## Algorithm · Standard gamma function value ?

Algorithm
:

1. Objective min or max f(x),
x=(x1,x2,x3,x4,x5…………………..xd.)t

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2. Initialize a population of n
flowers/pollen gametes with random solutions

3. Find the best solution in the
initial population

4. Define a switch probability p
? 0, 1

5. while (t < MaxGeneration) 6. for i = 1 to n ( all n flowers in the population) 7. if rand < p 8. Draw a (d-dimensional) step vector L which obeys a L´evy distribution 9. Global pollination via Xit+1= Xit +   L(?)? (Xit –g*) 10. else 11. Draw ? from a uniform distribution in 0,1 12. Local pollination via 13. end if 14. Evaluate new solutions 15. if new solutions are better, update them in the population 16. end for 17. Find the current best solution 18. end while   Parameters settings :       the parameter which are used in this paper ·         Population size : 10 to 25. ·         Probability switch :0.8 ·         Maximum interation (maxite):2000 ·         Standard gamma function value  ? =1.5 ·         The local random walk value (?) =(0,1) ·         The switch probability  value (p)=(0,1)  Operating system : ·         Processor :intel (R) core (TM) i3-2350M CPU @2.30GHz ·         RAM: 4GB ·         System type :32 bit operating system ·         Windows  edition : Windows 7   Result & performance analysis :   The objectives are to minimize the flowrate  F of experimental process control setup  by choosing optimal design variables: the Anemometer flowsensor output x(1), pipe diameter  x(2) , liquid conductivity x(3) and the liquid viscosity x(4).This objective  design problem can be written as : ObjectF=(0.350099*10^-3)*(x(1)^14.20)*(x(2)^-4.37947)*(x(3)^-12.94)*(x(4)^2.940      (3)                        It is worth  to pointing out the minimum value of the objective function . In this paper FPA has to be extended in combination with constraint handling techniques to deal with mixed integer problems efficiently under the simplest branch-and -bound method utilized here.In order to see how the proposed FPA perform for the real-world design problems,the same problem has also been solved using other available multiobjective algorithms. By using FPA to form an approximate to the true Pareto front after 2000 iterations  where the  error  is minimum i.e 5.0879e-06  ,   shown in Fig. 7 &  respective design parameter shown in table 1.Discussion & conclusion :Single objective optimization in engineering and industry is often very challenging to solve requied a  sophisticated techniques to tackle thatswhy a metaheuristic approaches have shown promise and popularity in recent years.In the present work, a new algorithm, called Flower pollination algorithm, has been formulated for liquid flow process control where minimum Flowrate is a single objective function optimized by mimicking the pollination process of Flowering Plants in a very simple way. The present experiment & design shown that FPA is very effective convergence rate .the standard FPA is a simple & flexible as because it has only one key parameter p together with a scaling factor ? .The following conclusions can be drawn from this work:(i) The MATLAB codes discussed here can be extended to solve any type of optimization  problem of any size.(ii) The codes discussed here are generalized for solving any optimization problem with boundary values  of the constrain.(iii) for the change of  population size & probability switch factor  the minimum value of the objective function & corresponding value  of the variables  x(1),x(2),x(3)& x(4) are same .(iv) elapsed time for executing the code is depends upon the computer configuration . In the future work it is worth pointing out that mathematical analysis is highly needed to gain insight into the true working mechanisms of the metaheuristic algorithms

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