Bio-Inspired Clustering of Complex Products Structure based on DSM

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1 (IJACSA) Interntionl Journl of Avnce Computer Science n Applictions, Vol., No. 8, 0 Bio-Inspire Clustering of Complex Proucts Structure bse on DSM Fn Yng Institute of Systems Science n Engineering Wuhn University of Technology College of Computer Hubei University of Euction Wuhn, Chin Pn Wng*, Sihi Guo*, Qibing Lu Institute of Systems Science n Engineering Wuhn University of Technology Wuhn, Chin Xingxing Liu School of Mngement Wuhn University of Technology Wuhn, Chin Abstrct Clustering plys n importnt role in the ecomposition of complex proucts structure. Different clustering lgorithms my chieve ifferent effects of the ecomposition. This pper ims to proposes bio-inspire genetic lgorithm tht is implemente bse on its relible fitness function n esign structure mtrix (DSM) for clustering nlysis of complex proucts. This new bio-inspire genetic lgorithm cptures the fetures of DSM, which is bse on the biologicl evolution theory. Exmples of these proucts inclue motorcycle engines tht re presente for clustering. The five cluster lterntives re obtine from the regulr clustering lgorithm n the bio-inspire genetic lgorithm, while the best cluster lterntive comes from the bio-inspire genetic lgorithm. The results show tht this lgorithm is well ptble, especilly when the prouct elements hve complicte n symmetric connections. Keywors Bio-inspire computtion; genetic lgorithm (GA); relible fitness function; DSM; complex proucts; clustering I. INTRODUCTION In this cse, complex proucts re those whose structure is more complicte n whose moule prtition is scttere. There re mny methos for the esigning the physicl structure of complex proucts, incluing the DSM metho [], the Htley/Pirbh metho [], the stochstic block moel [], n biclustering in mchine lerning. With fierce competition in the mnufcturing inustry, however, the issue of physicl structure is problem worthy of concern. The clustering methos for the physicl structure of complex proucts re thus key consiertion for core competition in business. In recent yers, stuies on the function moule prtition hve been frequently iscusse. The gol is to construct symmetric mtrix, trnsforme from ttributes of mny proucts [, ]. Then, the scholrs crete new methos to el with this mtrix, in orer to gther similr elements for optimize clustering. Erixon et l. [] propose moule prtition metho bse on impct fctors like technologicl innovtion, plnning, prmeters, n style. Gu et l. [7] propose prouct moulriztion for life cycle engineering, metho of constructing correltion mtrixes for the stge trgets. At this time, the esign professors then select the better moule prtition result by compring the results from ifferent esign objectives. Slhieh et l. [8] use esign for moulrity *Corresponing uthors. by the Fuzzy Theory, quntittive escription n nlysis lgorithm. Stone et l. [9] use heuristic metho for ientifying moules for prouct rchitectures bse on energy flow, mteril flow, n signl flow in rchitecture chrts. Go et l. [0] ientify functionl moules using generlize irecte grphs. Chen et l. [] propose the ynmic cluster nlysis of fuzzy equivlence mtrix to be pplie to ynmic prtition function moule. The bove stuies offer better routes for structuring prtitions for new proucts, but few of them consier the physicl structure or the symmetric connections between prouct components. DSM, first propose by Dr. Stewr, coul solve these problems prtly []. It consists of mtrix with homogenous rows n columns, n the vlue of ech cell is not rnom probbility. Thus, it is ifferent from the mtrix in the Stochstic Block Moel or the biclustering moel. Mny stuies concentrte on how to cluster n evlute the moule prtition bse on DSM []. For the efficiency of clustering, some stuies use GA for ientifying moules. Tseng et l. [] use grouping genetic lgorithm for clustering the components. Crossover mechnisms re moifie ccoring to the nee of moulr esign by resonble evlution. Zhou et l. [] propose function moule prtition metho for innovtive prouct esign in orer to meet customers iverse requirements n to shorten esign n ssembly time. Liu et l. [] estblish metho of ecomposition n clustering of the prouct rchitecture performe by GA. Their metho is bse on builing the prouct with DSM. With the help of litertures [,, ], in this pper, bioinspire genetic lgorithm is propose for components cluster bse on DSM. This lgorithm uses more resonble fitness function n n symmetric mtrix. Compre with regulr cluster metho, the bio-inspire genetic lgorithm is suitble for cluster optimize for complex prouct rchitecture. II. DSM IMPLEMENTATION AND EVALUATION The im of DSM is to ecompose elements of prouct first, n then ivie the elements into ifferent clusters. It is possible tht ll the elements my cluster into one, etermine by the connection egree between elements. Finlly, the best one cn be selecte by severl ifferent cluster lterntives through n evlution function. 8 P g e

2 (IJACSA) Interntionl Journl of Avnce Computer Science n Applictions, Vol., No. 8, 0 A. Physicl DSM DSM is prouct engineering mtrix tool, which hs four pplictions: components clustering, tem esign, tsk ssign n ction esign []. The first one is use here. Ech element in DSM correspons to ech component of the prouct. Cells inicte the connection mong elements, except those tht re igonl. Empty cells men no connection between corresponing elements, while cells with high vlue inicte high connections intensity. As shown in figure, six components s (,,,,, ) compose prouct A. The vlue of the connection egree between n is two. Prouct A cn be ivie into three moules using mnul clssifiction. Moule inclues,, n. Moule inclues n. Moule inclues only. The reltions of spce, energy, informtion, or mteril coul be consiere to confirm the vlue of the connection egree with the weighte verge. A lrger connection egree shows tht closer reltionship between the two elements. initil moel () Moule Moule Moule Fig.. DSM of prouct A mnul clustering (b) B. Clustering n evlution function The evlution influences the clustering process. The common simple clustering lgorithm is bse on specific evlution functions, which re performe using softwre tools like SPSS n Mtlb. In these tools, the clustering methos re lmost the sme, mening tht it is necessry to generte symmetric mtrix. We lso must complete clustering with evlution methos using mximum or minimum istnce s prmeter. This mtrix is similr to the DSM mentione bove, with the exception of igonl symmetry. The internl concentrtion n the externl linkge egree re key prmeters to the cluster lterntives. They cn be clculte by symmetricl DSM n the relte formul fter elements clustering. Then, the cluster lterntive with the higher internl concentrtion n the lower externl linkge egree is consiere to be the better one. In orer to obtin resonble evlution moel, the eqution for the internl concentrtion n the externl linkge egree re set with some ssumptions. The elements in DSM representing components of prouct often convert into one or more moules fter clustering. The ssumptions re s follows: ) Assume prouct is comprise of m components. The number of components is the sme s the elements of DSM. The DSM is m m mtrix. An ij is the vlue t the ith row, jth column (expresse cell (i,j)) in DSM where i, j (0,m). It represents the vlue of connection egree. ) The iniviul element mens it is the only element in moule where the internl concentrtion is 0. ) Overlpping elements re llowe, mening tht one element my belong to two or more moules. ) Unless correltion occurs, clusters ecompose. We mximize the totl internl concentrtion vlue n minimize the totl externl linkges. ) Assume g s the internl concentrtion of the th moule. For the purpose of system optimiztion, g is in irect proportion to the totl vlue of cells in the th moule; while it is inversely proportionl to the number of connections insie the th moule. A higher totl vlue shows strong cohesion, while the more connections my isperse the concentrtion. The formul for the internl concentrtion of the th moule is s follows: 0, k g ( ij ), k k( k ), i, jm () Assume the totl number of moules is D; k is the number k mens the cse of the only of elements in th moule. element in moule where the internl concentrtion is 0, nmely the "iniviul element". The totl vlue of internl concentrtion of system G is given by: D G g ) Assume r b s the externl linkges between th n bth moules. Also, for the purpose of optimizing the system, r b is in irect proportion to the totl vlue of cells between the th n the bth moules. It mens tht the higher the totl vlue, the tighter the connection between the two moules. The formul for the externl linkges between the th n the bth moules is s follows: r b i, jb ij The totl vlue of externl linkges of system R is s follows: R D D r b b () () () 8 P g e

3 (IJACSA) Interntionl Journl of Avnce Computer Science n Applictions, Vol., No. 8, 0 7) Accoring to the explntion of G n R, it is obvious tht higher G n smller R mens better clustering effect. Thus, the evlution vlue cn be set s follows: F G R () III. THE BIO-INSPIRED GENETIC ALGORITHM A. Fitness function When prouct is not complex, it cn cluster the DSM with mnul methos. The optiml lterntive cn then be selecte with the bove evlution moel from the set of lterntives. However, in the cse tht there re too mny components, connections between components re me complicte, n hnling it mnully is no longer suitble. In this section, the GA with n optimize fitness function is presente to select the clustere lterntives. Let s tke prouct A s n exmple. One of its chromosomes n the clustere lterntive is shown in Tble. It cn be escribe s 0-mtrix. When n element belongs to cluster, the gene vlue is, others re 0. The elements in one column shoul not ll be 0, mening n element must belong to one or more cluster(s). The length of chromosome is D m, D m/. TABLE I. THE CLUSTERING OF MODULES AND THE ENCODING OF A CHROMOSOME Encoing of chromosome Mo ule Mo ule Mo ule The chromosome 0-mtrix cn be presente s: rst () The corresponing clustering lterntive is: A,,,,, Bse on formuls () to (), the fitness function of every chromosome cn be esigne s: F( h) F Fit F F mx min min Where F(h) is the evlution vlue of the hth chromosome, F mx n F min is the mximum n the minimum respectively. Then, the selection probbility is: (7) (8) ph ( ) Fh ( ) n h Fh ( ) B. The flow of the bio-inspire lgorithm The equtions re n exception to the prescribe specifictions of this templte. You will nee to etermine whether or not your eqution shoul be type using either the Times New Romn or the Symbol font (plese no other font). To crete multilevele equtions, it my be necessry to tret the eqution s grphic n insert it into the text fter your pper is style. The prmeters, specificlly chromosome size n, crossover, n muttion probbility, of the bio-inspire genetic lgorithm re fixe priori. Bse on the fitness function n the selection probbility bove, the steps of the GA re s follows: Step : Generte rnomly n chromosomes, ctully 0- mtrixes by the requirement bove; Step : Generte corresponing clustere lterntives from chromosomes; Step : Clculte the evlution vlues of the lterntions bse on the evlution function; Step : Clculte the fitness function vlues n the selection probbilities bse on the evlution vlues; Step : Select the top m chromosomes n eliminte the b ones, n s new chromosomes so s to the totl number is n; Step : Relize the crossover n muttion with the - imension multiple-points crossover n -imension bsic muttion [] (the suitble vlues my be obtine by triln-error.). Step 7: Juge the terminte conition if the optiml one in one genertion keeps constntly evolves, stop; for others, return to step. IV. CASE STUDY A. Construction of the DSM For exmple, motorcycle engine with seventeen components woul crete DSM mtrix like Tble by experts evlution n the AHP metho. TABLE II DSM MATRIX (9) P g e

4 vlue (IJACSA) Interntionl Journl of Avnce Computer Science n Applictions, Vol., No. 8, TABLE III. COMPREHENSIVE EVALUATION ALTERNATIVES B. Regulr clustering Clustering it with MATLAB, firstly the symmetric mtrix is trnsferre into the symmetric one, tking the mens of ij n ji s the new ij n ji. The following results re obtine by opting the clustering lgorithm of the MATLAB (for better effectiveness, the element n re eliminte, n regre s inepenent elements). Then severl clustering lterntives cn be obtine: A ={[,7],[],[,,],[],[,7,8,9],[0,,],[,,,]} A ={[,7],[],[,,,7,8,9],[],[0,,],[,,,]} A ={[,7],[],[,,],[],[7,8,9],[0,,],[,,,]} A ={[,7],[],[,],[],[,7,8,9],[0,,],[,,,]} C. Genetic clustering Consiering the t in Tble, the genetic lgorithm is opte for clustering. When compre with the rnomness of the originl chromosomes, the results obtine by running the lgorithm re quite ifferent. The optiml one (shown s in Fig. ) is obtine from the mny itertions. In Fig., the x-coorinte represents the number of itertions n the y-coorinte mens the optiml vlue of ech genertion n the globl optimum is gotten in the erly evolution. From A, in Tble, elements n re shown s inepenent, while element is overlpping. A ={[,0,,],[8],[],[,9],[,7],[,,,7,,,,]} itertions Fig.. Genetic clustering A A A A A cluster lterntives [,7],[],[,,],[],[,7,8,9], [0,,],[,,,] [,7],[],[,,,7,8,9],[], [0,,],[,,,] [,7],[],[,,],[],[7,8,9], [0,,],[,,,] [,7],[],[,],[],[,7,8,9], [0,,],[,,,] [,0,,],[8],[],[,9], [,7],[,,,7,,,,] Tble shows the vlues of the five comprehensive evlution lterntives. Among them, the result of the genetic clustering is the best. The genetic clustering not only ccelertes optimiztion, but lso obtins high qulity. Moreover, lterntives,, re better thn lterntive, showing tht element shoul not belong to two clusters. V. CONCLUSIONS In this pper, the bio-inspire lgorithm with relible fitness function n DSM for complex proucts is propose. This genetic lgorithm cn chieve the better effect for ecomposing complex proucts. Compring the results of the regulr clustering n this genetic lgorithm, the bsic conclusions re s follows: () the regulr clustering metho hs limite rnge of pplictions; it cnnot pt to the physicl structure clustering of complex proucts; especilly, in the cse of the connection mtrix being symmetric, the optiml cluster lterntive cnnot be obtine by the regulr clustering; () it is significnt tht this genetic lgorithm is esigne with the fitness function n evlution function for clustering; () Introucing of the overlpping elements shows the better effect. Menwhile, the inepenent elements my pper in some sitution. However this genetic lgorithm is lck of consiering efficiency. There my be other methos to improve these clustering results, so the lgorithm cn be further improve. ACKNOWLEDGMENT This work ws supporte in prt by the Chinese Ntionl Nturl Science Fountion (No. 778); Chin postoctorl Fun Projects (No. 0 M080); Chin postoctorl Fun Specil projects (No.0T7070). REFERENCES Vlue [] R. ZhiJun, L. Ming, D. Binbin, C. Kuisheng, Anlysis of clustering hierrchy for prouct esign structure, Journl of Wuhn University of Science n Technology, vol. 8, pp. 90-9, June 0. [] A. Trek, E. Ho, Optimum grnulrity level of moulr prouct esign rchitecture, CIRP Annls - Mnufcturing Technology. vol., pp. -, April 0. [] J. Pnremenos, G. Chryssolouris, A neurl network pproch for the evelopment of moulr prouct rchitectures, Interntionl Journl of Computer Integrte Mnufcturing, vol., pp , September 0. [] B. Xioyong, Z. Tinxu, Z. Xiolong, Y. LuXin, L. Bo, Clusteringbse extrction of ner borer t smples for remote sensing imge clssifiction, Cognitive Computtion, vol., pp. 9-, Mrch 0. [] M. K. Prg, S. J. Tim, H. L. Robin, H. M. John., Clustering of gze uring ynmic scene viewing is Preicte by Motion, Cognitive Computtion, vol., pp. -, Mrch P g e

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