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Salp Swarm Algorithm
Represented by: Aya El-Sayed
Prof. Dr / Mohamed Nasef
Outline
 Salp Swarm Algorithm (SSA) (History and main idea)
 Nature behavior of Salp.
 The main characteristic of the Salp swarm.
 Salp Swarm Algorithm (SSA).
 Multi-objective Salp Swarm algorithm (MSSA).
 References.
Salp Swarm Algorithm (SSA)
(History and main idea)
 Salp Swarm Algorithm (SSA) is a recently
swam intelligence algorithm developed in
2017 by Mirjalili at. El.
 SSA mimicking the behavior of Salp swarms
and their social interaction.
Nature behavior of salp.
 It is a kind of Salpidae that have a
transparent barrel shaped body and similar
tissues like jellyfishes structure.
 They are living in deep oceans and moving
by water forces to find their food which
organized as swarms called Salp chains.
The main characteristic of the salp swarm.
 The salp chains mathematically divided into
two groups: head salp is a leader and others
are followers.
 Till now, the behavior of salp swarm is not
well expressed, hence, the researchers
consider the behavior of it has been done to
enhance their movement in seeking for
food.
Salp swarm algorithm (SSA)
 The position of salps is defined in an d-
dimensional search space where d is the
number of variables of a given problem.
 The food source F is the swarm's target.
 The leader updated its position according
to the Equation 3.1
Where x1
j is the position of leader in j-th
dimension, ubj and lbj are the upper and lower
boundary at j-th dimension, Fj is the food
source position. C2 and C3 = [0,1]
Salp swarm algorithm (SSA) (Cont.)
 The coefficient c1 plays an important role in SSA
which balances between the exploration and
exploitation.
 The exploration concentrates on finding better
solution by exploring a search space properly,
while exploitation concentrates on exploiting the
data in the local area.
 c1 is decreased over iterations and can be
computed as follows:
Where l is the current iteration and L is the maximum
number of iterations.
Salp swarm algorithm (SSA) (Cont.)
 The parameters c2 and c3 are random numbers
generated within the interval [0,1].
 c3 is responsible for indicating whether the next
position of current leader salp should to be
toward +∞ or - ∞.
 The followers update their position according to
Newton's law of motion using Equation 3.3
Salp swarm algorithm (SSA) (Cont.)
 Since the time is considered as iterations and v0 =
0, Equation 3.3 can be reformulated as in Equation
3.4
Salp swarm algorithm (SSA) (Cont.)
The main steps of the salp algorithm can be summarized as follow:-
Salp swarm algorithm (SSA) (Cont.)
The main steps of the salp algorithm can be summarized as follow:-
Pseudo code of the SSA algorithm
Benchmark function
Assume that indivduals n=2 and initial iteration l=0 so the fitness F=the best search agent
which is source of food Can be calculated from:
Min F(x)= X1²+X2² while x=[0,1] which still within the range [-100,100]
Consider Salp population Xi (i=1,2,.,.,5) and Maximum number of iterations L=2
So the best solution is F=.0139
i X1 X2 F(x)
1 .3 1 1.09
2 .25 .5 .3125
3 .2 .28 .1025
4 .15 .125 .038125
5 .1 .0625 .0139
Calculate C1 from eq 3.2 as the following:
l=1 and L=2 so
C1 =.037
C2=.4
Then to determine the position of the leader use eq 3.1
By solving the equation
X1j=.0139+.037((100-(-100)).4-100)=-0.7261
X1j=.0139-.037((100-(-100)).4-100)= 0.7539
Then to determine the position of the followers use eq 3.4
The 2ed follower
X2j=1/2(.25-.7261)=-0.23805 X2j=1/2(.5+.7539)= 0.62695
The 3rd follower
X3j=1/2(.2-.238)=-0.019025 X3j=1/2(.28+.627)= 0.4535
The 4th Follower
X4j=1/2(.15-.01903)= 0.06549 X4j=1/2(.125+.4535)= 0.5785
The 5th Follower
X5j=1/2(.1+.06549)=0.08274 X5j=1/2(.0625+.5785)= 0.32048
So the best solution is F=.1096
i X1 X2 F(X)
1 -0.7261 .7539 1.09
2 -0.23805 0.62695 .449
3 -0.019025 0.4535 .206
4 0.06549 0.5785 .3389
5 0.08274 0.32048 .10955
Calculate C1 from eq 3.2 where l=2 and L=2
C1=2.2507*10^(-7) C2=.41
By applying eq 3.1 to determine the position of the leader
X1j= 0.10959 X1j=0.1096 F(X)=0.024
By applying eq 3.4 to determine the position of the followers
The 2ed follower
X2j= -0.0642 X2j=0.7366 F(X)=0.5466
The 3rd follower
X3j= -0.04163 X3j=0.595 F(X)=0.3558
The 4th follower
X4j=0.0119 X4j=0.5867 F(X)=0.3444
The 5th follower
X5j=0.0473 X5j=0.4536 F(X)=0.2028
So the best solution for iteration 2 F= 0.024
Disadvantages of Salp swarm
algorithm.
 SSA is not able to solve multi-objective problems mainly due
to the following two reasons:
 SSA only saves one solution as the best solution so it cannot
store multiple solutions as the best solutions for a multi-
objective problem.
 SSA updates the food source with the best solution obtained
so far in each iteration, but there is no single best solution for
multi-objective problems.
References
S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H.
Faris, S. M. Mirjalili. Salp swarm algorithm: a bio-inspired
optimizer for engineering design problems. Advances
in Engineering Software, 114, 163-191, 2017.

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Salp_Swarm_Algorithm.pptx

  • 1. Salp Swarm Algorithm Represented by: Aya El-Sayed Prof. Dr / Mohamed Nasef
  • 2. Outline  Salp Swarm Algorithm (SSA) (History and main idea)  Nature behavior of Salp.  The main characteristic of the Salp swarm.  Salp Swarm Algorithm (SSA).  Multi-objective Salp Swarm algorithm (MSSA).  References.
  • 3. Salp Swarm Algorithm (SSA) (History and main idea)  Salp Swarm Algorithm (SSA) is a recently swam intelligence algorithm developed in 2017 by Mirjalili at. El.  SSA mimicking the behavior of Salp swarms and their social interaction.
  • 4. Nature behavior of salp.  It is a kind of Salpidae that have a transparent barrel shaped body and similar tissues like jellyfishes structure.  They are living in deep oceans and moving by water forces to find their food which organized as swarms called Salp chains.
  • 5. The main characteristic of the salp swarm.  The salp chains mathematically divided into two groups: head salp is a leader and others are followers.  Till now, the behavior of salp swarm is not well expressed, hence, the researchers consider the behavior of it has been done to enhance their movement in seeking for food.
  • 6. Salp swarm algorithm (SSA)  The position of salps is defined in an d- dimensional search space where d is the number of variables of a given problem.  The food source F is the swarm's target.  The leader updated its position according to the Equation 3.1 Where x1 j is the position of leader in j-th dimension, ubj and lbj are the upper and lower boundary at j-th dimension, Fj is the food source position. C2 and C3 = [0,1]
  • 7. Salp swarm algorithm (SSA) (Cont.)  The coefficient c1 plays an important role in SSA which balances between the exploration and exploitation.  The exploration concentrates on finding better solution by exploring a search space properly, while exploitation concentrates on exploiting the data in the local area.  c1 is decreased over iterations and can be computed as follows: Where l is the current iteration and L is the maximum number of iterations.
  • 8. Salp swarm algorithm (SSA) (Cont.)  The parameters c2 and c3 are random numbers generated within the interval [0,1].  c3 is responsible for indicating whether the next position of current leader salp should to be toward +∞ or - ∞.  The followers update their position according to Newton's law of motion using Equation 3.3
  • 9. Salp swarm algorithm (SSA) (Cont.)  Since the time is considered as iterations and v0 = 0, Equation 3.3 can be reformulated as in Equation 3.4
  • 10. Salp swarm algorithm (SSA) (Cont.) The main steps of the salp algorithm can be summarized as follow:-
  • 11. Salp swarm algorithm (SSA) (Cont.) The main steps of the salp algorithm can be summarized as follow:-
  • 12. Pseudo code of the SSA algorithm
  • 13. Benchmark function Assume that indivduals n=2 and initial iteration l=0 so the fitness F=the best search agent which is source of food Can be calculated from: Min F(x)= X1²+X2² while x=[0,1] which still within the range [-100,100] Consider Salp population Xi (i=1,2,.,.,5) and Maximum number of iterations L=2 So the best solution is F=.0139 i X1 X2 F(x) 1 .3 1 1.09 2 .25 .5 .3125 3 .2 .28 .1025 4 .15 .125 .038125 5 .1 .0625 .0139
  • 14. Calculate C1 from eq 3.2 as the following: l=1 and L=2 so C1 =.037 C2=.4 Then to determine the position of the leader use eq 3.1 By solving the equation X1j=.0139+.037((100-(-100)).4-100)=-0.7261 X1j=.0139-.037((100-(-100)).4-100)= 0.7539 Then to determine the position of the followers use eq 3.4
  • 15. The 2ed follower X2j=1/2(.25-.7261)=-0.23805 X2j=1/2(.5+.7539)= 0.62695 The 3rd follower X3j=1/2(.2-.238)=-0.019025 X3j=1/2(.28+.627)= 0.4535 The 4th Follower X4j=1/2(.15-.01903)= 0.06549 X4j=1/2(.125+.4535)= 0.5785 The 5th Follower X5j=1/2(.1+.06549)=0.08274 X5j=1/2(.0625+.5785)= 0.32048 So the best solution is F=.1096 i X1 X2 F(X) 1 -0.7261 .7539 1.09 2 -0.23805 0.62695 .449 3 -0.019025 0.4535 .206 4 0.06549 0.5785 .3389 5 0.08274 0.32048 .10955
  • 16. Calculate C1 from eq 3.2 where l=2 and L=2 C1=2.2507*10^(-7) C2=.41 By applying eq 3.1 to determine the position of the leader X1j= 0.10959 X1j=0.1096 F(X)=0.024 By applying eq 3.4 to determine the position of the followers The 2ed follower X2j= -0.0642 X2j=0.7366 F(X)=0.5466 The 3rd follower X3j= -0.04163 X3j=0.595 F(X)=0.3558 The 4th follower X4j=0.0119 X4j=0.5867 F(X)=0.3444 The 5th follower X5j=0.0473 X5j=0.4536 F(X)=0.2028 So the best solution for iteration 2 F= 0.024
  • 17. Disadvantages of Salp swarm algorithm.  SSA is not able to solve multi-objective problems mainly due to the following two reasons:  SSA only saves one solution as the best solution so it cannot store multiple solutions as the best solutions for a multi- objective problem.  SSA updates the food source with the best solution obtained so far in each iteration, but there is no single best solution for multi-objective problems.
  • 18. References S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, S. M. Mirjalili. Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163-191, 2017.