Gravitational search algorithm is a heuristic optimization algorithm inspired by the law of gravity. It models problem solutions as masses interacting under the laws of gravity, with the best solutions having higher masses. The algorithm initializes a population of random solutions and updates their positions and velocities based on the calculated gravitational force between solutions. Over iterations, solutions move towards better solutions under these forces until an optimal solution is found. The algorithm has been applied to problems like gene regulatory network inference, satellite link optimization, and reactive power dispatch.

1. GRAVITATIONAL SEARCH
ALGORITHM IN OPTIMIZATION
TECHNIQUES
Presented by
P.Anbukkarasi
M.Phil Mathematics

2. OVERVIEW
Introduction
Definitions
Algorithm
Applications
conclusion

3. Introduction
Gravitational search algorithm is a heuristic
optimization algorithm which has been gaining
interest among the scientific community recently.
Gravitational search algorithm (GSA) is a
population search algorithm proposed by Rashedi
et al . In 2009.The GSA based on law of gravity
and mass interactions. The solution in the GSA
population are called agents, these agents
interact with each other through the gravity
force.

4. • The performance of each agent in
the population is measured by its
mass. Each agent considered as
object and all object move towards
other objects with heavier mass
due to the gravity force . The best
solution is the solution with the
heavier mass

5. What is Optimization?
An act process, or methodology of
making something (as a design, system,
or decision) as fully perfect, functional,
or effective as possible ; specifically : the
mathematical procedures (as finding the
maximum of a function) involved in
this.

6. Law of Gravity
Each particle attracts every other
particle and the gravitational force
between two particles is directly
proportional to the product of their
masses and inversely proportional to the
square of the distance between them.

7. The objects masses are obeying the law of
gravity as following
•Above equation represents the Newton law
of gravity, where
• F is a magnitude of the gravitational force
•G is gravitational constant
•M1isthe mass of the first object
•M2 is the mass of the second object
•R is the distance between the two objects
M1, M2

8. Gravitational constant G
• The gravitational constant G at
iteration t is computed as follows.
G(t) =G0e-αt/T
where G0 and α are initialized in
the beginning of the search , and
their values will be reduced during
the search. T is the total number of
iterations.

9. Law of motion
The current velocity of any mass
is equal to the sum of the fraction of
its previous velocity and the
variation in the velocity. Variation
in the velocity or acceleration of any
mass is equal to the force acted on
the system divided by the mass of
inertia.

10. Mass
F = ma
The force of attraction
between all masses in the
universe, especially the attraction
of the earth’s mass for bodies near
its surface

11. Algorithm
The main steps of the GSA can be summarized
 Step 1. The algorithm starts by setting the values
of gravitational constant G0,α,ε and the iteration
counter t.
 Step 2. The initial population is generated
randomly and consists of N agents, the position
of each agent is defined by :
Xi(t) = (xi
1
(t),xi
2
(t),. . . ,xi
d
(t), . . . ,xi
n
(t)), (1)
i = 1,2,. . . .,N,

12.  Step 3. The following steps are repeated until
termination criteria satisfied
 Step 3.1. All agents in the population are evaluated
and the best, worst agents are assigned.
 Step 3.2 The gravitational constant is updated as
shown in equation 1
 Step 3.3. When agent j acts on agent i with force, at a
Specific time (t) the force is calculated as following:

13. Where Maj is the active gravitational mass of
agent j, mpi is the passive gravitational mass
of agent i, G(t) is gravitational constant at
time t
 Step 3.4 . At iteration t ,calculate the total
force acting on agent i as following
Where k best is the set of first k agents with
the best fitness value and biggest mass

14. Step 3.5 Calculate the inertial mass as
following:

15. Step 3.6 The acceleration of agent i is
calculated as following
Step 3.7. The velocity and the position of
agent i are computed as above equation
Step3.8 The iteration counter is increased
until termination criteria satisfied
Step 4 The best optimal solution is produced

16. Generate initial population
Evaluate the fitness for each agent
update the G, best and worst of the population
Calculate M and a for each agent
Update velocity and position
Meeting end of
criterion?
Return the best solution
No
yes
Flow chart

17. Applications
o The Inference of predictor set in
gene regulatory networks Using GSA
o Communication Satellite link
Budget Optimization using
Gravitational search Algorithm
o Gravitational search algorithm
based approach for reactive power
dispatch

18. conclusion
This presentation discussed about
concept of GSA , some definitions,
algorithm of GSA and their flow
chart and applications for some
flied