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Behavior of Squirrel Search Algorithm (SSA) using Meta-heuristics method – Transpire Online
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September 18, 2019
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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
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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
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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].
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Behavior of Squirrel Search Algorithm (SSA) using Meta-heuristics method – Transpire Online
Fig 2: Squirrel Search Algorithm
3.1. Steps for Squirrel Search Algorithm
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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].
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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
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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,
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Behavior of Squirrel Search Algorithm (SSA) using Meta-heuristics method – Transpire Online
5. Applications of SSA
App Management [19]
Induction motor
Blower and water pumps [20]
Printer machine
Vector Applications
Industrial Applications
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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].
Reference
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algorithm with restricted competition selection for multimodal function
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Behavior of Squirrel Search Algorithm (SSA) using Meta-heuristics method – Transpire Online
[3] Enokizono, M. (1988). Measurement and analysis of magnetic field of inverterdriven three-phase squirrel-cage induction motor. Electrical Engineering in Japan,
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for electric motor design. IEEE Transactions on Magnetics, 34(5), pp.2861-2864.
[19] Chakraborty, C. and Hori, Y. (2003). Fast efficiency optimization techniques for
the indirect vector-controlled induction motor drives. IEEE Transactions on
Industry Applications, 39(4), pp.1070-1076.
[20] Zhao, W., Wang, L. and Zhang, Z. (2019). Atom search optimization and its
application to solve a hydrogeologic parameter estimation problem. KnowledgeBased Systems, 163, pp.283-304.
[21] Singh, B., Nandan Singh, B. and Saxena, R. (1993). Experience in the design
optimization of a voltage source inverter fed squirrel cage induction motor. Electric
Power Systems Research, 26(2), pp.155-161.
[22] N, D. and Kaur, D. (2015). Selective Harmonic Elimination PWM Technique
Implementation for a Multilevel Converter. International Journal of Engineering
Research, 4(6), pp.303-308. [23] Chaudhry, R., Tapaswi, S. and Kumar, N. (2019). A
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pp.215-226.
Tags: Aerodynamics of gliding, AI, applications, Artificial Intelligence, Behavior of
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heuristics method, computer science, crossover, Declaration and Random
Selection, engineering, Fitness Evaluation, Inspiration of Squirrel Search Algorithm,
Meta-heuristics method, phd, Random Relocation at the end of winter season,
research, Seasonal Monitoring Condition, Sorting, Squirrel Search Algorithm, SSA,
Steps for Squirrel Search Algorithm
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