Inspired by Plants Survival An New Optimization is presented: Fertile Field Algorithm for Continuous Nonlinear Optimization Problems

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1. Introduction

Nature, as a rich source of solutions, can be an inspirational guide to answer scientific expectations [1]. Seed dispersal mechanism as one of the most common reproduction [2] method among the plants is a unique technique with millions of years of evolutionary history [3]. 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 fled. 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.

The Fertile Field algorithm as a nature-inspired optimization method consists of the following steps;

  • The initial seeding procedure.
  • Fertility evaluation of the points based on the objective function.
  • The regeneration of seeds.
  • Seed dispersal process by wind and animals
  • Convergence criteria evaluation

The proposed FFA mimics the dispersal of seeds, natural factors, and growth of plants in a fertile field. In a field, when the seeds fall on the land, the fertility of points in the area is the main factor in the plant growth. The fertility of a point on the field is evaluated through the objective function value at the corresponding point. Therefore, finding the most fertile point in the field is equivalent to find the global optimal solution in the optimization problem

Fig1: Fertile Field Algorithm

2. Inspiration of FFA

The fertile field algorithm is inspired by plants survival enhanced with fertile field [4]. Plants have a very long history of life on earth. Their evolved pattern of survival can be a unique source of inspiration to develop an evolutionary optimization algorithm. Each type of plants can be adapted to several climate conditions to survive and prosper. Seeding is the most common reproduction method among all the plants. In the seeding procedure of the plants, some seeds fall under the plants, while others are distributed in other zones by natural factors, such as wind force and animals. In this way, the proper opportunities for growth and development of new plants in different parts of the field can be provided. In the field, the growth of plants is directly related to fertility. On the other hand, the fertility of all zones of the field usually is not equal. When a seed is placed in a fertile zone of the field, all conditions for the growth and development are available.

After the growth stage, it can contribute seeding or the pollination procedure as a mature plant. Then new plants can be generated in the fertile zones, but if the area is not fertile, the seed cannot achieve enough growth for reproduction and it will be wasted. Therefore, it naturally will be eliminated from the life evolution cycle. After the growth of the new plants in successive generations, plants in more fertile areas are denser. Inspired by this natural pattern, an evolutionary-based optimization algorithm can be developed. According to this natural pattern, the distribution of the plants in different areas of the felid can be simulated based on the fertility values of zones. In the proposed algorithm, the fertility of a point in the field is taken equal to the objective function value at that point.

Fig 2: Inspiration of FFA

3. Flowchart of FFA

Fig 3: Flowchart of FFA

4. Nanotechnology in agriculture: Current status, challenges and future opportunities

Nanotechnology has shown promising potential to promote sustainable agriculture [5], further progress in the development of innovative [6] and improved synthesis methods with precise control over product [7] composition will be highly useful to improve their efficiency [8]. Role of NMs should also be explored in bioremediation to develop integrated remediation strategies [9]. At field level would be highly useful for large-scale implementation of nano-based strategies. Nano materials have many potential applications in agriculture to enhance crop productivity and to improve the soil health which has been highlighted in this section. Here, we illustrate various developments in the field of nanofertilizers, nanopesticides, nanobiosensors and nano-enabled remediation of contaminated soils.

            Nano materials play an important role regarding the fate, mobility and toxicity of soil pollutants and are essential part of different biotic and biotic remediation strategies. Efficiency and fate of nonmaterials is strongly dictated by their properties and interactions with soil constituents which is also critically discussed in this review. Investigations into the remediation applications and fate of nanoparticles in soil remain scarce and are mostly limited to laboratory studies. Once entered in the soil system, nonmaterial’s may affect the soil quality and plant growth which is discussed in context of their effects on nutrient release in target soils, soil biota, soil organic matter and plant morphological and physiological responses. The mechanisms involved in uptake and translocation of nonmaterials within plants and associated defense mechanisms have also been discussed. Future research directions have been identified to promote the research into sustainable development of nano-enabled agriculture [10].

Fig 4: Nanotechnology in agriculture

5. Pseudo Code of FFA

Fig 5: Pseudo Code of FFA

6. Advantages of FFA

Fig 6: Advantages of FFA

7. Application of FFA

A mechanical helical spring and its design variables is implemented in FFA [11].

Fig 7: Application of FFA


[1]M. Mohammad and S. Khodaygan, “An algorithm for numerical nonlinear optimization: Fertile Field Algorithm (FFA)”, 2020. .

[2]Eberhart R, Kennedy J (1995) Particle swarm optimization. Proceedings of the IEEE international conference on neural networks4:1942–1948

[3]Fenner M (ad) (2000) Seeds: the ecology of regeneration in plant communities, 2nd edn. CABI Publishing, Wallingford

[4]Fleming TH, Estrada A (eds ) (2012) Frugivory and seed dispersal:ecological and evolutionary aspects. In: Part of the advances invegetation science book series (AIVS, volume 15). SpringeDordrecht.

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

[6]Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019)

[7]Harris hawks optimization: algorithm and applications. FutureGener Comput Syst 97:849–872

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

[9]Jafari-Marandi R, Smith BK (2017) Fluid genetic algorithm (FGA). JComput Design Eng 4(2):158–167

[10]John H (1975) Adaptation in natural and artifcial systems: an introductory analysis with applications to biology, control, and artifcialintelligence. University of Michigan Press, Michigan

[11]Karaboga D (2005) An idea based on honey bee swarm for numericaloptimization, technical report TR06. Erciyes University, Kayseri

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