Research Article Towards the Novel Reasoning among Particles in PSO by the Use of RDF and SPARQL

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1 e Scentfc World Journal, Artcle I , 10 pages Research Artcle Towards the Novel Reasonng among Partcles n PSO by the Use of RF and SPARQL Iztok Fster Jr., 1 Xn-She Yang, 2 Karn LjubI, 3 ušan Fster, 1 Janez Brest, 1 and Iztok Fster 1 1 Unversty of Marbor, Faculty of Electrcal Engneerng and Computer Scence, Smetanova 17, 2000 Marbor, Slovena 2 Mddlesex Unversty Hendon Campus, London NW4 4BT, UK 3 Unversty of Marbor Faculty of Medcne, Taborska 8, 2000 Marbor, Slovena Correspondence should be addressed to Iztok Fster Jr.; ztok.fster2@un-mb.s Receved 15 January 2014; Accepted 26 February 2014; Publshed 27 March 2014 Academc Edtors: N. Chakrabort, P. Meln, and F. Ner Copyrght 2014 Iztok Fster Jr. et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. The sgnfcant development of the Internet has posed some new challenges and many new programmng tools have been developed to address such challenges. Today, semantc web s a modern paradgm for representng and accessng knowledge data on the Internet. Ths paper tres to use the semantc tools such as resource defnton framework (RF) and RF query language (SPARQL) for the optmzaton purpose. These tools are combned wth partcle swarm optmzaton (PSO) and the selecton of the best solutons depends on ts ftness. Instead of the local best soluton, a neghborhood of solutons for each partcle can be defned and used for the calculaton of the new poston, based on the key deas from semantc web doman. The prelmnary results by optmzng ten benchmark functons showed the promsng results and thus ths method should be nvestgated further. 1. Introducton Searchng for the optmal solutons of the hardest realworldproblemssanactvefeldespecallyncomputer scence. An eternal desre of computer scentsts s to develop a general problem solver that wll be able to cope wth all classes of real-world problems. Unfortunately, the most of the so-called clever algorthms are subject of the No Free Lunch Theorem [1]. Regardng ths theorem, f one algorthm s good on one class of problems, t does not mean that t wll also be good on the other classes of problems. Especally, three domans of algorthms have recently been appeared n the role of general problem solver, as follows: Artfcal Intellgence (AI) [2], evolutonary algorthms (EA) [3], and Swarm Intellgence (SI) [4]. Whle the former mmcs operatng a human bran, the latter domans are nspred by nature. Evolutonary algorthms are nspred by arwnan prncples of natural evoluton [5] accordng to whch the fttest ndvduals have the greater possbltes for survval and pass on ther characterstcs to ther offsprng durng a process of reproducton. Nowadays, evolutonary computaton (AC) [6] captures the algorthms nvolved n evolutonary doman and t consders genetc algorthms (GA) [7], genetc programmng [8], evoluton strateges (ES) [9], evolutonaryprogrammng [10], and dfferental evoluton (E) [11 13]. The mentoned algorthms dffer between each other accordng to representaton ofndvdual.asaresult,thesekndsofalgorthmshavebeen appled to varous optmzaton, modelng, and smulaton problems. However, ths paper concentrates on the SI doman that s concerned wth the desgn of multagent systems wth applcatons, for example, n optmzaton and n robotcs [4]. Inspraton for the desgn of these systems s taken from the collectve behavor of socal nsects, lke ants, termtes, and bees, as well as from the behavor of other anmal socetes, lke flocks of brds or schools of fsh. Recently, there exst a lot of dfferent algorthms from ths doman that s stll beng developed. Let us menton only the most mportant members of the SI algorthms, as follows: the partcle swarm optmzaton (PSO) [14], the frefly algorthm (FA) [15, 16], cuckoo search [17], the bat algorthm (BA) [18, 19], and so forth.

2 2 The Scentfc World Journal The PSO s populaton-based algorthm that mmcs movement of the swarm of partcles (e.g., brds) by flyng across a landscape, thus searchng for food. Each partcle n PSO represents the canddate soluton of the problem to be solved. Poston of the partcle conssts of the problem parameters that are modfed when the vrtual partcle s moved n the search space. The moton depends on the current partcle poston and the current poston of local best and global best solutons, respectvely. The local best solutons denote the best solutons that are whenever arsen on the defnte locaton n the populaton, whle the current best s the best soluton whenever found n the whole populaton. Thssolutonhasthemanmpactonthedrectonofmovng the swarm towards the optmal soluton. When ths soluton s not mproved anymore, the populaton gets stuck nto a local optmum. Manly, we focused on the new defnton of the neghborhood wthn the PSO algorthm. In place of the local best solutons, the neghborhood s defned usng the predefned radus of ftness values around each canddate soluton, thus capturng all canddate solutons wth the ftness value nsde the predefned vrtual radus. The sze of ths neghborhoodcanbevarable.therefore,atleastonebut maxmum three canddate solutons can be permtted to form ths neghborhood. Although ths s not the frst try how to defne the varable neghborhood wthn the PSO algorthm [20 22], n ths paper, such neghborhood s defned usng the Resource escrpton Framework (RF), SPARQL Protocol, and RF query language (SPARQL) tools taken from semantc web doman. As a result, the modfed RF-PSO algorthm was developed. Both web tools are approprate for descrbng and manpulatng decentralzed and dstrbuted data. On the other hand, the orgnal PSO algorthm mantans a populaton of partcles that are also decentralzed n ther nature. An am of usng these web tools was to smulate a dstrbuted populaton of partcles, where each partcle s placed on the dfferent locaton n the Internet. The remander of ths paper s structured as follows. In Secton 2, we outlne a short descrpton of the PSO algorthm. The secton s fnshed by ntroducng the semantc web tools, that s, RF and SPARQL. Secton3 concentrates on development of the modfed RF-PSO algorthm. Secton 4 presents the conducted experments and results obtaned wth the RF-PSO algorthms. Fnally, Secton 5 summarzes our work and potental future drectons for the future work are outlned. 2. Background 2.1. Partcle Swarm Optmzaton. Partcle swarm optmzaton (PSO) was one of the frst SI algorthms to be presented at aninternatonalconferenceonneuralnetworksbykennedy and Eberhart n 1995 [14]. PSO s nspred by the socal foragng behavor of some anmals such as flockng behavor of brds (Fgure 1) andschoolngbehavoroffsh[23]. In nature, there are some ndvduals wth better developed nstnct for fndng food. Accordng to these ndvduals, the Fgure 1: PSO. whole swarm s drected nto more promsng regons n the landscape. The PSO s a populaton-based algorthm that conssts of N partcles x (t) =(x 1,...,x ) T representng ther poston n a -dmensonal search space. These partcles move across ths space wth velocty k (t) =(V 1,...,V ) T accordng to the poston of the best partcle x (t) best towards the more promsng regons of the search space. However, ths movement s also dependent on the local best poston of each partcle p (t) and s mathematcally expressed, as follows: k (t+1) = k (t) +c 1 r (t) 1 (p(t) x (t) ) +c 2 r (t) 2 (x(t) best x(t) ), for,...,n, where r (t) 1, r(t) 2 denote the random numbers drawn from the nterval [0, 1], andc 1, c 2 are constrcton coeffcents that determne the proporton, wth whch the local and global best solutons nfluence the current soluton. Then, the new partcle poston s calculated accordng to the followng expresson: x (t+1) = x (t) (1) + k (t), for,...,n. (2) Pseudocode of the PSO algorthm s llustrated n Algorthm 1. After fnshng the ntalzaton n functon nt partcles (Algorthm 1), the PSO algorthm optmzes a problem by teratvely mprovng the canddate soluton [24, 25]. Thus, two functons are appled. The functon evaluate the new soluton calculates the ftness value of partcles obtaned after ntalzaton or movement. The movement accordng to (1) and(2) s mplemented n the functon generate new soluton RF. The RF s an XML applcaton devoted to encodng, exchangng, and reusng structural metadata [26]. It enables the knowledge to be represented n symbolcal form. Fortunately, ths knowledge s human readable. On the other hand, t s understandable to machnes. The man characterstc of ths framework s that RF data can be manpulated on decentralzed manner and dstrbuted among varous servers on the Internet. Resources dentfed by Unform Resource Identfer (URI) are descrbed n RF graphs, where each resource representng the node has many propertes that are assocated wth the resource usng the

3 The Scentfc World Journal 3 Input: PSO populaton of partcles x =(x 1,...,x ) T for,...,n. Output: The best soluton x best and ts correspondng value f mn = mn(f(x)). (1) nt partcles; (2) eval =0; (3) whle termnaton condton not meet do (4) for to N do (5) f =evaluate the new soluton(x ); (6) eval = eval +1; (7) f f pbest then (8) p = x ; pbest =f ; // save the local best soluton (9) end f (10) f f f mn then (11) x best = x ; f mn =f ; // save the global best soluton (12) end f (13) x = generate new soluton(x ); (14) end for (15) end whle Algorthm 1: Pseudocode of the classc PSO algorthm. (1) <rdf:rf> (2) <rdf:escrpton rdf:about= > (3) <ns1:name>john</ns1:name> (4) <ns1:surname>smth</ns1:surname> (5) </rdf:escrpton> (6) </rdf:rf> Algorthm 2: Pseudocode of the Person descrpton n RF. property-type relatonshp. Ths relatonshp represents an edge n RF graph. Thus, attrbutes may be atomc n nature (e.g., numbers, text strngs, etc.) or represent other resources wth ther own propertes [27]. The resource, property-type relaton, and attrbute present a trplet sutable for presentaton n RF graph. A sample of ths graph s presented n Fgure 2,fromwhchtwo trples (also 2-trples) can be translated from the dagram. These 2-trples are wrtten nto a RF database. In general, the format of ths RF data s seralzaton of N-trples obtaned from the RF graphs. For nstance, the descrpton of RF database obtaned from the RF graph n Fgure 2 s presented n Algorthm SPARQL. RF enables data to be decentralzed and dstrbuted across the Internet. On the other hand, the SPARQL Protocol has been developed for accessng and dscoverng RF data. SPARQL s an RF query language that has ts own syntax very smlar to SQL queres. The SPARQL query conssts of two parts[28]. The former SELECT clause dentfes the varables that appear n the query results, whle the latter WHERE clause provdes the basc patterns that match aganst the RF graph. Usually, these query patterns consst of three parts denotng the resource name, propertytype relaton, and attrbute. As a result, the matched patterns are returned by the query. A sample of SPARQL query s llustrated n Algorthm 3. John Person: name Person Person: surname Smth Fgure 2: agram llustrates a resource Person n RF graph. The resource conssts of two atomc attrbutes John and Smth that are assgned to t wth relatons PERSON: Name and PERSON: Surname. In other words, the name of the person s John and the surname of the same person s Smth. Note that the word PERSON: denotes a locaton (URI), where a name space contanng the descrpton of semantcs for ths relaton s located. As a result of query presented n Algorthm 3, thename John and surname Smth are returned. 3. The Modfed RF-PSO Algorthm The modfed RF-PSO algorthm mplements two features: ()usngthevarableneghborhoodofcanddatesolutons n place of the local best solutons,

4 4 The Scentfc World Journal (1) SELECT?name?surname (2) WHERE { (3) < PERSON:Name?name. (4) < PERSON:Surname?surname. (5) } Algorthm 3: Example of SPARQL query. Input: PSO populaton of partcles x =(x 1,...,x ) T for,...,n. Output: The best soluton x best and ts correspondng value f mn = mn(f(x)). (1) nt partcles; (2) eval =0; (3) whle termnaton condton not meet do (4) for to N do (5) f =evaluate the new soluton(x ); (6) eval = eval +1; (7) f f f mn then (8) x best = x ; f mn =f ; // save the global best soluton (9) end f (10) N(x )={p j p j s neghbor of x }; (11) x = generate new soluton(x, N(x )); (12) end for (13) end whle Algorthm4:TheproposedRF-PSOalgorthm. () usng the RF for descrbng and SPARQL for manpulatng ths neghborhood. The man reason for applyng these well-known tools from the semantc web doman was to develop a dstrbuted populaton model that could later be used n other SI algorthms. On the other hand, we try to use the semantc web tools for optmzaton purposes as well. Fortunately, RF s sutable tool for descrbng the dstrbuted populaton models, n general. In the PSO algorthm, t s appled for descrbng the relatons between partcles n populaton. For our purposes, a relaton s negbour of s mportant that each partcle determnes ts neghborhood. Furthermore, SPARQL s used for determnng the partcles n ts neghborhood. As a result, the RF-PSO algorthm has been establshed, whose pseudocode s presented n Algorthm 4. The three man dfferences dstngush the proposed RF-PSO wth the orgnal PSO algorthm, as follows: () no local best solutons that are mantaned by the RF-PSO (lnes omtted n the Algorthm1), () defnng the neghborhood of canddate soluton (lne 10 n Algorthm 4), () generatng the new soluton accordng to the defned varable neghborhood relaton (lne 11 n Algorthm 4). The relaton N(x )={x j x j s neghbor of x j } (lne 10 n Algorthm 4)sdefnedaccordngtothefollowngrelaton: f abs (f (x j ) f(x )) R then x j N (x ), (3) where radus R defnes the necessary maxmum ftness dstanceoftwocanddatesolutonsthatcanbenneghborhood. In fact, ths parameter regulates the number of canddate solutons n the neghborhood. Here, the radus s expressed as R = N f(x ) / N. Indeed, the neghborhood captures all solutons wth the ftness dfferences less than the radus R.Typcally,whenthe radus R ssmall,theszeofneghborhoodcanalsobesmall. However, ths asserton holds f the populaton dversty s hgher enough. When the partcles are scattered across the search space, no partcles are located n the vcnty of each other. Consequently, the sze of neghborhood becomes zero. On the other hand, when the partcles are crowded around some ftter ndvduals, the number of ts neghbors can be ncreased enormously. In order to prevent ths underszng and overszng, the neghborhood sze s defned n such a manner that t cannot exceed the value of three and cannot be zero; n other words, N(x ) [1, 3]. For each observed partcle x,thenewsolutonsgenerated accordng to the number of neghbors N(x ) n generate new soluton functon. The followng modfed equaton s used n RF-PSO for calculatng the velocty: k (t+1) =w k (t) +c 1 r (t) 1 (x(t) best x(t) ) N(x j) j=1 c + [ j+1 r (t) j+1 (p(t) j x (t) ) (4) [ N (x ], ) ] where, r 1,andr 2 are the real numbers randomly drawn from the nterval [0, 1], c 1 and c 2 denote the constrcton

5 The Scentfc World Journal 5 (1) <rdf:rf> (2) <rdf:escrpton rdf:about= > (3) <ns1:member of rdf:resource= /> (4) <ns1:member of rdf:resource= /> (5) (6) <ns1:member of rdf:resource= /> (7) </rdf:escrpton> (8) <rdf:escrpton rdf:about= > (9) <ns1:s neghbor of rdf:href= /> (10) <ns1:s neghbor of rdf:href= /> (11) <ns1:d>1</ns1:d> (12) </rdf:escrpton> (13) (14) </rdf:rf> Algorthm 5: Pseudocode of the PSO populaton n RF. coeffcents, p (t) j ={x k x k s neghbor of x 1 k N}, j [1, N(x ) ], and N(x ) j=1 c j+1 = 1. Thus, t s expected that the movement of more crowded neghborhood depends on more neghbors. Furthermore, the term between square parenthess ensures that the proporton of each neghbor as determned by constrcton coeffcents {c 2,c 3,c 4 } never exceeded the value of one. Populaton ns1:about Partcle 1 ns1:d ns1:s neghbor of 1 Partcle 5 ns1:s neghbor of Partcle Representaton of a strbuted Populaton. The rapd growth of the Internet means that new knds of applcaton archtectures have been emerged. The Internet applcatons are sutable to explot enormous power of the computers connected to ths huge network. Typcally, these applcatons search for data dstrbuted on many servers. These data need to be accessed easly, securely, and effcently. Ths paper proposes the frst steps of developng the dstrbuted populaton model wthn the PSO algorthm. In lne wth ths, the RF tool s appled that ntroduces a descrpton of relatons between partcles n the populaton. These relatons make us possble to manpulate populaton members on a hgher abstracton level. At the moment, only the relaton s neghbor of s mplemented that determnes the neghborhood of a specfc partcle n the populaton. For ths purpose, RF s devoted for defnng the varous resources on dfferent Internet servers. In our case, each partcle n the populaton represents the resource that s defned wth correspondng property-type relaton (e.g., s neghbor of ) and attrbutes. The RF graph of the dstrbuted populaton s llustrated n Fgure 3. The defnton of a dstrbuted populaton n RF s presented n Algorthm 5, from whch t can be seen that two knds of attrbutes are encountered n ths defnton, that s, the references to neghbors of specfc partcle and ts sequence number. Some detals are omtted n ths algorthm becauseofthespacelmtatonofthspaper.themssng parts of code are denoted by punctuaton marks. Fgure 3: Ths PSO dstrbuted populaton model contans the defntons of resources populaton and partcle. Thus,each partcle can relate to one or more neghbors and has an dentfcaton number. The former represents a reference to other partcles n a swarm, whle the latter s an atomc value. (1) SELECT?partcle (2) WHERE { (3) < (4) < neghbor of> (5)?partcle (6) } Algorthm 6: SPAQL query that returns partcles n the neghborhood of partcle4. language, whose syntax s smlar to the standard SQL syntax. An example of SPARQL query for returnng the neghborhood of fourth partcle s represented n Algorthm 6. Note that the SPARQL query from the mentoned algorthm wll return all attrbutes that are related to the resource4 wth the relaton s neghbor of Accessng the strbuted Populaton. The dstrbuted populaton n RF can be accessed usng the SPARQL query 3.3. Implementaton etals. The proposed RF-PSO algorthm was mplemented n Python programmng language

6 6 The Scentfc World Journal Table 1: efntons of benchmark functons. f Functon name efnton f 1 Grewangk s functon f 1 (x) = f 2 Rastrgn s functon f 2 (x) =n 10+ n 1 f 3 Rosenbrock s functon f 3 (x) = n 1 f 4 Ackley s functon f 4 (x) = n cos ( x n )+ f 5 Schwefel s functon f 5 (x) = f 6 e Jong s sphere functon f 6 (x) = x 2 f 7 Easom s functon f 7 (x) = ( 1) ( f 8 Mchalewcz s functon f 8 (x) = f 9 Xn-She Yang s functon f 9 (x) =( n x (x 2 10cos (2πx )) 100 (x +1 x 2 )2 +(x 1) 2 (20 + e 20 e (x2 +1 +x2 ) e 0.5(cos(2πx +1)+cos(2πx )) ) x sn ( x ) cos 2 (x )) exp [ sn (x )[sn ( A x π )] x ) exp [ sn (x 2 )] f 10 Zakharov s functon f 10 (x) = x 2 +( 1 x 2 ) +( x ) (x π) 2 ] 4 and executed on Lnux operatng system. Addtonally, the followng lbrares were used: () rdflb whchsapythonlbraryforworkngwthrf [29], () NumPy that s the fundamental package for scentfc computng wth Python [30] () matplotlb that s a python 2 plottng lbrary [31]. The decson for usng Python has been taken because there already exsted a lot of the PSO mplementaton. Furthermore, the RF and SPARQL semantc tools are also supportednthslanguageandultmately,programmngn Python s easy. 4. Experments and Results The goal of our expermental work was to show that the semantc web tools, that s, RF and SPARQL can be useful for the optmzaton purposes as well. Moreover, we want to show that usng the varable neghborhood n RF-PSO can also mprove the results of the orgnal PSO. In lne wth ths, the RF-PSO algorthm was appled to the optmzaton of ten benchmark functons taken from lterature. The functon optmzaton belongs to a class of contnuous optmzaton problems, where the objectve functon f(x) s gven and x ={x 1,...,x } s a vector of desgn varables n a decson space S. Each desgn varable x [Lb,Ub ] s lmted by ts lower Lb R and upper Ub R bounds. The task of optmzaton s to fnd the mnmum of the objectve functons. In the remander of ths secton, the benchmark sute s descrbed; then, the expermental setup s presented and fnally, the results of experments are llustrated n detal Test Sute. The test sute conssted of ten functons, whchwereselectedfromthelterature.however,theprmary reference s the paper by Yang [32] that proposed a set of optmzaton functons sutable for testng the newly developed algorthms. The defntons of the benchmark functons are represented n Table 1, whle ther propertes are llustrated n Table 2. Table 2 conssts of fve columns that contan the functon dentfcatons (tag f), ther global optmum (tag f ), the values of optmal desgn varables (tag x ), the lower and upper bounds of the desgn varables (tag Bound), and ther characterstcs (tag Characterstcs). The lower and upper bounds of the desgn varables determne ntervals that lmt theszeofthesearchspace.thewdersthenterval,thewder s the search space. Note that the ntervals were selected, so that the search space was wder than those proposed n the standard lterature. The functons wthn the benchmark sute can be dvded nto unmodal and multmodal. The multmodal functons have two or more local optma. Typcally, themultmodalfunctonsaremoredffculttosolve.themost complex functons are those that have an exponental number of local optma randomly dstrbuted wthn the search space.

7 The Scentfc World Journal 7 Table 2: Propertes of benchmark functons. f f x Bounds Characterstcs f (0, 0,..., 0) [ 600, 600] Hghly mult-modal f (0,0,...,0) [ 15,15] Hghly mult-modal f (1,1,...,1) [ 15,15] Multple local optma f (0, 0,..., 0) [ , ] Hghly mult-modal f (0, 0,..., 0) [ 500, 500] Hghly mult-modal f (0, 0,..., 0) [ 600, 600] Un-modal, convex f (π,π,...,π) [ 2π,2π] Multple local optma f ( , ) 1 [0, π] Multple local optma f (0,0,...,0) [ 2π,2π] Multple local optma f (0,0,...,0) [ 5,10] Un-modal 1 These values are vald for dmensons = Expermental Setup. Ths expermental study compares the results of the RF-PSO usng dfferent knd of dstrbuted populatons wthn the orgnal PSO algorthm. All PSO algorthms used the followng setup. The parameter w was randomly drawn from the nterval [0.4, 0.9], whle the constrcton coeffcents were set as c 1 = c 2 = 1.0. Asatermnatoncondton,thenumberofftnessfuncton evaluatonswasconsdered.itwassettofes = 1000, where denotes dmenson of the problem. In ths study, three dfferent dmensons of functons were appled; that s, =10, =30,and=50.However,thepopulatonszes a crucal parameter for all populaton-based algorthms that have a great nfluence on ther performance. In lne wth ths, extensve experments had been run n order to determne the most approprate settng of ths parameter by all algorthms n the test. As a result, the most approprate settng of ths parameter N = 100 was consdered for the experments. Parameters, lke the termnaton condton, dmensons of the observed functons, and the populaton sze were also used by the other algorthms n experments. The PSO algorthms are stochastc n nature. Therefore, statstcal measures, lke mnmum, maxmum, average, standard devaton, and medan, were accumulated after 25 runs of the algorthms n order to farly estmate the qualty of solutons Results. The comparatve study was conducted n whch we would lke to show, frstly, that the semantc web tools can be successfully appled to the optmzaton purposes as well and, secondly, that usng the dstrbuted populaton affects the results of the orgnal PSO algorthm. In the remander of ths secton, a detaled analyss of RF-PSO algorthms s presented Analyss of the RF-PSO Algorthms. In ths experment, the characterstcs of the RF-PSO algorthm were analyzed. In lne wth ths, the RF-PSO wth neghborhood sze of one (RF1), the RF-PSO wth neghborhood sze of two (RF2), and the RF-PSO wth neghborhood sze of tree (RF3) were compared wth the orgnal PSO algorthm (PSO) by optmzng ten benchmark functons wth dmensons = 10, = 30,and = 50.Theobtanedresults by the optmzaton of functons wth dmenson =30are aggregated n Table 3.Note that the best average values are for each functon presented bold n the table. From Table 3, t can be seen that the best average values were obtaned by the RF-1 algorthm eght tmes, that s, by f 1 f 4, f 6, f 8,andf 10. The best results were two tmes observed also by the orgnal PSO algorthm, that s, f 5 and f 9. On average, the results of the other two RF-PSO algorthms, that are, RF-2 and RF-3, were better than the results of the orgnal PSO algorthm. In order to statstcally estmate the qualty of soluton, the Fredman nonparametrc test was conducted. Each algorthm enters ths test wth fve statstcal measures for each of observed functons. As a result, each statstcal classfer (.e., varous algorthms) conssts of 5 10=50dfferent varables. The Fredman test [33, 34] compares the average ranks of the algorthms. The closer the rank to one, the better s the algorthm n ths applcaton. A null hypothess states that two algorthms are equvalent and, therefore, ther ranks should be equal. If the null hypothess s rejected, that s, the performance of the algorthms s statstcally dfferent, the Bonferron-unn test [35] s performed that calculates the crtcal dfference between the average ranks of those two algorthms. When the statstcal dfference s hgher than the crtcal dfference, the algorthms are sgnfcantly dfferent. The equaton for the calculaton of crtcal dfference can be found n [35]. Fredman tests were performed usng the sgnfcance level The results of the Fredman nonparametrc test are presented n Fgure4 where the three dagrams show the ranks and confdence ntervals (crtcal dfferences) for the algorthms under consderaton. The dagrams are organzed accordng to the dmensons of functons. Two algorthms are sgnfcantly dfferent f ther ntervals do not overlap. The frst dagram n Fgure 4 shows that the RF-1 algorthm sgnfcantly outperforms the RF-3 algorthm. Interestngly, the results of the orgnal PSO are also better than the results of the RF-2 and RF-3 algorthm. The stuaton s changed n the second (by = 30)andthrd dagram (by = 50), where RF-3 mproves the results

8 8 The Scentfc World Journal Table 3: Comparng the results of dfferent PSO algorthms ( =30). Alg. Meas. f 1 f 2 f 3 f 4 f 5 Best 7.40E E E E E Worst 1.41E E E E E PSO Mean 1.06E E E E E Stev 1.06E E E E E Mean 1.37E E E E E Best 8.87E E E E E Worst 3.33E E E E E RF-1 Mean 3.40E E E E E Stev 1.27E E E E E Medan 6.91E E E E E Best 1.10E E E E E Worst 2.42E E E E E RF-2 Mean 6.03E E E E E Stev 4.12E E E E E Mean 5.80E E E E E Best 3.07E E E E E Worst 2.52E E E E E RF-3 Mean 8.94E E E E E Stev 7.62E E E E E Mean 5.51E E E E E Evals Meas. f 6 f 7 f 8 f 9 f 10 Best 1.10E E E E E 001 Worst 3.75E E E E E PSO Mean 1.13E E E E E Stev 6.89E E E E E Mean 1.24E E E E E Best 7.80E E E E E 012 Worst 3.55E E E E E 007 RF-1 Mean 3.83E E E E E 008 Stev 2.97E E E E E 009 Mean 8.15E E E E E 007 Best 6.63E E E E E 001 Worst 2.03E E E E E RF-2 Mean 4.36E E E E E Stev 1.48E E E E E Mean 5.58E E E E E Best 5.21E E E E E Worst 2.09E E E E E RF-3 Mean 8.47E E E E E Stev 8.14E E E E E Mean 5.73E E E E E oftherf-3andtheorgnalpso,butnottherf-2 algorthm. Addtonally, the RF-2 s sgnfcantly better than the orgnal PSO also by =50. In summary, the RF-1 exposes the best results between all the other algorthms n tests by all observed dmensons of functons. On the other hand, the orgnal PSO algorthm s only comparable wth the modfed PSO algorthms by optmzng the low dmensonal functons ( = 10). The queston why the RF-PSO wth neghborhood sze of one outperformed the other RF-PSO algorthms remans open for the future work. At ths moment, t seems that here the prmary role plays the constrcton coeffcents that determne an nfluence of specfc neghbors. 5. Concluson The am of ths paper was twofold. Frst s to prove that the semantc web tools, lke RF and SPARQL, can also

9 The Scentfc World Journal 9 RF-3 RF-2 RF-1 PSO Average rank ( = 10) Average rank ( = 30) Average rank ( = 50) (a) (b) (c) Fgure 4: Results of the Fredman nonparametrc test. be used for the optmzaton purposes. Second s to show that the results of the modfed RF-PSO usng the varable neghborhood are comparable wth the results of the orgnal PSO algorthm. In lne wth the frst hypothess, a dstrbuted populaton model was developed wthn the PSO algorthm that s sutable for descrbng the varable neghborhood of partcles n the populaton. Furthermore, movng partcles across the search space depends on all the partcles n the neghborhood n place of the local best solutons as proposed n the orgnal PSO algorthm. In order to confrm the second hypothess, the benchmark sute of ten well-known functons from the lterature was defned. The results of extensve experments by optmzaton of benchmark functons showed that the optmal neghborhood sze wthn the RF-PSO algorthm s one (RF1). Ths varant of the RF-PSO also outperformed the orgnal PSO algorthm. The dstrbuted populaton model extends the concept of populaton n SI. Ths means that the populaton s no longer a passve data structure for storng partcles. Not only can the partcles now be dstrbuted, but also some relatons can be placed between the populaton members. In ths proof of concept, only one relaton was defned, that s, s neghbor of. Addtonally, not the whole defnton of the dstrbuted populaton was put onto Internet at ths moment. Although we are at the begnnng of the path of how to make an ntellgent partcle n swarm ntellgence algorthms, the prelmnary results are encouragng and future researches would nvestgate ths dea of dstrbuted populaton models n greater detal. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. References [1]. H. Wolpert and W. G. Macready, No free lunch theorems for optmzaton, IEEE Transactons on Evolutonary Computaton, vol. 1, no. 1, pp , [2] S. Russell and P. Norvg, Artfcal Intellgence: A Modern Approach, Prentce Hall, New York, NY, USA, [3] A. E. Eben and J. E. Smth, Introducton to Evolutonary Computng, Sprnger, Berln, Germany, [4] C. Blum and. Merkle, Swarm Intellgence: Introducton and Applcatons, Sprnger, Berln, Germany, [5] C. arwn, The Orgn of Speces, JohnMurray,London,UK, [6] W. Paszkowcz, Genetc algorthms, a nature-nspred tool: survey of applcatons n materals scence and related felds, Materals and Manufacturng Processes, vol.24,no.2,pp , [7]. Goldberg, Genetc Algorthms n Search, Optmzaton, and Machne Learnng, Addson-Wesley, Massachusetts, Mass, USA, [8] J. Koza, Genetc Programmng 2 Automatc scovery of Reusable Programs, The MIT Press, Cambrdge, Mass, USA, [9] T. Bck, Evolutonary Algorthms n Theory and Practce Evoluton Strateges, Evolutonary Programmng, Genetc Algorthms, Unversty Press, Oxford, UK, [10] L. Fogel, A. Owens, and M. Walsh, Artfcal Intellgence through Smulated Evoluton, John Wley & Sons, New York, NY, USA, [11] R. Storn and K. Prce, fferental evoluton a smple and effcent heurstc for global optmzaton over contnuous spaces, Journal of Global Optmzaton, vol. 11, no. 4, pp , [12] J. Brest, S. Grener, B. Boškovć, M. Mernk, and V. Žumer, Self-adaptng control parameters n dfferental evoluton: a comparatve study on numercal benchmark problems, IEEE Transactons on Evolutonary Computaton, vol.10,no.6,pp , [13] S. as and P. N. Suganthan, fferental evoluton: a survey of the state-of-the-art, IEEE Transactons on Evolutonary Computaton,vol.15,no.1,pp.4 31,2011. [14] J. Kennedy and R. Eberhart, Partcle swarm optmzaton, n Proceedngs of the IEEE Internatonal Conference on Neural Networks, vol. 4, pp , IEEE, Perth, Australa, ecember [15] I. Fster, I. Fster Jr., X. -S. Yang, and J. Brest, A comprehensve revew of frefly algorthms, Swarm and Evolutonary Computaton,vol.13,pp.34 46,2013.

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11 Journal of Advances n Industral Engneerng Multmeda The Scentfc World Journal Appled Computatonal Intellgence and Soft Computng Internatonal Journal of strbuted Sensor Networks Advances n Fuzzy Systems Modellng & Smulaton n Engneerng Submt your manuscrpts at Journal of Computer Networks and Communcatons Advances n Artfcal Intellgence Internatonal Journal of Bomedcal Imagng Advances n Artfcal Neural Systems Internatonal Journal of Computer Engneerng Computer Games Technology Advances n Advances n Software Engneerng Internatonal Journal of Reconfgurable Computng Robotcs Computatonal Intellgence and Neuroscence Advances n Human-Computer Interacton Journal of Journal of Electrcal and Computer Engneerng