A hybrid sine cosine optimization algorithm for solving global optimization problems

A hybrid sine cosine optimization algorithm for solving global optimization problems

• 1.
  A Hybrid SineCosine 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 isa 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 programmingproblem 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-basedoptimization algorithm that is established based on the mathematical sine and cosine functions Sine and cosine with range of [-2,2]
• 6.
  •Evaluation which isaccomplished 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 locationfor 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 thenext 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 anddisadvantages 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 procedurelooks 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 sometest functions are collected and reported in Table 1
• 12.
  F1 F2 Algorithm SCAModified 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 ofthe 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 resultshows 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.