Workshop on Intelligent System and Applications (ISA’17), Faculty of Computers and Informatics, Benha University.

1. A Hybrid Sine Cosine Optimization Algorithm
for Solving Global Optimization Problems
R. M. Rizk-Allah
Basic Engineering sciences Dept. – Menoufia University- Egypt
Scientific Research Group in Egypt (SRGE) May, 13, 2017

2.  SCA is a new efficient population-based optimization
algorithm proposed in 2016.
 SCA still may face the problem of getting trapped in
local optima regarding insufficient diversity of the agents
and their unbalanced exploration/exploitation trends in
some cases.
 To avoid these issues, SCA is integrated with a local
search techinque to solve the global optimization
problems.

3. A nonlinear programming problem is stated as follows:
1 2Min ( ) ( , ,..., )
Subject to: ,
nf f x x x 

x
x
| ( ) 0, 1,..., , ( ) 0, 1,...., ,
, 1,....,
j j
i i i
g j q h j q m
LB x UB i n
      
   
    
x x x
Global minimum : For the function : , ,n
f R     ¡
the value is called a global minimum if
and only if
*
: ( ) ( )f f  x x x
* *
( )f f x@

4. SCA is population-based optimization algorithm that is established
based on the mathematical sine and cosine functions
Sine and cosine with range of [-2,2]

6. •Evaluation which is accomplished using the objective
function
• Solutions update
The main stages of SCA
, 1 2 3 , , 4
, 1
, 1 2 3 , , 4
sin( ) | | 0.5
cos( ) | | 0.5
1,2,...,
i t i t i t
i t
i t i t i t
r r r P r
r r r P r
i PS

    
 
    

x x
x
x x
1
a t
r a
T

 

7. Yes
Initialize the location for search agents
Evaluate the search agents by using the objective function
Update the location of the obtained best solution so far
(destination)
Update the parameters r1, r2 , r3 and r4
Update the position of search agents
Records the best solution as the global optimum
End
Start
Is the iteration satisfied?
No

8. r1 dictates the next position regions.
r2 defines how far the movement should be towards or outwards
the destination.
r3 gives random weights for destination in order to stochastically
emphasize (r3 > 1) or deemphasize (r3 < 1) the
effect of desalination in defining the distance.
Finally, the parameter r4 equally switches between
the sine and cosine components .

9. The advantages and disadvantages of SCA
this algorithm might not be able to outperform other
algorithms on specific set of problems.
Existence of four random parameters
It is very simple from the mathematical and algorithmic
standpoints
it provides in many instances highly accurate results

10. The search procedure looks for the best solution “near”
another solution by repeatedly making small changes to a
starting solution until no further improved solutions can
be found.
(1 )
( ) (1 )
t T
t R r

  
( ). , ( 1, 2,.., )x x t e i nt i   

11. In section some test functions are collected and reported in Table 1

12. F1 F2
Algorithm SCA Modified SCA SCA Modified SCA
Best 6.664932E-014 2.078186E-085 1.7105E-011 7.18184E-044
Worst 8.457374E-009 9.425757E-071 1.02209E-009 7.05777E-025
Mean 9.143351E-010 3.142157E-071 3.18636E-010 7.49224E-026
Std. dev. 2.13809415E-009 5.441757E-071 2.405910E-010 2.21859E-025

13. Pareto front of the best compromise solutions
50 100 150 200
10
-50
10
0
Convergence curve
Iteration
Bestflame(score)obtainedsofar
SCA
QSCA
F1
50 100 150 200
10
-40
10
-20
10
0
Convergence curve
Iteration
Bestflame(score)obtainedsofar
SCA
QSCA
F2

14. The obtained result shows that the SCA based local serach is
superior to the SCA. Additionally, it can escape the local minima
and converge to the global minima efficiently.
Conclusion
For future works, it is possible to extent it to solve more
complex problems.