GRAVITATIONAL SEARCH ALGORITHM IN OPTIMIZATION TECHNIQUES

Presented by P.Anbukkarasi

M.Phil Mathematics

OVERVIEW

Introduction

Definitions

Algorithm

Applications

conclusion

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.

• 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

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.

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.

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

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.

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.

Mass

F = maThe force of attraction

between all masses in the universe, especially the attraction of the earth’s mass for bodies near its surface

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) = (xi1(t),xi

2(t),. . . ,xid(t), . . . ,xi

n(t)), (1)

i = 1,2,. . . .,N,

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:

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

Step 3.5 Calculate the inertial mass as following:

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

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

Noyes

Flow chart

Applications

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

conclusion

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