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

  • M. Mohammadi
  • S. KhodayganEmail author
Original Research


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.


Stochastic optimization algorithm Fertile field algorithm Evolutionary algorithm Nonlinear optimization 



  1. Arora JS (2011) Introduction to optimum design, 3rd edn. Academic Press, San DiegoGoogle 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):1583–1599CrossRefGoogle 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 182–186Google Scholar
  4. Bullock SH, Primack RB (1977) Comparative experimental study of seed dispersal on animals. Ecology 58(3):681–686CrossRefGoogle Scholar
  5. Cain ML, Milligan BG, Strand AE (2000) Long-distance seed dispersal in plant populations. Am J Bot 87(9):1217–1227CrossRefGoogle 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):193–203CrossRefGoogle 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 90–060Google Scholar
  8. Eberhart R, Kennedy J (1995) Particle swarm optimization. Proceedings of the IEEE international conference on neural networks 4:1942–1948CrossRefGoogle Scholar
  9. Fenner M (ed) (2000) Seeds: the ecology of regeneration in plant communities, 2nd edn. CABI Publishing, WallingfordGoogle Scholar
  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. 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):973–990CrossRefGoogle 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 97:849–872CrossRefGoogle Scholar
  13. Houck CR, Joines J, Kay MG (1995) A genetic algorithm for function optimization: a matlab implementation. Ncsu-ie tr 95(09):1–10Google Scholar
  14. Jafari-Marandi R, Smith BK (2017) Fluid genetic algorithm (FGA). J Comput Design Eng 4(2):158–167CrossRefGoogle 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, MichiganzbMATHGoogle Scholar
  16. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, technical report TR06. Erciyes University, KayseriGoogle Scholar
  17. Lanner RM (1985) Effectiveness of the seed wing of Pinus flexilis in wind dispersal. Great Basin Nat 45(2):318–320Google Scholar
  18. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579MathSciNetzbMATHGoogle Scholar
  19. Mehrabian AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inform 1(4):355–366CrossRefGoogle Scholar
  20. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67CrossRefGoogle Scholar
  21. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRefGoogle Scholar
  22. Nakrani S, Tovey C (2004) On honey bees and dynamic server allocation in internet hosting centers. Adapt Behav 12(3–4):223–240CrossRefGoogle Scholar
  23. Sacchi CF (1987) Variability in dispersal ability of common milkweed. Asclepias syriaca, seeds Oikos 49(2):191–198Google Scholar
  24. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Des 112(2):223–229CrossRefGoogle 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:1–24Google Scholar
  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 81–86Google Scholar
  27. Sorensen AE (1986) Seed dispersal by adhesion. Annu Rev Ecol Syst 17(1):443–463MathSciNetCrossRefGoogle 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. CrossRefGoogle Scholar
  29. Törn A, Žilinskas A (1989) Global optimization, (Vol 350). Springer, BerlinCrossRefGoogle Scholar
  30. Van der Pijl L (1982) Principles of dispersal. Springer, BerlinCrossRefGoogle 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):301–308CrossRefGoogle Scholar
  32. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle 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):137–159CrossRefGoogle 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):493–516MathSciNetCrossRefGoogle Scholar
  35. Yang XS (2008) Nature-Inspired Metaheuristic Algorithms, 1st Frome, UK. Luniver Press, BristolGoogle Scholar
  36. Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. Springer, Berlin, Heidelberg, pp 169–178zbMATHGoogle Scholar
  37. Yang XS (2010a) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, Heidelberg, pp 65–74CrossRefGoogle Scholar
  38. Yang XS (2010b) Nature-inspired metaheuristic algorithms. Luniver pressGoogle Scholar
  39. Yang XS (2012) Flower pollination algorithm for global optimization. Comput Sci 7445:240–249zbMATHGoogle Scholar
  40. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC). IEEE, pp 210–214Google Scholar
  41. Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343zbMATHGoogle Scholar
  42. Yang R, Douglas I (1998) Simple genetic algorithm with local tuning: Efficient global optimizing technique. J Optim Theory Appl 98(2):4MathSciNetCrossRefGoogle Scholar
  43. Yao X, Liu Y (1997) Fast evolution strategies. In: Proceedings of the 6th international conference on evolutionary programming VI. Springer, pp 151–162Google Scholar
  44. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3(2):82–102CrossRefGoogle Scholar
  45. Yazdani M, Jolai F (2016) Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. J Comput Design Eng 3(1):24–36CrossRefGoogle 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):633–638CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringSharif University of TechnologyTehranIran

Personalised recommendations