Tourism Demand Forecasting by Improved SVR Model

Transcription

1 Internatonal Journal of u- and e- Servce, Scence and Technology, pp Tours Deand Forecastng by Iproved SVR Model L Me Departent of Socal Servces,Zhengzhou Tours College,Henan,PRChna hnl00@63co Abstract The nboard tours deand forecastng s very portant to the developent of tours ndustry In ths paper, the SVR odel s adopted to forecast onthly nbound tours deand of Chna And the eltst Non-donated Sortng Genetc Algorth (NSGAII) s used to paraeter optzaton The NSGAII algorth can reduce coplexty of the algorth, keeps the dversty of populaton and ncreasng the forecastng accuracy At last, the proposed NSGAII-SVR odel s used to forecast onthly nbound tours deand of Chna fro July 0 to Deceber 0 And the experental results show that the NSGAII-SVR has the best perforance on forecastng copared wth other odels Keywords: Forecast, tours deand, SVR, NSGA Introducton Wth the globalzaton of the econoy and nternatonal exchanges contnuous to deepen, the nternatonal tours ndustry has been seen rapd developent Lots of countres have forulated polces to support and encourage the developent of tours ndustry The tours ndustry has rreplaceable functon n the balance of nternatonal payents and trade structure proveent It also plays an portant role on expandng the openng to the outsde world and prootng exchanges and cooperaton wth other countres Therefore, n the past 0 years, the study of tours ndustry got an unprecedented developent Whle tours deands forecastng s the focus of the study The tours deand forecastng have been studed by any researches [-] Early tours deand forecastng ethods anly use the econoetrcs odels [3-4] However, the econoetrcs odels are te-consung and dffcult to deterne the defect nfluence factor The te seres odel does not have to seek nner relatonshp between tours deand and nfluence factors copared wth econoetrcs odels It seeks nner relatons by the data of tours deand tself So n soe ways, te seres odel s ore sutable for tours deand forecastng The te seres odels nclude exponental soothng odel, Autoregressve odel(ar), Autoregressve and Movng Average Model(ARMA), Autoregressve Integrated Movng Average Model(ARIMA) etc These odels have been successfully used n tours deand forecastng[5-0] In recent years, the artfcal neural network odel (ANN) s wdely used n any research felds because of ts good ablty to handle coplex nonlnear functons[-5] And lots of researches also adopted neural network n tours deand forecastng[6-8] However, the neural network odel has ther own shortcongs, such as slow tranng speed, low generalzaton ablty, easy to fall nto local optu etc Support vector achne(svm) was proposed by Vapnk n 995[9] Support vector achne s a new algorth whch s based on the prncple of structural rsk nzaton as the foundaton It s better than the other algorths whch are based on the prncple of eprcal rsk nzaton At the sae te, t can guarantee the extreal soluton s global optal soluton because t s a convex secondary optzaton proble SVM can solve the probles whch characterstcs are sall saple, non-lnear, hgh denson and local ISSN: IJUNESST Copyrght c 05 SERSC

2 Internatonal Journal of u- and e- Servce, Scence and Technology na Qao et al[0] proposed a Bayesan evdence fraework to nfer the LS-SVR odel paraeters The results show that the Bayesan fraework of an LS-SVR sgnfcantly proves the speed and accuracy of the forecast Hong et al [] eploys GA-SA algorth to choose the sutable paraeter cobnaton for a SVR odel and used the SVRGA SA odel to forecast Tawanese 3G oble phone deand He et al[] used rando saplng ethod to prove SVM odel and dscussed coercal bank custoer churn predcton based on SVM odech et al [3] nvestgated the accuracy of the hybrd SVM-QPSO odel (support vector achne-quantu behaved partcle swar optzaton) n predctng onthly streaflows And t s eployed n forecastng the streaflow values of Vjayawada staton and Polavara staton of Andhra Pradesh n Inda In ths paper, the overall structure of the study s as follows: In secton, we frst ntroduce the standard SVR odel In secton 3, Non-donated Sortng Genetc Algorth(NSGA) s presented and the NSGAII-SVR odel s proposed In secton 4, we establsh the optzed odel and use t to predct nboard tours deand At last, the concluson s gven n secton 5 The Prncple of SVR Support vector achne was orgnally used for pattern recognton probles and t s anly appled to classfcaton Wth the ntroducton of nsenstve loss functon by Vapnk, Support vector regresson (SVR) s extended to solve the nonlnear regresson proble The prncple of SVR odel s ntroduced as follows Set a saple set S {( x, y ),( x, y),,( x, y)} Through a nonlnear appng, the data fro saple set S are apped nto a hgh densonal space F And the followng functon s used for lnear regresson n F space n f ( x) w ( x) b, : R F w F() Where b threshold value s w s regresson coeffcent vector The nfluence factors of w are the su of eprcal rsk and the flatness of the hgh-densonal space w, that s R( w) w C ( f ( x) y) () 0, f ( x) y ( f ( x) y) f ( x ) y, f ( x ) y (3) Where the nuber of saples s ( f ( x) y) s loss functon C s penalty factor In order to control the coplexty of functon, lnear regresson functon should be brought to flat as far as possble The relaxaton factors and are also ntroduced consderng the regresson error that beyond the precson The relaxaton factors are used to deal wth the ponts whch do not satsfy the Eq (3) Based on structural rsk nzaton crteron of statstcal learnng theory, the varable of w and b are deterned through support vector regresson ethod by nzng the objectve functon Rw: ( ) R( w,, ) w C ( ) y w x b s t w x b y, 0 (4) 404 Copyrght c 05 SERSC

3 Internatonal Journal of u- and e- Servce, Scence and Technology In the Eq (4), w akes the regresson functon ore flat and have better generalzaton ablty The second part of Eq(4) s used to reduce the error The penalty factor C s a constant nuber and C 0 It s used to control the degree of punshent of saples beyond the error Then establsh Lagrange's equaton: L( w,, ) w C ( ) [( ) y w ( x ) b] y w x b [( ) ( ) ] ( ) (5) In order to ake the Eq (5) be nu, functon Lw (,, ) of all paraeters of partal dervatve s equal to zero Then the followng dual optzaton proble can be get n{ ( )( j j )[ ( x ) ( x j )] ( y ) ( y )} (6) j st ( ) 0, [0, C] Then, the support vector regresson probles can be sued up n quadratc prograng proble By solvng the quadratc prograng proble Eq (6), we can get the functon w whch s descrbed by the tranng saple ponts ( ) ( x ) w (7) Where a and s the soluton of Rw (,, ) Then the regresson functon can be got That s ( ) ( ) (, ) f x k x x b (8) Where k( x, x) ( x) ( x) s the kernel functon Dfferent SVR odels can be got by selectng dfferent kernel functons In ths paper, the radal bass functon(rbf) s chosen n SVR odel The RBF s shown n bellow K( x, x ) exp( x x ) (9) 3 Iproved SVR Model The three paraeters,c, wll have a ajor pact on the forecastng results of SVR odel through the prncple of SVR algorth Thus, the proved Non-donated Sortng Genetc Algorth (NSGA) wll be used to paraeters optzaton 3 NSGA Algorth and ts Iproveents Non-donated Sortng Genetc Algorth (NSGA) s proposed by Srnvas and Deb [4] n 995 It s a genetc algorth based on pare to optal concept It can ebody Goldberg thought best fro these ult objectve genetc algorth optzaton ethods The NSGA proves the choce of regeneraton based on the basc genetc algorth Each Copyrght c 05 SERSC 405

4 Internatonal Journal of u- and e- Servce, Scence and Technology ndvdual s stratfed n accordance wth ther donated and non-donated relatons Before the selecton operaton, the populaton has been classfed and sorted accordng to the donated and non-donated relatons And all the ndvduals of the populaton are assgned a vrtual ftness valuethe ndvduals at the sae level have saevrtual ftness values Ths wll ensure that the ndvduals of sae level have the sae probablty of replcaton Then dong a selecton operaton, so that the algorth are obtaned very satsfactory results n the ult-objectve optzaton The characterstcs of NSGA are turnng ultple objectve functon calculaton nto vrtual ftness calculaton [5] The flow chart of NSGA s shown n Fg NSGA retans the excellent ndvduals by the non-donated sortng algorth and uses ftness sharng functon to keep the dversty of the populaton But NSGA also has obvous shortcongs, anly be reflected n two aspects: Hgh coputatonal coplexty; The sharng radus needs to be specfed n advance In order to overcoe the shortcongs of NSGA, Deb proposed the Eltst Non-donated Sortng Genetc Algorth (NSGAII) The algorth anly proved on NSGAn the followng three aspects: () The coplexty of the algorth s reduced by a proposed a fast non donated sortng algorth based on the classfcaton ()Put forward congeston and the congeston coparson operator The ftness sharng strateges do not need to specfy the sharng radus Asthe wnnng standards after sortng between sae classes, the pareto doan of the eleents can be extended to the entre pareto doan The dstrbuton s unforand keeps the dversty of populaton (3) Introduce the eltst strategy and ncrease the saplng space The populaton of the next generaton s got by the copetton of parent populaton and ts progeny populaton n order to get better next generaton The detaled process of NSGAII algorth s shown n bellow () Fast non-donated sortng algorth np s the nuber of donant ndvdual p n populaton s p s the set that controlled by ndvdual p Step : Fnd the ndvdual whch s np 0 n the populaton And they are stored n the current set E Step : For each ndvdual n the current set E, the donatng set for ndvdual s S Travel each ndvdual l fro S Let n n, f n 0, the ndvdual l s stored n set l l H Step 3: Let the ndvdual got fro E be the frst ndvdual of non-donated layer Let H be the current set, repeat the above steps untl the entre populaton s classfed () The deternaton of the degree of congeston Step :Let nd 0, n,,, N n d s the degree of congeston Step : For each objectve functon a The populaton s sorted based on the objectve functon b Let the degree of congeston of boundares of two ndvduals crowded be nfnte That s d N d c Calculate the updatng value n d Step 3: The coparson of the degree of congeston After a fast non-donated sortng algorth and congeston degree calculaton, each ndvdual n the populaton has two attrbutes: the non-donated order nrank and congeston degree n d The degree of congeston coparson operator s defnedas n If n j, let ndvdual s better than ndvdual j, f and only f rank jrank any d j d l 406 Copyrght c 05 SERSC

5 Internatonal Journal of u- and e- Servce, Scence and Technology Fnally, we gve the calculaton steps of NSGA II algorth Step : Randoly generate ntal populaton P 0 Then non-donated sortng s used to the populaton Each ndvdual s assgned wth pareto rank Then do selecton, crossover and utaton operaton of ntal populaton and get a new populaton Q 0, let t 0 Step : In the generaton teraton of t, for new groups Rt Qt Ut The non-donated sortng s used to the populaton R t Get the non-nferor front E, E, Step 3: Calculate all the degree of congeston of non-nferor front E Step 4: Do partal order selecton, choose the best N ndvduals to for populaton P t Step 5: Do selecton, crossover and utaton operaton to populaton Pt and get populaton Qt Step 6: Deterne whether the ternaton condton reaches If doesn t, turn to Step Then output results Intalze populaton gen=0 Front= Is populaton classfed? N Identfy nondonated ndvdual gen=gen+ Y Replcaton based on vrtual ftness values Appont vrtual ftness value Apply ftness sharng ethod Crossover Reappont vrtual ftness whch has been shared Y Mutaton gen<axgen? End N Ignore Nondonated solutons whch have been classfed Front=Front+ FgureThe Flow Chart of NSGA Copyrght c 05 SERSC 407

6 Internatonal Journal of u- and e- Servce, Scence and Technology 3 NSGAII-SVR Model The paraeters,c, play an portant role n the SVR odel How to get the paraeters accurately s very portant And n ths paper, NSGAII algorth s used n paraeters optzaton and the NSGAII-SVR odel s establshed n order to forecast tours deand of Chna The flow chart of NSGAII-SVR s shown n Fg and the basc steps of NSGAII-SVR algorth s as follow: Step : Experental desgn Select the portant nfluental varables as the desgn varables Choose the experental desgn ethod and desgn tranng saples Step : Optze the paraeters of SVR odel Step 3: Establsh SVR odel The SVR odel s establshed through tranng saples and optzed paraeters If approxaton accuracy of the SVR odel can not eet the requreents, each teraton optzaton results are chosen as a new tranng saple Then the new tranng saples are used to update odel and ncrease the accuracy Step 4: Mult-objectve optzaton of NSGAII The NSGAII algorth s used to optze SVR odel and desgn space exploraton Usng the cross valdaton ethod to optze NSGA II-SVR odel The qualty of pareto soluton set s evaluated by unforty and dversty of dstrbuton of pareto soluton set If t satsfes the requreent, then output the pareto soluton set If t doesn t, the populaton and the axu nuber of teratons of evoluton are ncreased Then turn to step 3 Step 5:Accordng to the preference nforaton, select the optal soluton Intalze paraeters Intalze populaton P t Experental desgn Generate populaton Q t by genetc operaton Sulaton and caculaton Generate populaton R t by ergerng P t wth Q t Establsh SVR odel and optze paraeters Generate non-donated set by non-donated sortng wth R t t=t+ Test accuracy of odel Calculate ndvdual congeston degree and select superor ndvduals, generate next populaton P t+ Reach the requreents? Y Reach the ternaton condton? N N Y Create new saples Output results SVR process NSGAII process FgureThe Flow Chart of NSGAII-SVR 408 Copyrght c 05 SERSC

7 Internatonal Journal of u- and e- Servce, Scence and Technology 4 Model Constructon and Predcton In ths paper, the NSGAII-SVR odel s establshed to forecast the onthly nbound tours deand of Chna The data s chosen fro January 000 to Deceber 0 The unt of nbound tours deand of Chna s ten thousand person-tes The forecastng data s fro July 0 to Deceber 0 The pact factor s shown n Table Table Ipact Factors Ipact factors Unt GDP per capta of passenger source Yuan The dsposable ncoe of resdents of passenger source Yuan Exchange rate(dollar aganst the RMB) Dollar/RMB The rato of CPI % The condtons of tours resources Score () GDP per capta of an passenger source The an passenger source refers to the countres whch ther nbound toursts account for ore than 80% of the total nbound toursts Calculatng forula of GDP per capta of an passenger source s X t M N M s the GDP of an passenger source N s the populaton of an passenger source () The dsposable ncoe of resdents of an passenger source The calculatng forula s X t CN N () C Is the ncoe per capta of an passenger source N s the populaton of an passenger source (3) Exchange rate (Dollar aganst the RMB) The exchange rates X 3t It eans the nuber of RMB that one dollar can be exchanged (4) The rato of CPI X 4t CPI t () CPI 000 CPIt Is consuer prce ndexat tet (5) The condtons of tours resources X L P (3) 5t L Is the nuber of dfferent types of tours resources P Is the score of dfferent types of tours resourcesthe score of dfferent types of tours resources s shown n Table (0) Copyrght c 05 SERSC 409

8 Internatonal Journal of u- and e- Servce, Scence and Technology Table The Score of Dfferent Types of Tours Resources Types of tours resources Score 5A tourst scenc spots 0 4A tourst scenc spots 5 3A tourst scenc spots In order to elnate the nfluence on the predcton results of unt, the 0- standardzed ethod s adopted That s x x x x x ax n n (4) Fg shows the forecastng curves of NSGAII-SVR odel, orgnal SVR odel and BP-NN odel Fro ths fgure, we can t obvously fnd out whch odel has the best perforance on forecastng the onthly nbound tours deand of Chna snce these three odels have slar forecastng curves Then we calculate the root ean squared error (RMSE) and ean absolute error (MAE) to copare the forecastng accuracy of dfferent odels Fro Table 3, we can clearly see that the NSGAII-SVR odel has the best perforance on RMSE and MAE for forecastng the onthly nbound tours deand of Chna copared wth the orgnal SVR odel and BP-NN odel True value NSGAII-SVR Orgnal SVR BP-NN Fgure 3 The Forecastng Curves of Dfferent Models Table 3The Perforance of Dfferent Models NSGAII-SVR Orgnal SVR BP-NN MAE RMSE Where RMSE n (yˆ y ), n n yˆ y MAE n y The Table 4 shows the absolute error of NSGAII-SVR odel and the copared odels fro July 0 to Deceber 0 In ths table, we can fnd that these three odels could gve accuracy forecastng But the NSGAII-SVR odel alost perfors best n each onth copared wth the other two odels n ths stuaton So the proposed NSGAII-SVR 40 Copyrght c 05 SERSC

9 Internatonal Journal of u- and e- Servce, Scence and Technology can ncrease the forecastng accuracy for the onthly nbound tours deand of Chna Table4 The Absolute Error of Dfferent Models NSGAII-SVR Orgnal SVR BP-NN Concluson In ths paper, the SVR odel s adopted to forecast the onthly nbound tours deand of Chna The eltst Non-donated Sortng Genetc Algorth(NSGAII) s used to search the optal paraeters of SVR odel Thus, the nonlnear and hgh volatle of onthly nbound tours deand proble can be solve by SVR odel whle the paraeters optzaton of SVR odel can be solved by NSGAII algorth And the experental results show that the NSGAII-SVR odel s better than the copared odels on forecastng onthly nbound tours deand of Chna References [] G L, H Song and S F Wtt, Recent developent n econoetrc odelng and Forecastng, Journal of Travel Research, vol 44, (005), pp 8-99 [] H Song and G L, Tours deand odellng and forecastng-a revew of recent research, Tours Manageent, vol 9, no, (008), pp 03-0 [3] J Quayson and T Var, A tours deand functon for the Okanagan, Tours Manageent, vol 3, no, (98), pp 08-5 [4] E Seral, S F Wtt and C A Wtt, Econoetrc forecasts: Tours trends, Annals of Tours Research, vol 9, no 3, (99), pp [5] M Geurts and I Ibrah, Coparng the Box Jenkns approach wth the exponentally soothed forecastng odel applcaton to Hawa toursts, Journal of Marketng Research, vol, (975),pp 8 88 [6] L Turner, N Kulendran and V Pergat, Forecastng New Zealand Tours deand wth dsaggregated data, Tours Econocs, vol, (995), pp 5 69 [7] N Kulendran and M L Kng, Forecastng nternatonal quarterly tourst flows usng error-correcton and te-seres odels, Internatonal Journal of Forecastng, vol 3, (997), pp [8] C A Martn and S F Wtt, Forecastng tours deand: A coparson of the accuracy of several quanttatve ethods, Internatonal Journal of Forecastng, vol 5, (989), pp 7 9 [9] C L and M McAleer, Te seres forecasts of nternatonal travel deand for Australa, Tours Manageent, vol 3, (00), pp [0] C Goh and R Law, Modelng and forecastng tours deand for arrvals wth stochastc nonstatonary seasonalty and nterventon, Tours Manageent, vol 3, (00), pp [] Y H Bao and J B Ren, Wetland Landscape Classfcaton Based on the BP Neural Network n DaLnor Lake Area, Proceda Envronental Scences, vol 0 (Part C), (0), pp [] F L Cao, Y P Tan and M M Ca, Sparse algorths of Rando Weght Networks and applcatons, Expert Systes wth Applcatons, vol 4, no 5, (04), pp [3] Y P Ba and Z Jn, Predcton of SARS epdec by BP neural networks wth onlne predcton strategy, Chaos, Soltons & Fractals, vol 6, no, (005), pp [4] H G Han, L D Wang and J F Qao, Effcent self-organzng ultlayer neural network for nonlnear syste odelng, Neural Networks, vol 4, (03), pp -3 Copyrght c 05 SERSC 4

10 Internatonal Journal of u- and e- Servce, Scence and Technology [5] A Saengrung, A Abtah and A Zlouchan, Neural network odel for a coercal PEM fuel cell syste, Journal of Power Sources, vol 7, no, (007), pp [6] O Clavera and S Torra, Forecastng tours deand to Catalona: Neural networks vs te seres odels, Econoc Modellng, vol 36, (04), pp 0-8 [7] J P Texera and P O Fernandes, Tours Te Seres Forecast -Dfferent ANN Archtectures wth Te Index Input, Proceda Technology, vol 5, (0), pp [8] R Law, Back-propagaton learnng n provng the accuracy of neural network-based tours deand forecastng, Tours Manageent, vol, no 4, (000), pp [9] V N Vapnk, The Nature of Statstc Learnng Theory, Sprnger, USA, (995) [0] M Y Qao, X P Ma, J Y Lan and Y Wang, Te-seres gas predcton odel usng LS-SVR wthn a Bayesan fraework, Mnng Scence and Technology (Chna), vol, no, (0), pp [] W C Hong, Y C Dong, L Y Chen and C Y La, Tawanese 3G oble phone deand forecastng by SVR wth hybrd evolutonary algorths, Expert Systes wth Applcatons, vol 37, no 6, (00), pp [] B L He, Y Sh, Q Wan and X Zhao, Predcton of Custoer Attrton of Coercal Banks based on SVM Model, Proceda Coputer Scence, vol 3, (04), pp [3] S Ch, N Anand, B K Pangrah and S Mathur, Streaflow forecastng by SVM wth quantu behaved partcle swar optzaton, Neurocoputng, vol 0, (03), pp 8-3 [4] K Deb, Mult-objectve optzaton usng evolutonary algorths, Chchester: John Wley & Sons, (00) [5] Z H Guan, OpertorsAnalysng of the Nondonated Sortng Genetc Algorth (NSGA), Journal of Industral Engneerng and Engneerng Manageent, vol 8, no, (004), pp Authors L Me,9740, Zhengzhou, Henan, P R Chna She s a lecturer of Departent of Socal Servces, Zhengzhou Tours College, Henan, PR Chna Her scentfc nterests are tours Manageent, Hotel Manageent, Golf Club Manageent 4 Copyrght c 05 SERSC