Behavior of Squirrel Search Algorithm (SSA) using Meta-heuristics method

1. Introduction

       A novel nature-inspired optimization paradigm, named as squirrel search algorithm (SSA). This optimizer imitates the dynamic foraging behavior of southern flying squirrels and their efficient way of locomotion known as gliding. Gliding is an effective mechanism used by small mammals for travelling long distances [1]. The present work mathematically models this behavior to realize the process of optimization. The efficiency of the proposed SSA is evaluated using statistical analysis, convergence rate analysis. An extensive comparative study is carried out to exhibit the effectiveness of SSA over other well-known optimizers in terms of optimization accuracy and convergence rate. The proposed algorithm is implemented on a real-time Heat Flow Experiment to check its applicability and robustness. The results demonstrate that SSA provides more accurate solutions with high convergence rate as compared to other existing optimizers [2]. The foraging behavior of flying squirrels is studied thoroughly and modeled mathematically including each and every feature of their food search.

    The most interesting fact about flying squirrels is that they do not fly, instead they use a special method of locomotion i.e. “Gliding” which is considered to be energetically cheap, allowing small mammals to cover large distances quickly and efficiently. Literature suggests that predator avoidance, optimal foraging and cost of foraging are the primary cause of evolution of gliding. The squirrels can optimally use food resources by showing a dynamic foraging behavior. For instance, to meet nutritional requirements in autumn, they prefer to eat acorns (a mast nut) as they are available in abundance while store other nuts such as hickories in nests, other cavities, and sometimes the ground. During winters when nutritional demands are higher due to low temperature, hickory nuts are eaten promptly at the site of discovery during foraging and are also taken out from reserve food stores [3]. Therefore, selectively eating some nuts and storing others depending upon the nutritional demands, allows optimum utilization of both types of available mast nuts. This intelligent dynamic foraging behavior of southern flying squirrel is the main source of motivation for proposed SSA. In this work dynamic foraging strategy and gliding mechanism of flying squirrels are modeled mathematically to design SSA for optimization [4].

2. Inspiration of Squirrel Search Algorithm

    There is number of flying squirrels in a deciduous forest and one squirrel is assumed to be on one tree. Every flying squirrel individually searches for food and optimally utilizes the available food resources by exhibiting a dynamic foraging behavior. In forest, only three types of trees are available such as normal tree, oak tree (acorn nuts food source) and hickory tree (hickory nuts food source) [5]. The forest region under consideration is assumed to contain three oak trees and one hickory tree. SSA starts with random initial location of flying squirrels similar to other population based algorithms. The location of a flying squirrel is represented by a vector, in dimensional search space [6].

Fig 1: Inspiration of SSA

3. Squirrel Search Algorithm (SSA)

    The search process begins when flying squirrels start foraging. During warm weather (autumn) the squirrels search for food resources by gliding from one tree to the other. While doing so, they change their location and explore different areas of forest. As the climatic conditions are hot enough, they can meet their daily energy needs more quickly on the diet of acorns available in abundance and hence they consume acorns immediately upon finding them. After fulfilling their daily energy requirement, they start searching for optimal food source for winter (hickory nuts) [7]. Storage of hickory nuts will help them in maintaining their energy requirements in extremely harsh weather and reduce the costly foraging trips and therefore increase the probability of survival. During winter, a loss of leaf cover in deciduous forests results an increased risk of predation and hence they become less active but do not hibernate in winter. At the end of winter season, flying squirrels again become active. This is a repetitive process and continues till the lifespan of a flying squirrel and forms the foundation of SSA. Flying squirrels are a diversified group of arboreal and nocturnal type of rodents that are exceptionally adapted for gliding locomotion. Currently, 15 genera and 44 species of flying squirrels are identified and majority of them are found in deciduous forest area of Europe and Asia, particularly South-eastern Asia [8]. The only species found outside Eurasia and most studied is Glaucomys Volans known as southern flying squirrel. The flying squirrels are considered to be the most aerodynamically sophisticated having a parachute-like membrane, which helps the squirrel in gliding from one tree to the other and makes them capable in modifying lift and drag [9].

Fig 2: Squirrel Search Algorithm

3.1. Steps for Squirrel Search Algorithm

  • Random Initialization
  • Fitness evaluation
  • Sorting, declaration and random selection[10]
  • Generate new locations
  • Aerodynamics of gliding
  • Seasonal monitoring conditions[11]
  • Random relocation at the end of winters seasons
  • Stopping criterion

3.1.1. Random Initialization

     SSA starts with random initial location of flying squirrels similar to other population based algorithms. There is number of flying squirrels (FS) in a forest and location of flying squirrel can be specified [12]. A uniform distribution is used to allocate the initial location of each flying squirrel in the forest.

3.1.2. Fitness Evaluation

    The fitness of location for each flying squirrel is calculated by putting the values of decision variable (solution vector) into a user defined fitness function and the corresponding values. The fitness value of each flying squirrel’s location depicts the quality of food source searched by it i.e. optimal food source (hickory tree), normal food source (acorn tree) and no food source (flying squirrel is on normal tree) and hence their probability of survival also [13].

3.1.3. Sorting, Declaration and Random Selection

    After storing the fitness values of each flying squirrel’s location, the array is sorted in ascending order. The flying squirrel with minimal fitness value is declared on the hickory nut tree. The next three best flying squirrels are considered to be on the acorn nuts trees and they are assumed to move towards hickory nut tree [14]. The remaining flying squirrels are supposed to be on normal trees. Further through random selection, some squirrels are considered to move towards hickory nut tree assuming that they have fulfilled their daily energy requirements. The remaining squirrels will proceed to acorn nut trees (to meet their daily energy need). This foraging behavior of flying squirrel is always affected by the presence of predators.

3.1.4. Generate new locations

     In each situation it is assumed that in the absence of predator, flying squirrel glides and searches efficiently throughout the forest for its favorite’s food, while presence of predator makes it cautious and is forced to use small random walk to search a nearby hiding location [15].

3.1.5. Aerodynamics of gliding

    Gliding mechanism of flying squirrels is described by equilibrium glide in which sum of lift and drag force produces a resultant force whose magnitude is equal and opposite to the direction of flying squirrel’s weight.

3.1.6. Seasonal Monitoring Condition

     Seasonal changes significantly affect the foraging activity of flying squirrels. They suffer significant heat loss at low temperatures, as they posses high body temperature and small size which makes foraging cost high as well as risky due to the presence of active predators. Climatic conditions force them to be less active in winters as compared to autumn. Thus movement of flying squirrels is affected by weather changes and inclusion of such behavior may provide a more realistic approach towards optimization [16]. Therefore a seasonal monitoring condition is introduced in SSA which prevents the proposed algorithm from being trapped in local optimal solutions.

3.1.7. Random Relocation at the end of winter season

     The end of winter season makes flying squirrels active due to low foraging cost. The flying squirrels which could not explore the forest for optimal food source in winter and still survived may forage in new directions. The incorporation of this behavior in modeling may enhance the exploration capability of proposed algorithm [17]. It is assumed that, only those squirrels which could not search the hickory nuts food source and still survived will move to different directions in order to find better food source.

3.1.8. Stopping Criterion

     Function tolerance is a commonly used convergence criterion in which a permissible but small threshold value is defined between the last two consecutive results. Sometimes maximum execution time is also used as stopping criterion. In the present study maximum number of iterations is considered as stopping criterion.

3.2. Flow Chart of SSA

Fig 3: Flowchart of SSA

4. Numerical Methods of SSA

      The individuals update their positions by gliding to the hickory trees or acorn trees [18]. The specific updating formulas are shown as Formulas respectively and the individual randomly selected from dg is the gliding distance which is given by,

5. Applications of SSA

  • App Management [19]
  • Induction motor
  • Blower and water pumps [20]
  • Printer machine
  • Vector Applications
  • Industrial Applications
Fig 4: Applications of SSA

6. Advantages of SSA

  • SSA provides more accurate solutions with high convergence rate as compared to other existing optimizers.
  • They give maximum power output and operating power factor [21].
  • In squirrel cage induction motors the rotor is simplest and most rugged in construction.
  • Cylindrical laminated core rotor with heavy bars or copper or aluminium or alloys are used for conductors [22].
  • Frequent maintenance is required due to presence of brushes.
  • The development is due to advances in electric machine theory in conjunction with rapid developments in and ever decreasing costs of micro and power electronics [23].


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