gravitational search algorithm

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LOGO

Scientific Research Group in Egypt (SRGE)

Gravitational search algorithm

(GSA)Dr. Ahmed Fouad Ali

Suez Canal University,

Dept. of Computer Science, Faculty of Computers and informatics

Member of the Scientific Research Group in Egypt .

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LOGO Scientific Research Group in Egypt

www.egyptscience.net

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LOGO Outline

1. Gravitational search algorithm (History and main idea)

3. The gravity low

7. References

2. Gravitational constant G

6. Gravitational search algorithm

4. Acceleration of agents

5. Agent velocity and positions

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LOGO Gravitational search algorithm (History and main idea)

•Gravitational search algorithm (GSA) is apopulation search algorithm proposed byRashedi et al. in 2009.

• The GSA is based on the low of gravityand mass interactions.

•The solutions in the GSA population arecalled agents, these agents interact witheach other through the gravity force.

•The performance of each agent in thepopulation is measured by its mass.

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LOGO Gravitational search algorithm (History and main idea)

•Each agent is considered as object and allobjects move towards other objects withheavier mass due to the gravity force.

•This step represents a global movements(exploration step) of the object, while theagent with a heavy mass moves slowly,which represents the exploitation step ofthe algorithm.

•The best solution is the solution with theheavier mass.

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LOGO Gravitational constant G

•The gravitational constant G at iterationt is computed as follows.

•Where G0 and 𝛼 are initialized in thebeginning of the search, and theirvalues will be reduced during thesearch. T is the total number ofiterations.

(1)

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LOGO The gravity low

•The objects masses are obeying the lowof gravity as following

•Equation 2 represents the Newton lawof gravity, where• F is a magnitude of the gravitationalforce• G is gravitational constant•M1 is the mass of the first object•M2 is the mass of the second object•R is the distance between the twoobjects M1,M2.

(2)

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LOGO The gravity low (Cont.)

•According to the Newton's second low,when a force F is applied to an object,the object moves with acceleration adepending on the applied force and theobject mass M as shown in Equation 3.

(3)

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LOGO Acceleration of agents

There are three kind of masses

Active gravitational mass MaPassive gravitational mass MpInertial mass Mi.

The gravitational force Fij that actson mass i by mass j is defined by:

(4)

Where Maj, Mpi are the active andpassive masses of objects j, i,respectively.

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LOGO Acceleration of agents (Cont.)

•The acceleration of object (agent) i iscomputed as follows.

(5)

Where Mii is inertia mass of agent i.

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LOGO Agent velocity and positions

•During the search, the agents updatetheir velocities and positions as shown inEquations 6, 7, respectively.

(6)

(7)

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LOGO Gravitational search algorithm

The main steps of the GSA can besummarized as follows.

Step 1. The algorithm starts bysetting the initial values ofgravitational constant G0, 𝛼, 𝜀 and theiteration counter t.

Step 2. The initial population isgenerated randomly and consists of Nagents, the position of each agent isdefined by:

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LOGO Gravitational search algorithm (Cont.)

Step 3. The following steps arerepeated until termination criteriasatisfied

Step 3.1. All agents in the populationare evaluated and the best, worst agentsare assigned.

Step 3.2. The gravitational constant isupdated as shown in Equation 1

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LOGO Gravitational search algorithm (Cont.)

Step 3.3. When agent j acts on agent i with force, at aspecific 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

(8)

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LOGO Gravitational search algorithm (Cont.)

Step 3.4. At iteration t, calculate the total force acting onagent i as following:

Where Kbest is the set of first K agents with the best fitnessvalue and biggest mass

Step 3.5. Calculate the inertial mass as following:

(9)

(10)

(11)

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LOGO Gravitational search algorithm (Cont.)

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 shown in Equations 6, 7

Step 3.8. The iteration counter is increased until termination criteria satisfied

Step 4. The best optimal solution is produced.

(12)

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LOGO Gravitational search algorithm (Cont.)

Parameters

initialization

Initial population

Solution s evaluation

Solutions Update

Produce the best solution

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LOGO References

E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, GSA: “A Gravitational Search Algorithm ”, Information Sciences, vol. 179, no. 13, pp.2232-2248, 2009.

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LOGO

Thank you

http://www.egyptscience.net

Ahmed_fouad@ci.suez.edu.eg