Optimal Choice of Random Variables in D-ITG Traffic Generating Tool using Evolutionary Algorithms

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1 Optmal Choce of Random Varables n D-ITG Traffc Generatng Tool usng Evolutonary Algorthms M. R. Mosav* (C.A.), F. Farab* and S. Karam* Abstract: Impressve development of computer networks has been requred precse evaluaton of effcency of these networks for users and especally nternet servce provders. Consderng the extent of these networks, there are numerous factors affectng ther performance and thoroughly nvestgaton of these networks needs evaluaton of the effectve parameters by usng sutable tools. There are several tools to measure network's performance whch evaluate and analyze the parameters affectng the performance of the network. D-ITG traffc generator and measurng tool s one of the effcent tools n ths feld wth sgnfcant advantages over other tools. One of D-ITG drawbacks s the need to determne nput parameters by user n whch the procedure of determnng the nput varables would have an mportant role on the results. So, ntroducng an automatc method to determne the nput parameters consderng the characterstcs of the network to be tested would be a great mprovement n the applcaton of ths tool. In ths paper, an effcent method has been proposed to determne optmal nput varables applyng evolutonary algorthms. Then, automatc D-ITG tool operaton would be studed. The results ndcate that these algorthms effectvely determne the optmal nput varables whch sgnfcantly mprove the D-ITG applcaton as the tme cost of determnng optmal DITG varables n automatc GA, ICA and ACO based methods has been mproved up to 67.3 %, 69.7 % and 82.2 %, respectvely. Keywords: Ant Colony Optmzaton, D-ITG, Genetc Algorthm, Imperalst Compettve Algorthm, Optmzaton. 1 Introducton1 Recently, the computer networks have been extremely complcated n software, protocols, equpment and etc [1] and lots of efforts have been made to understand the behavor of these networks [2]. There are many factors affect the network performance, ncludng network congeston and load, network equpment and hardware, the amount of network users, the power of wreless network sgnal and the operatng system used by users [3, 4]. In order to evaluate the networks performance there are several tools such as DSLProbe [5], Asymprobe [6], Spruce [7], Pathload [8], Netalyzy [9], Iperf, Netperf, IPtraffc, MGEN and D-ITG whch measurng the parameters affectng the network performance. D-ITG has sgnfcant advantages over other traffc generators. D-ITG supports IPv4 and IPv6 Iranan Journal of Electrcal & Electronc Engneerng, Paper frst receved 25 Apr and n revsed form 18 Jan * The Authors are wth the Department of Electrcal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran. E-mals: and and measures key parameters such as throughput, latency, jtter and packet loss n packet level. Ths tool s capable to reproduce varous known applcaton program traffc (e.g. Telnet, VoIP, DNS and network games) and support Transmsson Control Protocol (TCP), User Datagram Protocol (UDP), Stream Control Transmsson Protocol (SCTP), Datagram Congeston Control Protocol (DCCP) and also Internet Control Message Protocol (ICMP) n transfer layer. Besdes presentng exact outputs, the results are hghly dependent to nput parameters lke packet number, packet sze and packet sendng tme. Thus, the determnaton of optmal nput parameters s a major challenge n applyng ths software. In ths research, Evolutonary Algorthms (EAs) have been used to determne the best value for the Internet Dstrbuted Traffc (IDT) and Packet Sze (PS) random varables. Therefore optmzed results can be obtaned based on these varables. In the followng, we wll nvestgate the effects of proposed methods to mprove D-ITG operaton. At the second secton, the purpose of evaluatng computer networks performance and ther Iranan Journal of Electrcal & Electronc Engneerng, Vol. 11, No. 2, June

2 effectve parameters wll be presented. In addton, n order to measure computer networks, D-ITG tool wll be ntroduced. In the thrd secton, we examne the structure of proposed EAs and at the forth secton the smulaton results wll be presented. The research concluson s presented at the ffth secton. 2 Computer Networks Evaluaton usng DITG Evaluaton of computer networks effcency s performed n order to compare the proposed networks structures and selectng the best one, based on the observable parameters affectng the servce qualty. Generally, the purposes of evaluaton the performance of computer networks are as followng: Determnng the crtera of performance of exstng systems. Modelng of exstng systems and systems wll be proposed n the future. Developng analytcal bascs. Fndng the ways to apply and confrm new approaches, e.g. constructng and evaluatng performance models. There are several parameters defnng servce qualty ncludng: bandwdth, throughput, average bt rate, latency, jtter, bt error rate, packet loss, sgnal to nose rato, attenuaton and lne length. Recently, many efforts have been made to model nternet traffc and dervate nternet behavoral model. Excessve complcaton of huge topologes and ther traffc characterstc have made the model analyzng so dffcult. In ths stuaton, traffc generaton and network behavor smulaton usng smulaton tools would be an effcent method to analyze complcated networks operaton. In recent years, ncreasng mprovements n traffc generator tools lead to a new generaton of traffc generators whch perform smulaton, analyss and real traffc generaton thoroughly. Due to the fundamental dfferences between the traffc generator tools n performance procedures, the operatonal envronment, supportng protocols of varous network layers, archtecture and the generated output, examnng and comparng them would be a dffcult task. D-ITG s able to generate traffcs wth IPv4 and IPv6 base through accurate repetton of traffc load n the nternet applcaton programs. Moreover, D- ITG s capable to measure the network performance based on performance measurement common parameters such as throughput, latency, jtter and packet loss. Ths tool could apply random models to PS and IDT. Determnng the dstrbutons of PS and IDT random varables make t possble to apply varous reconstructon processes for packet generatng. Ths tool s able to regenerate traffc statstcal specfcatons of dentfed varous applcatons such as Telnet, VoIP, DNS and network based games. D-ITG supports TCP, UDP, SCTP, DCCP and also ICMP protocols n transfer level. Recently, D-ITG supports SCTP and DCCP protocols n order to overcome some lmtatons of UDP and TCP [10]. The dstrbuted structure of D-ITG traffc generator s represented n Fg. 1. Ths structure s made up of four man parts ncludng sender/recever, logger, controller and analyzer. All these platform components apply multthread programmng [11, 12]. Regardless all the benefts of D-ITG mentoned above, determnng the proper and optmal nput varables s an mportant challenge n usng of ths tool. In the next secton, we wll ntroduce some dfferent EAs to fnd optmal nput varables for mprovng the accuracy of DITG. 3 Revew of Proposed EAs for Optmzng D-ITG In ths secton an attempt has been made to use EAs for optmzng the performance of DITG. Optmzaton algorthms would lead to the most optmal response by reducng the search space and prevent gettng stuck n local mnma by provdng the requste perturbaton to brng t out of the local mnma. An effectve optmzaton algorthm would be able to fnd the optmal response wthout consderng the ntal values of optmzaton varables. Three of the most common EAs and applcaton of them n fndng D-ITG optmal nput varables wll be descrbed subsequently. 3.1 Optmzaton Based on Genetc Algorthm Genetc Algorthms (GAs) are a famly of computatonal models nspred by evoluton. These algorthms encode a potental soluton to a specfc problem on a smple chromosome-lke data structure and apply recombnaton operators to these structures so as to preserve crtcal nformaton [13]. An mplementaton of a GA begns wth a random populaton of chromosomes. In our proposed algorthm, each chromosome has a length equal to three genes named packet sze, number of packets and nter departure tme. Then these chromosomes wll be evaluated and allocated wth reproductve opportuntes n such a way that those chromosomes whch represent a better soluton to the target are gven more chances to reproduce. The ftness of each chromosome s determned by ftness functon. In ths research, the ftness values of chromosomes are obtaned by Eq. (1): b BtRate Ftness = * α * delay + β * Jtter + γ * PacketLoss (1) Accordng to above ftness functon the fnal purpose s to fnd the optmal responses n a way that maxmum bt rate, mnmum delay and mnmum jtter wll be acheved. Furthermore, the packet loss would be mnmzed n responses. Thus, t could be guaranteed that the best response for the under test network can be acheved by resultant D-ITG nput parameters. Moreover, by choosng approprate coeffcents n ftness functon, we would be able to determne each of four parameters (bt rate, delay, jtter and packet loss) weght based on the mportance of them n our network. 102 Iranan Journal of Electrcal & Electronc Engneerng, Vol. 11, No. 2, June 2015

3 Fg. 1 D-ITG archtecture. Fg. 2 Flowchart of GA based proposed algorthm. Fg. 2 shows the flowchart of ths algorthm. Each stage of ths flowchart wll be descrbed subsequently. In the frst step of the algorthm all chromosomes are evaluated usng the ftness functon to determne ther ftness. These ftness values are then used to decde whether the chromosomes are elmnated or retaned. Accordng to the prncple of survval of the most ftted, the more adaptve chromosomes are kept, and the less adaptve ones are dscarded n the course of generatng a new populaton. After selecton has been carred out the crossover can occur. Ths can be vewed as creatng the next populaton from the selected chromosomes. In one-pont crossover, frst, one pont s selected as the reproducton start pont. Then, the frst chromosome left hand genes would be coped n new chromosome tll the start pont of reproducton. Then, the second chromosome rght hand genes are coped nto the rght hand genes of the new chromosome. In other word, swappng the fragments between the two parents produces the offsprng. After crossover we apply the mutaton operator. In mutaton process, one of the genes of the randomly selected chromosome would be changed randomly. In our algorthm the mutaton rate s appled wth 1 % probablty. After the process of selecton, crossover and mutaton s completed, the next populaton can be evaluated. The algorthm contnues as descrbed untl the stoppng condtons wll be reached. In ths case reachng a maxmum number of teratons or havng no more mprovement (or mprovement less than a determned threshold) n fnal results for several consecutve teratons may be chosen as stoppng crtera. At the end of the algorthm, the most ftted chromosome would be selected as the optmal soluton and each of the genes would be regarded as one of the D-ITG random varables. 3.2 Optmzaton Based on Imperalst Compettve Algorthm Imperalsm s the polcy of extendng the power and rule of a government beyond ts own boundares. Imperalst Compettve Algorthm (ICA) s a novel global search strategy that uses mperalsm and mperalstc competton process as a source of nspraton. Ths algorthm s based on that n real world countres try to extend ther power over other countres n order to use ther resources and bolster ther own government [14-16]. The block dagram of ths algorthm s shown n Fg. 3. As shown n ths fgure, ICA starts wth some ntal countres that are randomly dspread n search space. Each country has a vector of cultural, socal and economcal features. Here the countres are arrays of three real numbers whch each of them represents one of the D-ITG nput parameters. After formng prmary countres, the power of each country s equvalent to ftness value and s calculated by usng Eq. (1) [16]. After calculatng the power of all countres, some of the stronger countres (N mp most ftted countres) n the populaton are selected to be the mperalsts and then durng a compettve process all the other N col countres are dvded among mperalsts based on ther normalzed power. In fact the ntal number of colones of each mperalst should be drectly proportonate to ts normalzed power. The normalzed power of an mperalst s defned by [17]: P n = C n N m p C = 1 (2) Mosav et al: Optmal Choce of Random Varables n D-ITG Traffc Generatng Tool usng 103

4 mperalst, the colony moves to the poston of the mperalst and vce versa. The total power of an empre s defned by the power of mperalst state plus a percent of the mean power of ts colones. In mperalstc competton, the weakest colony of weakest empre would be transferred to the most powerful empre and the empres wth no colones would be omtted and the mperalst would be added to the most powerful empre. As a result of mperalstc competton, the colones of powerless empres wll be dvded among other mperalsts and the empre wll be collapsed. Ths process would be repeated untl just one empre remans or a certan amount of decades be passed. As a result, all the countres converge to a state n whch there exsts only one empre that possesses all other countres as ts colones. In ths stuaton the mperalst conssts of an array of varables whch s an optmal soluton of the problem. In addton to ths stoppng condton, n ICA lke other EAs reachng a maxmum number of teratons (decades) or havng no mprovement n fnal results for several consecutve teratons may be chosen as stoppng crtera. In these stuatons, the soluton of problem s determned by the mperalst of the most powerful empre. Fg. 3 Flowchart of ICA based proposed algorthm. where C n s the normalzed cost of n-th mperalst and s defned as dfference between the cost of mperalst and total cost of all mperalsts. The number of colones of each empre s calculated by Eq. (3) [17]: N. C = round{ P. N } (3) n n col After creatng the ntal empres, colones start movng toward ther relevant mperalst state. Ths process s called assmlaton polcy. In assmlaton, each colony moves on the lne that connects the colony and t's mperalst by x unts, whch x s a random varable wth unform dstrbuton. To creatng new postons for colones around the mperalst n dfferent drectons a random devaton angle θ s added to the drecton of movement. If ths movement causes to fnd a colony wth better poston (more power) than that of 3.3 Optmzaton Based on Ant Colony Optmzaton Method The nsprng source of Ant Colony Optmzaton (ACO) s the foragng behavor of real ants. When searchng for food, ants ntally explore the area surroundng ther nest n a random manner. As soon as an ant fnds a food source, t evaluates the quantty and the qualty of the food and carres some of t back to the nest. Durng the return trp, the ant deposts a chemcal pheromone tral on the ground. The quantty of pheromone deposted, whch may depend on the quantty and qualty of the food, wll gude other ants to the food source [18]. Ths algorthm s a repettve three phase algorthm ncludng development of the soluton, updatng process and local research. Dfferent stages of ths algorthm are shown n Fg. 4. At the frst step, m ants are dstrbuted unformly n the search area. The optmzaton process s started wth some random solutons and then each -th ant would develop a three dmenson soluton X = (x 1, x 2, x 3 ) for three-dmensonal problem by developng three normal dstrbutons and samplng them [18]. The j-th dmenson of N (μ j, s j ) normal dstrbuton has the mean and varance equal to μ j and s j, respectvely. To form dstrbuton features, each ant needs a gude soluton (X gude ). For selectng the gude soluton, we allocate a P c probablty to each ant. Each ant would select the best overall soluton as gude soluton wth P c probablty and would consder the best soluton n ts memory as the gude soluton wth 1-P c probablty. Ths process s llustrated n Eq. (4) [19]: 104 Iranan Journal of Electrcal & Electronc Engneerng, Vol. 11, No. 2, June 2015

5 Fg. 4 Flowchart of ACO based proposed algorthm. X best f rand(0.1) > Pc X gude = (4) X else Dfferent P c values would lead to more varety n ant populaton and so, better results would be obtaned. By selectng dfferent P c for each ant, dfferent levels of extracton and dscovery would be acheved by ants. P c probablty s calculated by Eq. (5) [19]: 10( 1) exp 1 6 s P 1 Pc = * ( exp(10) 1) (5) The elements of gude soluton are regarded as normal dstrbuton mean, so we have [19]: μ = { μ, μ, μ } = { X gude, X gude, X gude } = X (6) gude The j-th dstrbuton varance s equal to the gude soluton dstance from j-th dmenson of the best soluton of the other ants multpled by ρ (Eq. (7)) [19]: m j σ = ρ j j X X gude l (7) l= 1 m 1 Postve ρ s equal n all dmensons and has smlar effect as the pheromone evaporaton rate n ACO. Hgher values of ths parameter would reduce the convergence rate of the algorthm. Pheromone evaporaton rate affects long term memory and causes to forget worse solutons more quckly. At the second step, the ftness value would be calculated for new solutons and for each ant a new soluton would be presented. If the presented soluton by m-th ant be better than the soluton exstng n ts memory then the ant s memory would be updated usng the new soluton. In order to ncrease the accuracy of the algorthm, a local research strategy s appled to mprove the solutons founded by the algorthm. In each repetton, the local research process s recalled for the best ant n the colony. HJ s a pattern search method beng presented by Hooke and Jeeves n 1961 and n spte of passng a long tme, for many local search problems, ths algorthm s appled as the frst choce [20]. HJ method selects the soluton obtaned from overall search as a base pont and mproves t applyng dscovery movement and pattern movement. In dscovery movement, all base pont varables move n predefned steps n turn and f no mprovement observe, they would move toward an opposte drecton. Then the pattern movement smultaneously repeats all the successful changes n the dscovery phase. Then the results obtaned by the movements would be evaluated and n case of successful movement; the new pont would be regarded as the base pont. The process s contnuously repeated tll there would be no mprovement at any dmenson. The step sze s reduced by passng tme and the reducton should be n a way that a new pattern could be developed by that. A great decrease of the step sze could result reducton n search process. The fnal search would be stopped when the step sze s small suffcently [19]. 4 Expermental Results In ths secton, we present the results of our research. The expermental results are provded applyng our three proposed optmzaton algorthms on real dfferent data sets. These data sets are collected by measurng D- ITG software output wth dfferent nputs on ADSL lne wth 256K speed rate. These algorthms are mplemented n C#.Net software and the experments have been repeated 100 tmes. In our three-dmensonal search space we consdered the number of ntal chromosomes, countres and ants equal to 50. In the proposed GA based method the crossover rate and mutaton rate are consdered 50% and 30%, respectvely. In ICA, we consder 5 ntal mperalsts and ACO evaporaton rate s equal to 0.45 and the prmary step s equal to 8, each step would decrease to 1/2. Mosav et al: Optmal Choce of Random Varables n D-ITG Traffc Generatng Tool usng 105

6 In ftness functon the values of b, α, β and γ varables llustrate the effects of bt rate, delay, jtter and packet loss rate parameters n the ftness functon and ther expermental values are consdered 2, 0.01, 2 and 0.01, respectvely. These values are defned n a way that optmal responses wth hgh bt rate and low delay, jtter and packet loss would be acheved. Moreover, these weghts should be proportonate wth the effect of each parameter on output value. Thus, snce bt rate and jtter could have notable effects on network performance, the weghts should be selected n a way that even ther neglgble change could sgnfcantly affect the ftness value. Fg. 5 llustrates the ntal nput values n threedmensonal feature space and Fg. 6 shows ther correspondng ftness values. The values of ftness functon and the changes durng dfferent teratons for GA, ICA and ACO are shown n Fgs. 7-9, respectvely. In order to ndcate the promsng ablty of the proposed algorthms n determnng the optmal nput parameters of D-ITG, the best D-ITG nput parameters obtaned by automatc D-ITG, are compared to manually results (results obtaned by D-ITG wth manual nput parameters). The comparatve results are shown n Table 1. As shown n Table 1 our proposed algorthms have ndcated ther ablty n fndng the best responses wth hgh ftness values n compare wth manual method. Moreover, among three proposed methods the ftness value obtaned by ICA based method s greater than the others. On the other hand, we compare the speed of convergence of proposed ICA based algorthm and related GA based and ACO based methods to ther desred value of ftness. Results obtaned from runs of the algorthms when they are allowed to executed for a maxmum of 200 teratons, show that the GA based and ACO based algorthms are able to arrve at the desred ftness value n average 11 teratons, whle ICA based technque s able to obtan the desred ftness value, n relatvely more number of teraton (average n 14 teratons). Fg. 6 Smulated data ftness. Fg. 7 Convergent of the GA toward the ftness best value. Fg. 8 Convergent of the ICA toward the best ftness. Fg. 9 Convergent of the ACO toward the best value of ftness. Table 2 llustrates the percentage of mprovement of results obtaned by three proposed algorthms n compare wth the manual method. Fnally, expermental results show that the automatc D-ITG s able to fnd the best nput varables and the fnal solutons of all three proposed algorthms are convergent toward one response. Fg. 5 Smulated data n three dmensonal spaces. 106 Iranan Journal of Electrcal & Electronc Engneerng, Vol. 11, No. 2, June 2015

7 Table 1 Manual D-ITG and automatc D-ITG compared to GA, ICA and ACO. Methods Manual D-ITG Automatc D-ITG by GA Automatc D-ITG by ICA Automatc D-ITG by ACO Maxmum Ftness Mnmum Ftness Mean Varance Number of Tests Testng Tme [sec.] Number of Iteratons to Acheve Convergence Table 2 Comparng the ntroduced methods mprovements to the manual one. Methods Automatc D-ITG by GA Automatc D-ITG by ICA Automatc D-ITG by ACO Mean to Varance Rato Percent Improvement n Number of Tests 65.34% 74.34% 82% Percent Improvement n Testng Tme 67.3% 69.7% 82.2% 6 Concluson In ths paper, GA, ICA and the ACO have been appled n order to obtan the best D-ITG nput parameters and to present automatc soluton to analyze the network performance parameters. These algorthms are mplemented on data derved from 256K ADSL lne. By usng the proposed methods, t was shown that all three algorthms were able to determne the optmal values of D-ITG nput parameters wth a hgh accuracy. Results show the promsng ablty of these algorthms n automatng the D-ITG traffc generatng tool. The results ndcated that the algorthms would fnd the optmzed varables n predetermned ranges and would mprove the experments tme and number of test n compare wth the manual method. The results llustrated that the ACO has a hgher mprovement percentage n relaton to the GA and ICA. Acknowledgment The authors would lke to thank Telecommuncaton Company of Tehran for ther valuable support durng the authors research work. References [1] A. Botta, A. Danott and A. Pescape, Mult- Protocol and Mult-Platform Traffc Generaton and Measurement, Proceedngs of the 26-th IEEE Conference on Computer Communcaton (INFOCOM 2007) DEMO Sesson, pp , [2] S. Molnar, P. Megyes and G. Szabo, How to Valdate Traffc Generators?, Proceedngs of IEEE Conference on Communcatons Workshops (ICC), pp , [3] J. Balen, G. Martnovc and Z. Hocensk, Network Performance Evaluaton of Latest Wndows Operatng System, Proceedngs of 20th Internatonal Conference on Software, Telecommuncatons and Computer Networks (SoftCOM), pp. 1-6, [4] S. Debbarma and A. Das, Emprcal Measurng IPv4/IPv6 Network Performance on Mcrosoft s Wndows Operatng Systems, Proceedngs of Thrd Internatonal Conference on Advances n Computng and Communcatons, pp , [5] L. Chen, T. Sun, G. Yang, M. Y.Sanadd and M. Gerla, End-to-end Asymmetrc Lnk Capacty Estmaton, Proceedngs of the 4th IFIP-TC6 Internatonal Conference on Networkng Technologes, pp , [6] W. W. Chan, A. Chen, X. Luo, R. K. P. Mok, W. L and R. K. C. Chang, TRIO: Measurng Asymmetrc Capacty wth Three Mnmum Round-trp Tmes, Proceedngs of the Seventh Conference on Emergng Networkng Experments and Technologes, pp. 1-12, [7] J. Strauss, D. Katab and F. Kaashoek, A Measurement Study of Avalable Bandwdth Estmaton Tools, Proceedngs of the 3rd ACM Mosav et al: Optmal Choce of Random Varables n D-ITG Traffc Generatng Tool usng 107

8 SIGCOMM Conference on Internet Measurement, pp , [8] M. Jan and C. Dovrols, End to End Avalable Bandwdth: Measurement Methodology, Dynamcs, and Relaton wth TCP Throughput, Journal of IEEE/ACM Transactons on Networkng (TON), Vol. 11, No. 4, pp , [9] C. Krebch and N. Weaver, Netalyzr: Illumnatng the Edge Network, Proceedngs of the 10th ACM SIGCOMM Conference on Internet Measurement, pp , [10] A. Trumala, F. Qn, J. Dugan, J. Ferguson and K. Gbbs, Throughput Analyss and Measurements n IEEE WLANs wth TCP and UDP Traffc Flows, IEEE Transacton on Moble Computng, Vol. 7, No. 2, pp , [11] A. Botta, A. Danorr and A. Pescape, A Tools for the Generaton of Realstc Network Workload for Emergng Networkng Scenaros, Journal of Computer Networks, Vol. 56, No. 15, pp , [12] A. Botta, W. Donato and A. Danorr, D-ITG Manual, Computer for Interacton and Communcatons (COMICS) Group, pp. 3-6, [13] I. Abuzah and N.Shakarneh, A Revew of Genetc Algorthm Optmzaton, Internatonal Journal of Physcal, Nuclear Scence and Engneerng, Vol. 7, No. 12, pp , [14] S. Karam and S. B. Shokouh, Optmal Herarchcal Remote Sensng Image Clusterng usng Imperalst Compettve Algorthm, Recent Advances n Computer Scence and Informaton Engneerng, Vol. 124, No. 1, pp , [15] S. Arsh, A. Amr and K. Noor, FICA: Fuzzy Imperalst Compettve Algorthm, Journal of Zhejang Unversty SCIENCE C, Vol. 15, No. 5, pp , [16] S. Najaf Ravadanegh, A Multstage Expanson Plannng Method for Optmal Substaton Placement, Iranan Journal of Electrcal & Electronc Engneerng, Vol. 10, No. 1, pp , [17] E. Atashpaz-Gargar, F. Hashemzadeh and C. Lucas, Evolutonary Desgn of PID Controller for a MIMO Dstllaton Column usng Colonal Compettve Algorthm, Internatonal Journal of Intellgent Computng and Cybernetcs, Vol. 1, No. 3, pp , [18] M. R. Mosav and A. A. Akhyan, PMU Placement Methods n Power Systems based on Evolutonary Algorthms and GPS Recever, Iranan Journal of Electrcal & Electronc Engneerng, Vol. 9, No. 2, pp , [19] M. Abed and S. Jall, An Ant Colony Optmzaton Algorthm for network Vulnerablty Analyss, Iranan Journal of Electrcal & Electronc Engneerng, Vol. 2, No. 3, pp , [20] R. Hooke and T. A. Jeeves, Drect Search Soluton of Numercal and Statstcal Problems, Journal of the ACM (JACM), Vol. 8, No. 2, pp , Mohammad-Reza Mosav receved hs B.Sc., M.Sc., and Ph.D. degrees n Electronc Engneerng from Iran Unversty of Scence and Technology (IUST), Tehran, Iran n 1997, 1998, and 2004, respectvely. He s currently faculty member of Department of Electrcal Engneerng of IUST as professor. He s the author of more than 210 scentfc publcatons on journals and nternatonal conferences. Hs research nterests nclude crcuts and systems desgn. processng. Fatemeh Farab receved her B.Sc. degree n Computer Engneerng from Iran Unversty of Scence and Technology n 2009 and her M.Sc. degree n Computer Engneerng from Unversty of Islamc Azad of Qazvn n Hs research nterests nclude computer networks and ntellgent systems. Samaneh Karam receved her B.Sc. degree n Electrcal Engneerng from Amrkabr Unversty, Tehran, Iran n 2006 and the M.Sc. degree n Electrcal Engneerng from Iran Unversty of Scence and Technology (IUST), Tehran, Iran n She s currently Ph.D. student n IUST. Her research nterests are sgnal and mage 108 Iranan Journal of Electrcal & Electronc Engneerng, Vol. 11, No. 2, June 2015

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