stochastic optimization is (almost) as easy as deterministic optimization. In: Proceedings of the 45th annual IEEE symposium on foundations of computer science, 2004, pp 228–237

    Google Scholar 

  5. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1:28–39

    Article  Google Scholar 

  6. Kennedy J (2011) Particle swarm optimization. In: Encyclopedia of machine learning, edn. Springer, pp 760–766

  7. Knowles J, Corne D (1999) The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. In: Proceedings of the 1999 congress on evolutionary computation, 1999. CEC 99

    Google Scholar 

  8. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  MATH  Google Scholar 

  9. Padhye N, Mittal P, Deb K (2013) Differential evolution: performances and analyses. In: 2013 IEEE congress on evolutionary computation (CEC), pp 1960–1967

    Chapter  Google Scholar 

  10. Padhye N, Bhardawaj P, Deb K (2010) Improving differential evolution by altering steps in EC. In: Asia-Pacific conference on simulated evolution and learning, pp 146–155

    Google Scholar 

  11. BoussaïD I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117

    Article  MathSciNet  MATH  Google Scholar 

  12. Helbig M, Engelbrecht AP (2013) Performance measures for dynamic multi-objective optimisation algorithms. Inf Sci 250:61–81

    Article  MATH  Google Scholar 

  13. Padhye N, Zuo L, Mohan CK, Varshney PK (2009) Dynamic and evolutionary multi-objective optimization for sensor selection In sensor networks for target tracking. In: Proceedings of the international joint conference on computational intelligence - volume 1: ICEC, (IJCCI 2009). ScitePress, INSTICC, pp 160–167. doi:10.5220/0002324901600167, ISBN: 978-989-674-014-6

  14. Padhye N, Zuo L, Mohan CK, Varshney P (2009) Dynamic and evolutionary multi-objective optimization for sensor selection in sensor networks for target tracking. In: IJCCI, pp 160–167

    Google Scholar 

  15. Beyer H-G, Sendhoff B (2007) Robust optimization–a comprehensive survey. Comput Methods Appl Mech Eng 196:3190–3218

    Article  MathSciNet  MATH  Google Scholar 

  16. Coello CAC (1999) A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl Inf Syst 1:269–308

    Article  Google Scholar 

  17. Deb K (2001) Multi-objective optimization using evolutionary algorithms, vol 16. Wiley

  18. von Lücken C., Barán B., Brizuela C (2014) A survey on multi-objective evolutionary algorithms for many-objective problems. Comput Optim Appl 58:707–756

    MathSciNet  MATH  Google Scholar 

  19. Nguyen TT, Yang S, Branke J (2012) Evolutionary dynamic optimi- zation: a survey of the state of the art. Swarm Evol Comput 6:1–24

    Article  Google Scholar 

  20. Padhye N, Mittal P, Deb K (2015) Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization. Comput Optim Appl 62:851–890

    Article  MathSciNet  MATH  Google Scholar 

  21. Padhye N, Deb K, Mittal P (2013) An efficient and exclusively-feasible constrained handling strategy for evolutionary algorithms. Technical Report

  22. Asrari A, Lotfifard S, Payam MS (2016) Pareto dominance-based multiobjective optimization method for distribution network reconfiguration. IEEE Trans Smart Grid 7:1401–1410

    Article  Google Scholar 

  23. Zhou A, Qu B-Y, Li H, Zhao S-Z, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1(3//):32–49

    Article  Google Scholar 

  24. Deb K (2014) Multi-objective optimization. In: Search methodologies, edn. Springer, pp 403–449

  25. Padhye N, Deb K (2010) Evolutionary multi-objective optimization and decision making for selective laser sintering. In: Proceedings of the 12th annual conference on genetic and evolutionary computation, pp 1259–1266

    Google Scholar 

  26. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197

    Article  Google Scholar 

  27. Coello CC, Lechuga MS (2002) MOPSO: A proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 congress on evolutionary computation, 2002. CEC’02, pp 1051–1056

    Google Scholar 

  28. Padhye N (2008) Topology optimization of compliant mechanism using multi-objective particle swarm optimization. In: Proceedings of the 10th annual conference companion on genetic and evolutionary computation, pp 1831–1834

    Google Scholar 

  29. Padhye N (2009) Comparison of archiving methods in multi-objective particle swarm optimization (MOPSO): empirical study. In: Proceedings of the 11th annual conference on Genetic and evolutionary computation, pp 1755–1756

    Google Scholar 

  30. Alaya I, Solnon C, Ghedira K (2007) Ant colony optimization for multi-objective optimization problems. In: ICTAI (1), pp 450– 457

    Google Scholar 

  31. Xue F, Sanderson AC, Graves RJ (2003) Pareto-based multi-objective differential evolution. In: The 2003 congress on evolutionary computation, 2003. CEC’03, pp 862–869

    Google Scholar 

  32. Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8:149–172

    Article  Google Scholar 

  33. Wolpert D (1997) No free lunch theorem for optimization. In: IEEE transactions on evolutionary computation, pp 467–482

  34. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: IEEE congress on evolutionary computation, pp 2419–2426

    Google Scholar 

  35. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26:369– 395

    Article  MathSciNet  MATH  Google Scholar 

  36. Deb K, Padhye N, Neema G (2007) Multiobjective evolutionary optimization-interplanetary trajectory optimization with swing-bys using evolutionary multi-objective optimization. Lect Notes Comput Sci 4683:26–35

    Article  Google Scholar 

  37. Jin Y, Olhofer M, Sendhoff B (2001) Dynamic weighted aggregation for evolutionary multi-objective optimization: Why does it work and how?

  38. Branke J, Deb K, Dierolf H, Osswald M (2004) Finding knees in multi-objective optimization. In: International conference on parallel problem solving from nature, pp 722–731

    Google Scholar 

  39. Kollat JB, Reed P (2007) A framework for visually interactive decision-making and design using evolutionary multi-objective optimization (VIDEO). Environ Model Softw 22:1691– 1704

    Article  Google Scholar 

  40. Topaz CM, Bernoff AJ, Logan S, Toolson W (2008) A model for rolling swarms of locusts. Eur Phys J Special Topics 157:93– 109

    Article  Google Scholar 

  41. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Article  Google Scholar 

  42. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197

    Article  Google Scholar 

  43. Zitzler E, Laumanns M, Thiele L, Zitzler E, Zitzler E, Thiele L et al (2001) SPEA2: Improving the strength Pareto evolutionary algorithm, ed: Eidgenössische Technische Hochschule Zürich (ETH). In: Institut für Technische Informatik und Kommunikationsnetze (TIK)

    Google Scholar 

  44. Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248

    Article  Google Scholar 

  45. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Parallel problem solving from nature—PPSN V, pp 292–301

    Chapter  Google Scholar 

  46. Deb K, Padhye N (2014) Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms. Comput Optim Appl 57:761–794

    Article  MathSciNet  MATH  Google Scholar 

  47. Padhye N, Bhardawaj P, Deb K (2013) Improving differential evolution through a unified approach. J Glob Optim 55:771

    Article  MathSciNet  MATH  Google Scholar 

  48. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: Empirical results. Evol Comput 8:173–195

    Article  Google Scholar 

  49. Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 congress on evolutionary computation, 2002. CEC’02, pp 825–830

    Google Scholar 

  50. Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the CEC 2009 special session and competition. University of Essex, Colchester, UK and Nanyang Technological University, Singapore, Special Session on Performance Assessment of Multi-Objective Optimization Algorithms, Technical Report

  51. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Applic 27:1053– 1073

    Article  Google Scholar 

  52. Mirjalili S, Jangir P, Saremi S (2016) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Applied Intelligence, pp 1–17

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computing, University of Newcastle, Callaghan, NSW, 2308, Australia

    Seyedeh Zahra Mirjalili

  2. Institute for Integrated and Intelligent Systems, Griffith University, Nathan, QLD, 4111, Australia

    Seyedali Mirjalili & Shahrzad Saremi

  3. Business Information Technology Department, King Abdullah II School for Information Technology, The University of Jordan, Amman, Jordan

    Hossam Faris & Ibrahim Aljarah

Authors
  1. Seyedeh Zahra Mirjalili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seyedali Mirjalili
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shahrzad Saremi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hossam Faris
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ibrahim Aljarah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyedali Mirjalili.

Appendix: Multi-objective test problems utilised in this work

Appendix: Multi-objective test problems utilised in this work

Table 7 ZDT test suite
Full size table
Table 8 Bi-objective test problems (CEC2009)
Full size table
Table 9 Tri-objective test problems (CEC2009)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mirjalili, S., Mirjalili, S., Saremi, S. et al. Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48, 805–820 (2018). https://doi.org/10.1007/s10489-017-1019-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-017-1019-8

Keywords

Search

Navigation