Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 do:10.21311/001.39.7.10 A Parallel Genetc Algorthm for the Verfyng Smulaton of the Performance Prototype Yuan Xu School of automaton, Northwestern Polytechncal Unversty, Xan 710072, Chna Hufeng Xue School of automaton, Northwestern Polytechncal Unversty, Xan 710072, Chna Along Lu* School of automaton, Northwestern Polytechncal Unversty, Xan 710072, Chna *Correspondng author(e-mal: 369455990@qq.com) Abstract There s a huge dfference n the computatonal tme and effcency between dfferent smulaton tasks for the performance prototype. In order to mprove the effcency of coordnated operaton, the parallel technologes are used n the runnng processes of collaboratve smulaton for the performance of aerodynamc mssle. Ths paper presents a parallel optmzaton programmng based on genetc algorthm for the performance smulaton of aerodynamc mssle. The smulaton envronment s based on LSF platform wth PC cluster, the man performance of the aerodynamc mssle s smulated and the computatons requred by genetc algorthm, whch s nherently parallel, are performed n a parallel computng envronment. The smulaton results show that the genetc algorthm s employed to solve ths parameters optmzaton problem effectvely wth hgh accuracy. Key words: Aerodynamc Mssle, Genetc Algorthm, Collaboratve Smulaton, Parallel Computatons. 1. INTRODUCTION Fast trajectory optmzaton for mssle to ntercept the ncomng target effectvely s a challenge work and plays an mportant role n the feld of natonal defense. The flght velocty and avalable overload could be ncreased when the mssle fles along the optmal trajectory. It s mportant to take several factors nto consderaton when the mssle trajectory optmzaton s performed. These factors nclude the followng aspects: the performance ndex, such as the total flght tme or the termnal velocty of the trajectory, should be chosen approprately; Specfed boundary condtons should be satsfed wth the optmal trajectory, for example, the mssle must arrve at the predcted ntercept pont wth tolerance mss dstance; Specfed path constrans should also be satsfed, for nstance, the mssle should ascend vertcally several seconds after launch for safety and extenson of the attackng area. All above factors make parallel optmzaton becomes more complcated, especally when the mssle s multstage because mult-stage ar defense mssle wll drop some mass n the course of stage separaton, and the thrust characterstcs are dfferent between stages, whch wll brng dversty to the dynamcs of dfferent stages. Hence, dffcultes of fndng the optmal soluton are ncreased and make t very hard for the tradtonal ndrect and drect method to resolve ths problem (Yokoyama N. and Suzuk, 2005). Ths paper presents a parallel optmzaton programmng based on genetc algorthm for the performance smulaton of aerodynamc mssle. The smulaton envronment s based on MATLAB/Smulnk software, the man performance of the aerodynamc mssle s smulated and the computatons requred by genetc algorthm, whch s nherently parallel, are performed n a parallel computng envronment wth 512 cores. The LSF (Load Sharng Faclty) s employed n parallel computatons (Phllps, C.A. and Drake, J.C., 1994). 2. GENETIC ALGORITHM MODEL WITH PARALLEL COMPUTATIONS In the feld of artfcal ntellgence, a genetc algorthm (GA) s a search heurstc that mmcs the process of natural selecton (Pontan and Conway, 2010). Ths heurstc (also sometmes called a metaheurstc) s routnely used to generate useful solutons to optmzaton and search problems (Haupt, Haupt, 1998). Genetc algorthms belong to the larger class of evolutonary algorthms (EA), whch generate solutons to optmzaton problems usng technques nspred by natural evoluton, such as nhertance, mutaton, selecton, and crossover(wrght, 1991). 80
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 2.1. The Structure of Genetc Algorthm After selectng a target functon of the problem, based on experence can set the parameters of the search range, thereby determnng the codng and decodng as well as the search of the populaton sze, and then by calculatng genetc program produces an optmal soluton of the problems, whle calculaton process yet to determne the condtons of convergence, as a bass for calculaton of termnaton, and the best of the group n queston represents a preferred approxmate optmal soluton(adewuya, 1996). Genetc calculus of ths study desgn s by the mechansm of bologcal evoluton n the applcaton of optmal solutons to solve the search problem wth the above (Erck and Goldberg, 2000), the system of selfevoluton toward better solutons (H. Safouh, M. Mouattamd and U. Hermann. A., 2011), based on genetc algorthms wrtten the followng steps to follow(tomoyuk, Mtsunor, and Yusuke, 2000). 1. Codng procedures Genetc algorthm s done for the calculaton of the encoded strng work, the varable to a strng of a certan length, va the selected encodng, number of dgts depends on the accuracy of the research needs may be. The codng methods are commonly used bnary-coded and real-number coded (Dorgo and Manezzo, 1993). The more commonly used bnary codng method, the ntal establshment of the group s made by a random number generator generates a random strng of bnary combnaton. For example, the preferred mode of the CCP need to have sx decson varables, each varable to 3 bnary dgts sad that the soluton of the set of genes expressed n each mode s equvalent to a chromosome, as shown n Fg.1: 001 000 010 001 101 111 x 1 x 2 x 3 x 4 x 5 x 6 Fgure 1. Schematc dagram of bnary encodng 2. The establshment of the ntal populaton After the ntal populaton of the genetc algorthm s a random number generator generates a random strng of bnary coded cluster, and then converted nto the actual value of the varable decodng va, compared to tradtonal optmzaton methods from a sngle startng pont of any (ntal startng pont) starts at the genetc algorthm can be a startng pont as much as the group for a more comprehensve search. The selected communtes are often due to the sze of the subject-specfc solutons. De Jong (1975) recommended that the group range between 50-100, Goldberg (1975) that the length of the strng can affect the sze of the best of the group, he proposed a formula related to the sze of the strng groups, such as Formula 1 Shows: 0.21 p 1.65*2 c where:p s the populaton sze, C s the total length of the strng, the scope of applcaton of ths formula strng length of between 30-60. 3. Decodng procedure Decodng process requred to set a lower lmt on the decson varables, for example, when a problem wth k decson varables X, = 1,2,......, k, and ts range s X [L, U ], L and U s a real number, each decson varable s compled nto a bnary strng of length m, the j-bt bnary strng as the value b j, of formula 2 can be coded for each varable decodng converts the actual argument: U L X L b 2 m m j 2 1 j 1 Bnary encodng, the resultng value of the varable s dscrete, yet dscrete varables to represent contnuous varables, the error s not avodable. If α as a contnuous varable X accuracy requred, the length of the strng and the accuracy of the relatonshp expressed by the formula 3: m U L 10 2 1 4. Ftness Ftness s based on the "survval of the fttest" theory, used to represent the group of ndvduals ablty to survve n the competton. The use of genetc algorthms to assess the selected functon to calculate the ftness of the ndvdual, and the ndvdual has been selected to replcate the chances of the next generaton wth ts own ftness nto a proportonal relatonshp. j 1 81
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 5. Selecton and Reproducton There are many methods that can be used to select an ndvdual copy of the wll, of whch the smplest and most wdely used s "roulette wheel". Ths s dfferent from the alquot of a roulette wheel grd, ts man feature s the wheel n each slot are based on a percentage of the sze of the ftness of each ndvdual set, whch s sutable for the hgher degree dsk proporton who occuped the greater the selecton process so that t s easer to stand out n the wheel, and ts populaton n the more nferor solutons of ftness s low, so n the selecton process easy to be elmnated. Its sze can be ruled proporton determned by the formula 4: W f f Where: f for the th ndvdual ftness value, W s the probablty of the -th ndvdual s selected, the approprate value for the -th sum. 6. Crossover Dfferent groups of ndvduals can through random nterleaved, the swap genes to produce new progeny (offsprng). Frst, pck any one of the two chromosomes, called parents (parents), and then randomly selected parents n the N gene strng (bt) a pont called cross pont (crossover pont), then staggered located the rght of the parent gene nterchange pont, generate two new ndvduals, staggered process s now complete. The nterleavng process shown n Fg.2: Fgure 2. Schematc staggered mplementaton modaltes of restructurng 7. Mutaton Mutant progeny process after the handover, accordng to a preset mutated mutaton probablty. Its practce of randomly selected bts are reversed (0 becomes 1, 1 becomes 0) as shown n Fg.3. Although mutatons n the genetc algorthm manly staggered replcaton and recombnaton, but can ntroduce new genes style, avodng premature convergence. Moreover, the mutaton tself s a walk n the parameter random walk stochastc process can develop new search areas to prevent local optmal converges to, and are more lkely to search for the best global optmal, but due to the probablty of mutaton t s usually not hgh; t does not make genetc algorthm flow for the full mgraton calculatons. Fgure 3. Schematc vew of mplementaton of the mutaton 8. Stop crteron The convergence crtera genetc algorthm There are many ways, ths study set the maxmum generaton (maxmum generaton) number of stop crteron n the search reaches a stop when gven the maxmum number of generatons. 2.2. The Operatng Envronment of Parallel Genetc Algorthm Snce the computatonal complexty of envronmental problems often encountered preferred calculaton of the problem s too large, so the search for the chosen method of genetc algorthm, usng ts potental characterstcs of parallel work of parallel, ts desgn flow shown n Fg.4. Frst, randomly generated ntal 82
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 populaton to be carred out preferably ssues, encodng, decodng and then calculate the approprate value of the LSF computer clusters handler based(mehd Hossen, Hedar Al Shayanfar and Mahmoud Fotuh Fruzabad, 2008), and the results returned to the sendng of the machne(chang, Chu and Wang, 2007), be more sutable degrees select the optmum reproducton of ndvduals mechansms and match set the termnaton condton has reached the desred qualty of the soluton, and the completon of ths study parallel genetc mechansm for solvng the problem s preferable(deva and Geethanjal, 2014). Host process program Generate an ntal populaton Strng decoded process1 Calculates the approprate value 1 Dspersed communtes process 2 Calculates the approprate value 2 process N Calculates the approprate value 3 Host process program Sutable aggregate value selecton, cross and mutaton to produce new generaton Meets the orgnal stop otherwse? Yes Stop No Fgure 4. Parallel genetc algorthm desgn 2.3. The Development of Optmzaton Procedures 1. Obtan the geometrc parameters of the mssle s obtaned and the coordnate converson s completed(fesanghary, Mahdav, Mnary-Jolandan and Alzadeh, 2008). 2. The ntal performance parameters of the mssle s calculated, whch ncludng the mssle parameters of angle of attack, flght path angle and trajectory (Betts, Huffman, 1993). 3. Ethnc ntalzaton (1) In accordance wth the parameters of screenng, ncludng accordng to the number of shots, weght, collmator sze and the coordnates for correspondng coordnates for each shot s encodng. After the gene encodng an array of patterns, the man performance parameters of the mssle s shown n table 1: Table 1. Major parameters of mssle performance performance parameters angle of attack( ) flght path angle( ) X Y Z Unt deg rad m m m (2) Each computng node based on dfferent random probablty of default and the gene to produce the desred genetc algorthm at the begnnng of chromosome composed of the ntal progeny populaton. 4. Ftness Based on genetc algorthm search procedure, the progeny populaton of each computng node s calculated. In the present study, we referred to the former formula as the ftness functon, whch s the cost functon, publcty and defntons set out below: F= WL RD WN RD Where: WL and WN are of the leson tssue and normal tssue of the rght weghtng factor; component costs ΔRDL and ΔRDN respectvely n lesons and normal tssue relatve dose dfference (related dose L N 83
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 dfference). In the calculaton of the cost functon value and sent to the desgnated operator node, and a new generaton gene (offsprng). 5. Adaptaton assessments gene A new generaton of strng s calculated cost functon value (Egene), and the cost functon value of the mnmum gene (Genebest) beng adjacent to a computng node to replace the node cost functon value of the lowest strng. 6. Crossover and Mutaton Suppose you want to optmze the development of two tmes mssle performance parameters, each gene gene pool (compute nodes) random number generated at random. We selected two of a gene pool of the best startng base generaton of mutant genes and matng process. Respectvely Genep1 and Genep2, ther ndvdual soluton s: Gene1 ={ 1, 1,X1,Y1,Z1} Gene2 ={ 2, 2,X2,Y2,Z2} 7. Create new groups The last reproducton accordng to ther degree of adaptaton level, and create new groups. The new generaton of these groups as a new startng pont to search the entre search space for successve searches. 8. Repeat Evoluton Program Contnue to repeat the above steps untl the front master server to fnd the best ftness of the offsprng from other computng soluton pont, and further determnes whether the optmum rradaton pont. If not met, repeat steps 4-8. 3. NUMERICAL EXPERIMENTS AND DISCUSSION In ths chapter, two expermental cases are carred out. The frst case s to verfy the feasblty of the present algorthm; the second and thrd case s a performance comparson experment wth the genetc algorthm wth PC cluster and sngle PC. Experment condtons are defned as follows: launch states are x 0=0m, y 0=0m, v 0=0.001m, 0 =1.57rad. The predct ntercept pont coordnates are x 3f=107181m, y 3f=205741m. Attack angle constrants s max (- 10deg, 10deg). And the frst stage duraton tme s t frst=37s, second stage duraton tme s t second=27s, three stage coast tme s free. 3.1. Verfcaton Case Optmal desgn results based on the present algorthm are: the fnal mss dstance s 6.0715m, the termnal velocty s 5440.5345m/s, the optmal angle of attack varables are X opt=(4.4977,7.7589,27.1434,8.495) and the optmzaton tme requred s 16.237s. (a) (b) 84
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 (c) (d) Fgure 5. Plots of optmal trajectory for (a) AOA hstory, (b) velocty change curve, (c) flght path angle change and (d) optmal trajectory Fg.5 shows the optmal ntercept trajectory and the parameters along ths trajectory. From the results of verfcaton case, the fnal mss dstance s very small and tolerable, and all constrants ncludng vertcal launch requrement, bounded AOA are all met absolutely. The present algorthm proves to be feasble to solve ths optmal ntercept trajectory problem. 3.2. Comparatve Case Two conventonal algorthms ncludng genetc algorthm (GA wth sngle PC) and genetc algorthm (GA wth PC Cluster) are employed to solve the same problem defned n chapter 2. In order to catch characters of each algorthm, three types of performance are chosen ncludng optmzaton tme requred, optmzaton stablty and soluton optmalty. 100 smulatons are carred out and the results are lsted n Table 2. Table 2. Statstcal performance comparson of three algorthms wth 100 runs Comparson parameters Genetc Algorthm Parallel GA Wth Genetc Algorthm (Sngle PC) (PC Cluster) (PC Cluster) Tme consumpton (s) 69.207 34.478 16.868 Iteraton Tme (s) 7.2 3.3 2.1 Mss dstance (m) 126.218 38.576 6.529 Termnal velocty (m/s) 5274.129 5436.167 5441.44 1 Standard devaton of termnal velocty (m/s) 47.560 28.544 4.378 Max angle of attack (deg) 9.862 9.897 8.473 Table 2 show that the present algorthm can fnd a better soluton based on the parallel calculaton, but the tradtonal algorthms are usually trapped n some relatve bad solutons. By nvestgatng the optmzaton requred tme n table1, t can be concluded that the present algorthm has an apparent mprovement on the optmzaton speed. The most mportant pont s that the present algorthm ganed the best soluton, from above table, the max AOA obtaned by the present algorthm s smaller than the value obtaned through other two algorthms, the small max AOA smoothest and straghtens the optmal trajectory. Ths s very useful for gudance, navgaton and control system desgn of mssle. 4. SUMMARY AND CONCLUSIONS Ths paper presents a parallel optmzaton programmng based on genetc algorthm for the performance smulaton of aerodynamc mssle. The smulaton envronment s based on LSF platform wth PC cluster, the man performance of the aerodynamc mssle s smulated and the computatons requred by genetc algorthm, whch s nherently parallel, are performed n a parallel computng envronment. The smulaton results show that the present algorthm fnds a better soluton based on the parallel calculaton, but the tradtonal algorthms are usually trapped n some relatve bad solutons, meanwhle, the present algorthm has an apparent mprovement on the optmzaton speed. Those advantages make the present algorthm have more practcal applcaton value n engneerng than tradtonal GA algorthms. 85
Rev. Téc. Ing. Unv. Zula. Vol. 39, Nº 7, 80-86, 2016 Acknowledgements Ths work s partally supported by the Defense basc research projects of #A0420131501, and Thanks for the help. REFERENCE A. A. Adewuya. (1996) New methods n genetc search wth real-valued chromosomes, Master thess, Cambrdge: Massachusetts Instute of Technology. A. Wrght (1991) Genetc Algorthms for Real Parameter Optmzaton, Foundaton of Genetc Algorthms, San Mateo, CA: Morgan Kaufmann. Betts, J.T., Huffman, W. P. (1993) Path-Constraned Trajectory Optmzaton Usng Sparse Sequental Quadratc Programmng, Journal of Gudance, Control, and Dynamcs, 16(1), pp. 55-68. Dorgo, M., and Manezzo, V. (1993) Parallel Genetc Algorthms Introducton and overvew of current research,n Stender, ISO Press, pp.5-42. Erck, C. P, and D. E. Goldberg (2000) Effcent Parallel Genetc Algorthms: Theory and Practce, Comput. Methods Appl. Mech. Engrg, 186, pp.221-238. Fesanghary, M., Mahdav, M., Mnary-Jolandan, M., Alzadeh Y. (2008) Hybrdzng Harmony Search Algorthm wth Sequental Quadratc Programmng for Engneerng Optmzaton Problems, Computer Methods n Appled Mechancs and Engneerng, 33(40), pp. 3080-3091. G.W. Chang, S.Y. Chu, H.L. Wang (2007) An mproved backward/forward sweep load flow algorthm for radal dstrbuton systems, IEEE Trans Power Syst, 22, pp. 882 884. H. Safouh, M. Mouattamd, U. Hermann, A, Hend. (2011) An algorthm for the calculaton of feasble moble crane poston areas, Autom. Constr., 20(4), pp. 360 367 Mehd Hossen, Hedar Al Shayanfar, Mahmoud Fotuh Fruzabad (2008), Modellng of seres and shunt dstrbuton FACTS devces n dstrbuton systems load flow, J Electr Syst, 4(4), pp. 1 12 Phllps, C.A., Drake, J.C. (1994) Trajectory optmzaton for SAM usng a mult-ter approach, AIAA-94-4404. Pontan, M., Conway, B.A.(2010) Partcle Swarm Optmzaton Appled to Space Trajectores, Journal of Gudance, Control, and Dynamcs, 33(5), pp.1429-1441. R. L. Haupt, S. E. Haupt. (1998) Practcal Genetc Algorthms, Wley Interscence publcaton. S. Deva,M. Geethanjal.(2014) Optmal locaton and szng determnaton of Dstrbuted Generaton and DSTATCOM usng Partcle Swarm Optmzaton algorthm, 62(9), pp. 562-570. Tomoyuk, H.,Mtsunor, M, Yusuke, T. (2000) The Dfferences of Parallel Effcency between the Two Models of Parallel Genetc Algorthms on PC Cluster Systems, Proc.of Internatonal Conference/exhbton on Hgh Performance Computng n the Asa-pacfc Regon, pp.945. Yokoyama N., Suzuk, S. (2005) Modfed Genetc Algorthm for Constraned Trajectory Optmzaton, Journal of Gudance, Control, and Dynamcs, 28(1), pp.139-144. 86