Skip to main content

An algorithm for numerical nonlinear optimization: Fertile Field Algorithm (FFA)

Abstract

Nature, as a rich source of solutions, can be an inspirational guide to answer scientific expectations. Seed dispersal mechanism as one of the most common reproduction method among the plants is a unique technique with millions of years of evolutionary history. In this paper, inspired by plants survival, a novel method of optimization is presented, which is called Fertile Field Algorithm. One of the main challenges of stochastic optimization methods is related to the efficiency of the searching process for finding the global optimal solution. Seeding procedure is the most common reproduction method among all the plants. In the proposed method, the searching process is carried out through a new algorithm based on the seed dispersal mechanisms by the wind and the animals in the field. The proposed algorithm is appropriate for continuous nonlinear optimization problems. The efficiency of the proposed method is examined in details through some of the standard benchmark functions and demonstrated its capability in comparison to other nature-inspired algorithms. Obtained results show that the proposed algorithm is efficient and accurate to find optimal solutions for multimodal optimization problems with few optimal points. To evaluate the effects of the key parameters of the proposed algorithm on the results, a sensitivity analysis is carried out. Finally, to illustrate the applicability of FFA, a continuous constrained single-objective optimization problem as an optimal engineering design is considered and discussed.

This is a preview of subscription content, access via your institution.

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

Notes

  1. 1.

    Fast Evolutionary Strategy.

  2. 2.

    Classical Evolutionary Strategy.

  3. 3.

    Fast Evolutionary Programming.

  4. 4.

    Classical Evolutionary Programming.

References

  1. Arora JS (2011) Introduction to optimum design, 3rd edn. Academic Press, San Diego

    Google Scholar 

  2. Belegundu AD, Arora JS (1982) A study of mathematical programming methods for structural optimization. Part I: Theory. Int J Numer Methods Eng 21(9):1583–1599

    Article  Google Scholar 

  3. Birge B (2003) PSOt-a particle swarm optimization toolbox for use with Matlab, In Proceedings of the 2003 IEEE Swarm Intelligence Symposium SIS’03 (Cat No 03EX706), pp 182–186

  4. Bullock SH, Primack RB (1977) Comparative experimental study of seed dispersal on animals. Ecology 58(3):681–686

    Article  Google Scholar 

  5. Cain ML, Milligan BG, Strand AE (2000) Long-distance seed dispersal in plant populations. Am J Bot 87(9):1217–1227

    Article  Google Scholar 

  6. Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  7. Colorni A, Dorigo M, Maniezzo V (1992) A genetic algorithm to solve the timetable problem. Technical Report, 90-060 revised, Politecnico di Milano, Milan, Italy, pp 90–060

  8. Eberhart R, Kennedy J (1995) Particle swarm optimization. Proceedings of the IEEE international conference on neural networks 4:1942–1948

    Article  Google Scholar 

  9. Fenner M (ed) (2000) Seeds: the ecology of regeneration in plant communities, 2nd edn. CABI Publishing, Wallingford

  10. Fleming TH, Estrada A (eds ) (2012) Frugivory and seed dispersal: ecological and evolutionary aspects. In: Part of the advances in vegetation science book series (AIVS, volume 15). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1749-4

    Google Scholar 

  11. He S, Wu QH, Saunders JR (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evol Comput 13(5):973–990

    Article  Google Scholar 

  12. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872

    Article  Google Scholar 

  13. Houck CR, Joines J, Kay MG (1995) A genetic algorithm for function optimization: a matlab implementation. Ncsu-ie tr 95(09):1–10

    Google Scholar 

  14. Jafari-Marandi R, Smith BK (2017) Fluid genetic algorithm (FGA). J Comput Design Eng 4(2):158–167

    Article  Google Scholar 

  15. John H (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Michigan

    MATH  Google Scholar 

  16. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, technical report TR06. Erciyes University, Kayseri

    Google Scholar 

  17. Lanner RM (1985) Effectiveness of the seed wing of Pinus flexilis in wind dispersal. Great Basin Nat 45(2):318–320

    Google Scholar 

  18. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  19. Mehrabian AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inform 1(4):355–366

    Article  Google Scholar 

  20. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  21. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  22. Nakrani S, Tovey C (2004) On honey bees and dynamic server allocation in internet hosting centers. Adapt Behav 12(3–4):223–240

    Article  Google Scholar 

  23. Sacchi CF (1987) Variability in dispersal ability of common milkweed. Asclepias syriaca, seeds Oikos 49(2):191–198

    Google Scholar 

  24. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Des 112(2):223–229

    Article  Google Scholar 

  25. Sharma TK, Abraham A (2019) Artificial bee colony with enhanced food locations for solving mechanical engineering design problems. J Ambient Intell Hum Comput:1–24

  26. Shi Y (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat No 01TH8546), vol 1, pp 81–86

  27. Sorensen AE (1986) Seed dispersal by adhesion. Annu Rev Ecol Syst 17(1):443–463

    MathSciNet  Article  Google Scholar 

  28. Su S, Zhao S (2017) A hierarchical hybrid of genetic algorithm and particle swarm optimization for distributed clustering in large-scale wireless sensor networks. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-017-0619-9

    Article  Google Scholar 

  29. Törn A, Žilinskas A (1989) Global optimization, (Vol 350). Springer, Berlin

    Book  Google Scholar 

  30. Van der Pijl L (1982) Principles of dispersal. Springer, Berlin

    Book  Google Scholar 

  31. Willson MF, Crome FHJ (1989) Patterns of seed rain at the edge of a tropical Queensland rain forest. J Trop Ecol 5(3):301–308

    Article  Google Scholar 

  32. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  33. Wu SJ, Chow PT (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim 24(2):137–159

    Article  Google Scholar 

  34. Xiang Y, Peng Y, Zhong Y, Chen Z, Lu X, Zhong X (2014) A particle swarm inspired multi-elitist artificial bee colony algorithm for real-parameter optimization. Comput Optim Appl 57(2):493–516

    MathSciNet  Article  Google Scholar 

  35. Yang XS (2008) Nature-Inspired Metaheuristic Algorithms, 1st Frome, UK. Luniver Press, Bristol

    Google Scholar 

  36. Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. Springer, Berlin, Heidelberg, pp 169–178

    MATH  Google Scholar 

  37. Yang XS (2010a) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, Heidelberg, pp 65–74

    Chapter  Google Scholar 

  38. Yang XS (2010b) Nature-inspired metaheuristic algorithms. Luniver press

  39. Yang XS (2012) Flower pollination algorithm for global optimization. Comput Sci 7445:240–249

    MATH  Google Scholar 

  40. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC). IEEE, pp 210–214

  41. Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343

    MATH  Google Scholar 

  42. Yang R, Douglas I (1998) Simple genetic algorithm with local tuning: Efficient global optimizing technique. J Optim Theory Appl 98(2):4

    MathSciNet  Article  Google Scholar 

  43. Yao X, Liu Y (1997) Fast evolution strategies. In: Proceedings of the 6th international conference on evolutionary programming VI. Springer, pp 151–162

  44. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3(2):82–102

    Article  Google Scholar 

  45. Yazdani M, Jolai F (2016) Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. J Comput Design Eng 3(1):24–36

    Article  Google Scholar 

  46. Zhang C, Yang Y, Du Z, Ma C (2016) Particle swarm optimization algorithm based on ontology model to support cloud computing applications. J Ambient Intell Hum Comput 7(5):633–638

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. Khodaygan.

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

Verify currency and authenticity via CrossMark

Cite this article

Mohammadi, M., Khodaygan, S. An algorithm for numerical nonlinear optimization: Fertile Field Algorithm (FFA). J Ambient Intell Human Comput 11, 865–878 (2020). https://doi.org/10.1007/s12652-019-01598-3

Download citation

Keywords

  • Stochastic optimization algorithm
  • Fertile field algorithm
  • Evolutionary algorithm
  • Nonlinear optimization