Sunflower optimization algorithm (SFO): population-based nature inspired algorithm mimicking the sunflowers movement towards the sun

1. Introduction

The SFO is a new meta-heuristic algorithm which is stimulated by the moving of sunflowers towards the sunlight by considering the pollination between adjacent sunflowers. Also, the SFO is stimulated by the inverse square law radiation and it is a technique is a population-based iterative heuristic global [1] optimization algorithm for multi-modal problems. Compared to traditional algorithms, SFO employs terms as root velocity and pollination providing robustness. These flowers are believed to have originated in Mexico and Peru. In the United States, sunflowers are known to have been cultivated during ancient times. The Native Americans used sunflowers for more than 5,000 years [2]. They not only used the seeds as premium food and an oil source, but also utilized the flowers, roots, and stems for different purposes such as for dye pigment. These flowers were introduced to Europe by Spanish explorers. They were first grown in Spain and then subsequently introduced to other neighboring countries. Currently, sunflower oil is one of the most popular oils in the world [3]. Today, the major commercial markets of sunflowers include Russia, Spain, Argentina, France, Peru, and China. You are probably familiar with the refined cooking oil used in the majority of kitchens, which is composed of sunflower oil.

2. Inspirations of SFO

Sunflowers are scientifically known as Helianthus annuus, and belonging to the Asteraceae plant family.  This large and diverse plant family also includes the asters and the daisies, flowers which typically has a flower head [4]. A sunflower maintains homeostasis through their cell membrane, letting only some minerals get in and out. first want to plant the seed then the root starts to grow out of the seed and spread into the soil (anchors the plant to the ground) after that the shoot begins to come out of the seed in the opposite direction of the roots and then the shoot grows into a sprout then the sprout starts to grow leaves and a bud starts to form after that the bud starts to bloom (petals and a flower head are formed) then the seeds and pollen are on the flower head (bees spread the pollen: pollination) petals begin to fall off and the flower begins to wither and die then  the seeds fall to the ground, they scatter, and the process starts all over again.

3. Sunflower Optimization Algorithm (SFO)

Sunflowers are usually tall annual or perennial plants that in some species can grow to a height of 300 cm (120 in) or more. They bear one or more wide, terminal capitulate (flower heads), with bright yellow ray florets at the outside and yellow or maroon (also known as a brown/red) disc florets inside. Several ornamental cultivars of H. annuus have red-colored ray florets; all of them stem from a single original mutant [5]. During growth, sunflowers tilt during the day to face the sun but stop once they begin blooming. This tracking of the sun in young sunflower heads is called heliotropism. By the time they are mature, sunflowers generally face east [6]. The rough and hairy stem is branched in the upper part in wild plants but is usually unbranched in domesticated cultivars. The petiolate leaves are dentate and often sticky.

The lower leaves are opposite, ovate, or often heart-shaped. They are distinguished technically by the fact that the ray florets (when present) are sterile, and by the presence on the disk flowers of a pappus that is of two awn-like scales that are caducous (that is, easily detached and falling at maturity). Some species also have additional shorter scales in the pappus, and one species lacks a pappus entirely [7]. Another technical feature that distinguishes the genus more reliably, but requires a microscope to see, is the presence of a prominent, multicellular appendage at the apex of the style. Further, the florets of a sunflower are arranged in a natural spiral. [8] Variability is seen among the perennial species that make up the bulk of those in the genus. Some have most or all of the large leaves in a rosette at the base of the plant and produce a flowering stem that has leaves that are reduced in size.

4. Life cycle of SFO

Plants begin as a seed and in order to grow the seed must first germinate. Germination is what happens to a seed that has been dormant (asleep) and with enough sunlight, water and warmth it will sprout. Once germinated, a root develops and grows down into the soil. Roots are like straws and absorb the water and nutrients a plant needs from the soil [9]. You will know your seed has sprouted when you can see a little green shoot pushing up through the soil. The sprout will grow into a baby plant or seedling. It starts with little leaves, then grows new ones (true leaves) that look different to the others. The plant stem has grown wider and taller, and more leaves have grown. The sunflower flower bud has started to develop and open up, and the plant is beginning to mature [10]. This is shows a fully grown sunflower that’s flower is in bloom. Plants begin as a seed and in order to grow the seed must first germinate. Germination is what happens to a seed that has been dormant (asleep) and with enough sunlight, water and warmth it will sprout.

4.1. Stages for the growth of sunflower

• Planting the seed
• Germination
• Development of seedling, leaf and plant
• Growing a Bud
• Pollination
• Seed development
• Harvesting

Stage 1: Planting the seed

The seed is the dormant undeveloped stage of the plant. The seed of sunflower is a single dried out fruit of a plant in its whole form [11]. In botanical terms it is called a cypsela. Within this whole seed is all the nutrients and genetic information needed to grow another sunflower plant.

Stage 2: Germination (2 to 10 days)

After the seed has been planted germination starts to happen. This is the first stage of the seeds awakened life [12]. Underneath the soil, out of sight, the wispy roots reach out and a developing shoot appears we know we are on our way to growing a sunflower.

Stage 3: Development of seedling, leaf and plant (10 to 35 days)

Our seedling has become a young sunflower plant. The newly sprouted sunflower usually has two baby leaves on it and quickly grows many more as the steam starts to get taller [13].  The young plant starts to develop rapidly, getting as strong and tall as it can. Sunflower gets energy through photosynthesis.

Stage 4: Growing a bud (35 to 65 days)

The tall leafy maturing sunflower has grown big and strong enough to produce a bud. The sunflower plant is still growing and our bud is trying to get all the hours of sunlight it can in order to get much energy for the bud to develop and enlarge [14]. This is also the stage to keep the sunflower hydrated. Regular watering is important for the budding and flowering stage of its life, so it can grow strong and big.

Stage 5: Flowering (65 to 85 days)

The bud has grown as big as it can start to flower. At this stage the sunflower is reached blooming and gently opens its petals.

Step 6: Poillination (65 to 85 days)

Within the flowering stage the pollination will take place and the pollinators, mainly bees sip on the nector while pollen get stuck on their fluffy bodies [15]. They transfer this pollen to another flower which starts the pollination and fertilize process.

Step 7: Seed development (85 to 105 days)

After pollination the fertilized seeds start to develop and ripen. The back of the sunflower head turns to yellow this is perfectly natural tells us that the seeds are ripening [16]. The ripening seeds attack birds, animals and bugs to feast on.

Stage 8: Harvesting

The ripened seeds are ready to harvest and at this stage the sunflower head starts to droop and turn brown.  By cutting the stem about 4 inches below the sunflower head, store it upside down in a breathable bag in a dry place [7]. Them the warmth of the following spring the seeds wake up, they starts to germinate and a sunflower seedling will appear.

4.2. Steps for SFO

• Initialize parameters
• Initialize Sunflower
• Select the objective
• Update the Sunflower
• New Sunflower generated
• Termination

4.2.1. Initialize parameters

Initialize parameters of SFO algorithm, such as the number of sunflower, the solution dimension space and the maximum number of iteration.

4.2.2. Initialize Sunflower

The parameters of pollination rate best values (0.01 < p < 0.10), mortality rate, best values (0.01 > m < 0.10) and the survival rate, best values (0.80 > s < 0.90)

4.2.3. Objective function

The best objective of each sunflower is randomly selected

4.2.4. Update the Sunflower

The best sunflower is updated respectively. Else, utilize to update the individual.

4.2.5. Generated New Sunflower

Based on the pollination and mortality the new sunflower was generated.

4.2.6. Termination

Finally, parameters in guidance compensation are optimized to achieve higher landing accuracy with less height error integration.

4.3. Flowchart of SFO

5. Numerical Expressions of SFO algorithm

The mathematical model of this behavior is represented as follows:

6. Applications of SFO

• Magnetic Drum
• Vibrating Sieve
• Destoner
• Flakers
• Presser
• Dehuller

7. Advantages of SFO

• Applied to damage identification on laminated composite plates.
• SFO employs terms as root velocity and pollination providing robustness.
• To solve the direct problem due to the complexity of an anisotropic material.
• To find a global optimum efficiently and not get stuck in a local optimum.
• sunflower only produces one pollen gamete and reproduces individually.

Reference

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