Pattern Synthesis Using Real Coded Genetic Algorithm and Accelerated Particle Swarm Optimization

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1 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Patter Sythesis Usig Real Coded Geetic Algorithm ad Accelerated Particle Swarm Optimizatio P A Suy Dayal Research Scholar, Dept. of ECE, Ceturio Uiversity of Techology ad Maagemet, Paralakhemudi, Odisha, Idia. G S N Raju Hoorary Distiguished Professor, Dept. of ECE, AU College of Egieerig (A), Adhra Uiversity, Idia. S Mishra Professor ad Head of the Dept., Dept. of ECE, Ceturio Uiversity of Tech. & Maagemet, Paralakhemudi, Odisha, Idia. Abstract A atea patter sythesis is oe of the most importat problems to be addressed i all commuicatio ad radar applicatios. Real Coded Geetic Algorithm ad Accelerated Particle Swarm Optimizatio are useful to solve such problems. I the preset work, these algorithms are applied to optimize the sum patters. They are optimized i terms of side lobe levels ad mai beamwidth. Amplitude distributios are umerically computed usig Real Coded Geetic Algorithm ad Accelerated Particle Swarm Optimizatio algorithms. The resultat distributios are itroduced for the arrays of discrete radiators. Small ad large arrays are desiged. The patters are preseted i u domai ad it has bee possible to cotrol side lobe level as per the specificatios. Keywords: Liear array, Real Coded Geetic Algorithm, Accelerated Particle Swarm Optimizatio, Patter sythesis. Itroductio The radiatio patter of a sigle elemet is fixed ad it is costraied by gai. I may applicatios it is ecessary to desig ateas with very high gais to meet the demads of log distace commuicatios, ad moder radars. Elargig the dimesios of sigle elemets ofte leads to high gai characteristics. Aother way is to use array ateas. I most of the cases, the elemets are idetical i the array. To provide very high gai patters, it is ecessary that the fields from the elemets of the array are costructively added i the desired directios ad destructively cacelled each other i the remaiig space [1]. I this paper, to cotrol the overall patter, for liear geometrical cofiguratio with half wavelegth relative displacemet betwee the elemets, the excitatio amplitudes of idividual elemets ad with o additioal phase are computed. It is ofte required that the patter should exhibit a desired distributio, arrow beamwidth ad low side lobes ad decayig mior lobes. I this paper, the patters are realized with arrow beamwidth ad low side lobe levels with small ull-to-ull beamwidth. Classical ad umerical methods of array sythesis are well developed ad reported i literature [1-9]. Some of the methods like Biomial, Dolph-Tschebyscheff, ad Taylor lie-source are traditioal techiques. Optimizig atea arrays to produce desired far field is topic of cosiderable iterest i aalogous. It ofte ivolves may parameters, ad these parameters may be discrete. A example is optimizig the low side lobes of large array ateas [10]. The Geetic Algorithm is a optimizatio ad search techique based o the priciples of geetics ad atural selectio. It allows a populatio composed of may idividuals to evolve uder specified selectio rules to a state that maximizes the cost fuctio. The method was reported by Joh Hollad i 1975 [11] ad popularized by his studet David Goldberg i 1989 [12]. Sice the, may versios of evolutioary programmig have bee tried with varyig degrees of success. Some of the advatages of a Geetic Algorithm icludes that it optimizes with cotiuous or discrete variables, does t require derivative iformatio, simultaeously searches from a wide samplig of the cost surface, well suited for parallel computers, optimizes variables with extremely complex cost surfaces, provides a list of optimum variables, ot just a sigle solutio, may ecode the variables so that the optimizatio is doe with the ecoded variables, ad works with umerically geerated data, experimetal data or aalytical fuctios. These advatages are may ad produce useful results better tha those of traditioal methods. The particle swarm optimizatio was formulated by Eberhart ad Keedy i 1995 [13]. The thought process behid the algorithm was ispired by the social behaviour of aimals, such as bird flockig or fish schoolig. Particle swarm optimizatio is similar to the cotiuous Geetic Algorithm i that it begis with a radom populatio matrix. Ulike the Geetic Algorithm, particle swarm optimizatio has o evolutio operators such as crossover ad mutatio. Particle swarm optimizatio is a recetly iveted high performace optimizer that possesses several highly desirable attributes, icludig the fact that the basic algorithm is very easy to 3753

2 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. uderstad ad implemet. It is similar i some ways to Geetic Algorithms ad evolutioary algorithms, but requires less computatioal time ad geerally fewer lies of code. I this paper, the liear arrays of isotropic elemets with uiform spacig betwee them are cosidered. For achievig the desired level of side lobe level ad miimum desired value of first ull beamwidth, the idividual elemet amplitude excitatio has bee computed usig the RCGA ad APSO algorithms, takig sidelobe level ito accout. Desig of Sum Patters Sythesis of array ateas is very importat to get the desired patter ad how to achieve low side lobe i the coditio of a fixed mai beamwidth has bee cosidered sice a log period of time [14-16]. The liear array is oe of the commoly used arrays i may applicatios owig to its simplicity. The represetatio of such geometry is as show i below Figure 1. Figure 1: Geometry Cofiguratio of Liear Array with uiform spacig d 0.5 Cosiderig a liear array of N isotropic ateas [17], atea elemets are equally spaced at distace d apart from each other alog the x axis. The free space far-field patter E u is give by [18]. N A cosk 0.5d u E u 2 (1) 1 u o Here, k wave umber 2 wave legth agle betwee the lie of observer ad broadside sca agle o A excitatio of the th elemet o either side of the array d spacig betwee the radiatig elemets u si ad uo sio Normalized far-field i db is give by: Eu E u 20log 10 (2) E u max The excitatio amplitudes are take as parameters to be optimized with the objective of achievig reduced sidelobe level. Equatio (1) is used to fid the far field patter iformatio of curret amplitude excitatio A for all the elemets, with elemet spacig d 0.5 with zero additioal phase. The fitess fuctio provides the iterface betwee the physical problem ad the optimizatio algorithm. I the optimizatio process, a attempt is made to reduce the sidelobe level of the radiatio patter while retaiig the gai of the mai beam. The problem of miimizig the maximum SLL i the patter with prescribed beamwidth from a liear half wavelegth spaced array is solved usig the fitess fuctio. The mai objective of this work is to determie a appropriate set of required elemet amplitudes that achieve a reduced sidelobe level. Thus, the fitess fuctio for achievig this objective is formulated as Fitess PSLL o PSLL d 1 u 1, u u (3) 0 Here Eu Obtaied Peak SLL PSLL o max 20log 10 E uo max Desired Peak SLL PSLL d 40dB. Evolutioary Optimizatio Techiques Real Coded Geetic Algorithm (RCGA) Geetic Algorithm is a kid of heuristic search techique, which came ito existece from Darwi s theory of Natural Evolutio. It uses certai methods based o the priciple of atural geetics ad atural selectio to obtai the optimizatio procedures that best satisfies a pre-defied goal. At each geeratio, it maitais a populatio of idividuals where each idividual is a coded form of a possible solutio of the problem at had ad is called chromosome. Each chromosome is evaluated by a fuctio kow as fitess fuctio which is usually the fitess fuctio or the objective fuctio of the correspodig optimizatio problem. A ew populatio is geerated from the preset oe through selectio, crossover ad mutatio operatios. Purpose of selectio is to select more fit idividuals (parets) for crossover ad mutatio. Crossover causes the exchage of geetic materials betwee the parets to form offsprig, whereas mutatio icorporates ew geetic materials i the offsprig. Real Coded Geetic Algorithm (RCGA) uses floatig-poit umber represetatio for the real variables. I floatig-poit represetatio, each chromosomes or idividual vector is coded as a vector of floatig-poit umbers of the same legth which is same as the solutio vector. Sice Real Coded Geetic Algorithm uses floatig poit umbers, there is o eed of biary ecodig ad decodig. It takes less memory space ad faster tha Biary Geetic Algorithm. Itroductory material o Real Coded Geetic Algorithm (RCGA) is reported by Michalewicz [19] ad applicatios of geetic algorithms i the field of electromagetic are discussed i [20-24]. Some of the advatages of Real Coded Geetic Algorithm over other traditioal search techiques are by optimizig complex discrete parameters, does t require derivative iformatio, simultaeously searches from a wide samplig of cost surface, works with large umber of variables, well suited for parallel computers, optimizes variables with extremely complex cost surfaces, ad works with umerically geerated data or experimetal data. 3754

3 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Accelerated Particle Swarm Optimizatio (APSO) The particle swarm optimizatio has bee show to be effective i optimizig difficult multidimesioal discotiuous problems [25]. Recetly, this techique has bee successfully applied to atea desig [26]. Particle swarm optimizatio is based o the movemet ad itelligece of swarms, has bee show i certai istaces to outperform like Geetic Algorithms [27 & 28]. Accelerated Particle Swarm Optimizatio (APSO) is oe of the variats of stadard PSO algorithm. APSO was developed by Xi She Yag i 2008 [29]. The stadard PSO uses both the idividual persoal best ad the curret global best but APSO uses global best oly. The p is used probably to icrease the best diversity i the quality solutios ad this diversity ca be simulated usig some radomess. Hece, there is o compellig reaso for usig the idividual persoal best. A simplified versio that could accelerate the covergece of the algorithm is to use oly the global best. The other advatage of usig this algorithm is to reduce the radomess as the umbers of iteratios proceed. The APSO starts from iitializig a swarm of particles with radom positios ad velocities. The fitess fuctio of each particle i the swarm is evaluated ad the g value is calculated. Later, actual best positio is updated for each ad every particle. This process is repeated for each ad every particle i the swarm util the optimum g value is obtaied. Some of the advatages of best APSO over other traditioal optimizatio techiques ad GA are to use objective fuctio iformatio to guide the search i the problem space, it has the flexibility to cotrol the balace betwee the global ad local exploratio of the search space, ad it has implicit parallelism. Accelerated Particle Swarm Optimizatio is well suited for a broad rage of problems ecoutered i electromagetic. APSO is cosiderably more efficiet, ad provides much faster covergece tha radom searches. Results Real Coded Geetic Algorithm ad Accelerated Particle Swarm Optimizatio are applied to evaluate amplitude distributio required to maitai sum patters with sidelobe level at-40db. The patters are umerically computed for differet arrays cotaiig 20, 40, 60, 80, ad upto 100 elemets. The resultat amplitude distributio is foud to be a taper o either side. As the umber of elemets icreased i the array, the Null to Null Beamwidth is foud to vary. The results are preseted i Tables. 1-5 ad Figs Null to Null Beamwidth, ad First Sidelobe Level are preseted i Tables Table 1: Optimized elemet amplitude weights for N=20 Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 1 & & & & & & & & & & Table 2: Optimized elemet amplitude weights for N=40 Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 1 & & & & & & & & & & & & & & & & & & & & Table 3: Optimized elemet amplitude weights for N=60 Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 1 & & & & & & & & & & & & & & & & & & & & & &

4 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios & & & & & & Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 29 & & Table 4: Optimized elemet amplitude weights for N=80 Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 1 & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & Table 5: Optimized elemet amplitude weights for N=100 Elemet A Real Coded A Accelerated Particle Number Geetic Algorithm Swarm Optimizatio 1 & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &

5 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Figure 2: Elemet amplitude weights obtaied by RCGA ad APSO method for N=20 Figure 5: Optimized Sum Patter obtaied by RCGA ad APSO method for N=40 Figure 3: Optimized Sum Patter obtaied by RCGA ad APSO method for N=20 Figure 6: Elemet amplitude weights obtaied by RCGA ad APSO method for N=60 Figure 4: Elemet amplitude weights obtaied by RCGA ad APSO method for N=40 Figure 7: Optimized Sum Patter obtaied by RCGA ad APSO method for N=

6 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Figure 8: Elemet amplitude weights obtaied by RCGA ad APSO method for N=80 Figure 11: Optimized Sum Patter obtaied by RCGA ad APSO method for N=100 Table 6: First Null Beamwidth for Optimized Sum Patter N Number of Elemets FNBW deg FNBW deg Real Coded Geetic Algorithm Accelerated Particle Swarm Optimizatio Table 7: Half Power Beamwidth for Optimized Sum Patter Figure 9: Optimized Sum Patter obtaied by RCGA ad APSO method for N=80 N Number of Elemets First SLL db First SLL db Real Coded Geetic Algorithm Accelerated Particle Swarm Optimizatio Figure 10: Elemet amplitude weights obtaied by RCGA ad APSO method for N=100 Coclusio From the results, it is clear that the amplitude distributio obtaied for eve umber of elemets is foud to exhibit equal excitatio level for the cetred two elemets. I fact, it is symmetric. That is, the first elemet ad last elemet is foud to have equal excitatio levels ad similarly others. Itroducig the amplitude distributio so obtaied i the evaluatio of radiatio patter, it is foud to have sidelobe level at about-40db which is specified. It is also evidet that the Accelerated Particle Swarm Optimizatio techique is foud to be better tha Real Coded Geetic Algorithm i terms of patter characteristics. 3758

7 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Refereces [1] G. S. N. Raju, Ateas ad wave propagatio, 3 rd ed., Pearso Educatio, 2005 [2] R. E. Colli ad F.J. Zucker, Atea theory, New York: McGraw-Hill, [3] B. D. Stieberg, Priciples of Aperture ad Array System Desig. New York: Joh Wiley ad Sos, [4] Robert S. Elliot, Atea Theory ad Desig, Pretice- Hall of Idia, New Delhi, [5] Y. T. Lo ad S.W. Lee, Atea Hadbooks: Theory, Applicatios, ad Desig, New York, [6] C. A. Balais, Atea Theory: Aalysis ad Desig, 2 d ed. New York: Wiley, [7] W. L. Stutzma ad G.A. Thiele, Atea Theory ad Desig, 2 d ed. New York, Wiley, [8] R. C. Hase, Phased Array Ateas, New York: Wiley, [9] R. J. Mailloux, Phased Array Atea Hadbook, Bosto, Artech House,1994. [10] R. Haupt, Simultaeous ullig i the sum ad differece patters of a moopulse atea, IEEE Tras. Ateas Propag., Vol. 32, No.5, pp , May [11] J. H. Hollad, Adaptatio i Natural ad Artificial Systems, The Uiversity of Michiga Press, [12] D. E. Goldberg, Geetic algorithms, New York: Addiso-Wesley, [13] J. Keedy ad R. C. Eberhart, Particle Swarm Optimizatio, Proc., IEEE It. Cof-Neural Networks, Vol. IV, pp , Perth, Australia, Nov/ Dec [14] V. Rajya Lakshmi ad G.S.N. Raju, Sythesis of liear atea arrays usig array desig ad Real Coded Geetic Algorithm. IJAEST, Vol. 18, pp 44-48, [15] P. V. Florece, ad G. S. N. Raju, Sythesis of Liear Atea Arrays Usig Accelerated Particle Swarm Optimizatio, Iteratioal Joural of Computer Applicatio, Vol. 103, No. 3, pp , [16] T. A. N. S. N. Varma ad G. S. N.Raju, Ivestigatios o geeratio of ultra low sidelobe patters, Iteratioal Joural of Egieerig Sciece ad Techology, Vol. 6, No. 6, Jue [17] P. K. Murthy ad A. Kumar, Sythesis of Liear Atea Arrays, IEEE Tras. Ateas Propagat., Vol. AP-24, pp , November [18] M. T. Maa, Theory ad Applicatios of Atea Arrays, New York: Joh Wiley ad Sos, [19] Z. Michalewicz, Geetic algorithms + Data Structures = Evolutio Programs, Spriger-Verlag, Berli, [20] R. L. Haupt, A itroductio to Geetic Algorithm i electromagetics, IEEE AP-S Mag. Vol. 37, pp. 7-15, April [21] J. M. Johso, Y. Rahmat-Samii, Geetic Algorithm Optimizatio ad its applicatio to atea desig, Ateas ad Propagatio Society Iteratioal Symposium, Vol. 1, pp , Jue [22] J. M. Johso, Y. Rahmat-Samii, Geetic Algorithms i egieerig electromagetic, IEEE Trasactios o Ateas ad Propagatio Magazie, Vol. 39, pp. 7-25, [23] Y. Rahmat-Samii, ad E. Michielsse Electromagetic Optimizatio by Geetic Algorithms, Wiley, New York, [24] R. L. Haupt, Real Coded Geetic Algorithm i electromagetics, IEEE press, Wiley Iter Sciece, [25] J. Robiso, S. Sito, ad Y. Rahmat-Samii, Particle swarm, Real Coded Geetic Algorithm, ad their hybrids: optimizatio of profiled corrugated hor atea, i Proc. IEEE It. Symp. Atea Propoagatio, Vol. 1, Sa Atoio, TX, 2002, pp [26] J. Robiso ad Y. Rahmat-Samii, Particle Swarm Optimizatio i Electromagetics, i IEEE Trasactios o Ateas ad Propagatio, Vol. 52, No. 2, pp , February [27] J. Keedy ad W. M. Spears, Matchig algorithms to problems: a experimetal test of the particle swarm ad some Geetic Algorithms o multi modal problem geerator, i Proc. IEEE It. Cof. Evolutioary computatio, [28] P. A. Suy Dayal, Desig of X Bad Pyramidal Hor Atea, Iteratioal Joural of Applied Cotrol, Electrical ad Electroics Egieerig (IJACEEE), Vol. 3, No. 1/2, pp , May [29] X. S. Yag, Nature-Ispired Metaheuristics Algorithms, Luiver Press,

8 Iteratioal Joural of Applied Egieerig Research ISSN Volume 11, Number 6 (2016) pp Research Idia Publicatios. Authors: P.A. Suy Dayal received his M.Tech i Radar & Microwave egieerig from AU College of Egieerig (A), Adhra Uiversity with Distictio First Class ad obtaied B.Tech i Electroics ad Commuicatio Egieerig from Jawaharlal Nehru Techological Uiversity, Hyderabad. At preset he is research scholar i departmet of ECE, Ceturio Uiversity of Techology ad Maagemet. He worked as Associate Professor i Dept. of ECE, Viswaadha Istitute of Techology ad Maagemet. He preseted ad published may papers i various atioal ad iteratioal cofereces ad jourals of repute. He is a Member of ACES ad IEEE, Life Member of IETE, SEMCE ad IAENG. His research iterests are Atea Arrays, EMI/EMC ad Soft Computig. Dr. S. Mishra has completed his Ph.D i (Electroics ad Commuicatio Egieerig) from Biju Pataik Uiversity ad Techology, Odisha ad M.Tech (Electroics System ad Commuicatio) from NIT Rourkela, Odisha. He has published research papers i differet atioal ad iteratioal i jourals. Presetly he is Professor ad Head of the Electroics ad Commuicatio Egieerig departmet i Ceturio Uiversity of Techology ad Maagemet, Bhubaeswar. His research areas are soft computig, sigal processig ad image processig. Dr. G.S.N. Raju received his B.E., M.E., with distictio ad first rak from Adhra Uiversity ad Ph.D., from IIT, Kharagpur. At preset, he is the Hoorary Distiguished Professor i departmet of Electroics ad Commuicatio Egieerig, AU College of Egieerig (A), Adhra Uiversity. He was the former Vice Chacellor of Adhra Uiversity. He is i teachig ad research for the last 35 years i Adhra Uiversity. He guided 46 Ph.D.s i the fields of Ateas, Electromagetics, EMI/EMC ad Microwave, Radar Commuicatios, Electroic circuits. Published about 390 techical papers i Natioal/ Iteratioal Jourals/ Coferece Jourals ad trasactios. He is the recipiet of The State Best Teacher Award from the Govermet of Adhra Pradesh i 1999, The Best Researcher Award i 1994, Prof. Aiya Memorial Natioal IETE Award for his best Research guidace i 2005, Dr. Sarvepalli Radhakrisha Award for the Best Academicia of the year 2007, The Natioal EMC Egieer of the Year Award i 2008, ad IEI Emiet Electroics ad Telecommuicatio Egieer i He was a visitig Professor i the Uiversity of Paderbor ad also i the Uiversity Karlsruhe, Germay i He held the positios of Pricipal, Adhra Uiversity College of Egieerig (A), Visakhapatam, Chief Editor of Natioal Joural of Electromagetic Compatibility. Prof. Raju has published 11 textbooks o Ateas ad Wave Propagatio, Electromagetic Field Theory ad Trasmissio Lies, Electroics Devices ad Circuits, Microwave Egieerig, Radar Egieerig ad Navigatioal Aids. Prof. Raju has bee the best faculty performer i Adhra Uiversity with the performace idex of 99.37%. 3760

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