Forecasting petroleum consumption using hybrid SVR-DE model emphasizing on optimal parameter selection technique

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1 Sogklaakar J. Sc. echol. 41 (6), , Nov. - Dec Orgal Artcle Forecastg petroleum cosumpto usg hbrd SVR-DE model emphaszg o optmal parameter selecto techque hora Sujjavrasup* Departmet o Logstcs Egeerg, School o Egeerg, Uverst o the ha Chamber o Commerce, Ddeag, Bagkok, hal Receved: 17 Jauar 2018; Revsed: 23 March 2018; Accepted: 23 Jul 2018 Abstract At preset, lqud uels rema the domat source o trasportato eerg cosumpto all over the world. Accordgl, the uture dem predcto o petroleum cosumpto s a ver challegg task wth regard to ecet suppl maagemet. I ths paper, a hbrd SVR-DE model s developed proposed to address the problem. he developed model takes ablt o SVR model to ormulate complex predctve ucto whle DE algorthm s used to search the optmal parameters o SVR model. Moreover, the hbrd model s compared wthboth ARIMA SVR models as tradtoal sgle models. he expermetal results dcated that the developed model outperorms tradtoal orecastg models based o MAE, MAPE, smape crtera. Furthermore, the orecast perormace o hbrd model s sgcatl deret rom both tradtoal sgle models at 0.05 sgcace level. Cosequetl, the proposed model ca be a promsg tool or aual petroleum cosumpto. Kewords: combed model, petroleum cosumpto, ARIMA, support vector regresso, deretal evoluto 1. Itroducto From a logstcs pot o vew, oe o several ke actvtes s trasportato that s used to traser goods servces order to ulll customer satsactos. Subsequetl, umerous dems o eerg are geerated to drve the trasportato actvt. Cocerg trasportato sector eerg cosumpto (U.S. Eerg Iormato Admstrato, 20 16), lqud uels stll rema the ma source o trasportato eerg cosumpto all over the world. Although reewable eerg has bee developed proposed to ulll trasporttato eerg cosumpto, the dem o lqud uels teds to crease auall. Pertag to ecet suppl maagemet, a uture dem o petroleum cosumpto s useul ormato (Chroma et al., 2016; de Olvera & Olvera, 2018; L, Wag, Wag, & L, 2018) s eeded to realze beore makg a crtcal decso. hus, the accurac o uture dem s a *Correspodg author Emal address: thora_suj@utcc.ac.th ver challegg problem. However, the patter o uture dem s luctuato hard to be estmated b tradtoal methods. Accordgl, several orecastg methods are proposed to estmate the uture dem recet ears. Oe o orecastg methods s tme seres aalss, whch s ormulated rom prevous observatos s wdel used b decso makers all over the world to extrapolate the uture dem o eerg cosumpto as a gudele or decso makg. For statstcal methods, autoregressve tegrated movg average (ARIMA) s a tme seres orecastg model has domated lear problems. he ARIMA models are wdel used lteratures o eerg cosumpto are exteded ma elds o scece preset. Noetheless, ts major dsadvatage s a assumpto based o lear orm o tme seres so approxmato b ARIMA models ma ot be sucet or complex olear real-world problems. I addto, t s ote dcult to determe whether a tme seres s geerated rom a lear or olear uderlg process. hereore, the ARIMA models are stll used to orecast eerg cosumpto recet ears (Al-Musalh, Deo, Adamowsk, & L, 2018; Edger & Akar, 2007; Hussa, Rahma, & Memo, 2016; Se, Ro, & Pal, 2016).

2 . Sujjavrasup / Sogklaakar J. Sc. echol. 41 (6), , For that reaso, mache learg methods are wdel developed proposed eerg orecastg. I ths regard, ts advatages over statstcal models those make them attractve orecastg problems. Frst, these models mpose ew pror assumptos o the model ormulato due to datadrve models. Secod, the models have lexble olear ucto mappg ablt. he last, these models are adaptve ature. Oe o several mache learg methods s support vector regresso (SVR), whch s mplemeted b usg structural rsk mmzato prcple. Based o the prcple, the SVR models acheve a optmum etwork structure alwas provde a uque as well as globall optmal soluto. hereore, the SVR models are successull eerg orecastg tasks (Hu, Bao, Chog, & Xog, 2015; Jag & Dog, 2017; Wag, Hou, Wag, & She, 2016; Yag, Che, L, Zhao, & Zhu, 2016). However, the perormace o SVR models depeds heavl o a approprate selecto o hperplae parameters. Cosequetl, the optmal selecto o hper-plae parameter s a major cocer or developg predctve models regardg SVR models. I order to reduce a rsk o mproper parameter selecto o SVR models, metaheurstcs are emploed to provde a sucetl good soluto the optmal parameter selecto o SVR models. Deretal evoluto (DE) s a method eld o evolutoar computato has proved to be a well-kow algorthm o the most successul evolutoar algorthms (Wu et al., 2018; Jado, war, Sharma, & Basal, 2017). hus, the DE ca be a useul method to provde the sucetl good parameters o SVR model (Wag, L, Nu, & a, 2012; Zhag, Deb, Lee, Yag, & Shah, 2016). I ths paper, a hbrdzato o SVR DE s developed proposed to orecast seve datasets o petroleum cosumpto. Relatg to the proposed model, the SVR models are utlzed to ormulate a predcto ucto. Meawhle, the DE s exploted to search the most approprate parameters o SVR models. Moreover, the proposed model s compared to both ARIMA SVR models based o three accurac measures. All orecastg models are evaluated ts perormaces based o MAE, MAPE, smape. For comparso across deret datasets, the MAPE s used to det sgcatl derece betwee orecast perormaces o those orecastg models based o romzed block desg as aalss o varace uke s Hoestl Sgcat Derece as post hoc test. 2. Materals Methods 2.1 Datasets o petroleum cosumpto he aual datasets o petroleum cosumpto rom 1980 to 2015 are obtaed rom U.S. Eerg Iormato Admstrato (U.S. Eerg Iormato Admstrato, 2015). Relatg to the aual data sets, tred compoet s the domat compoet o tme seres patter. he summar o all datasets s preseted Fgure Methodologes he autoregressve tegrated movg average model he ARIMA model s geeralzato o autoregressve movg average a case o o-statoar tme seres data s geerall reerred to as a ARIMA (p, d, q) model. he mathematcal expresso o the ARIMA (p, d, q) model wth the mea s descrbed as Equato (1). where perod q t t p q d j 1 B 1 B t jb 1 (1) t 1 j1 t are the actual value rom error at tme, respectvel. B s the backward sht operator; are reerred to orders o autoregressve tegrated movg average model, whch are tegers as well. Recetl, several sotware vedors have mplemeted automated tme seres orecastg procedure or uvarate autoregressve tegrated movg average b usg several crtera.e., Akake s ormato crtero (AIC), Baesa ormato crtero (BIC), Akake s ormato crtero wth a correcto or small sample szes (AICc). Sce the varous ARI- MA models ca mmc the behavor o tpe o seres. he p Fgure 1. Datasets o petroleum cosumpto.

3 1296. Sujjavrasup / Sogklaakar J. Sc. echol. 41 (6), , 2019 automated ucto (Hdma et al., 2015; Melard & Pasteels, 2000; Müller & Bogeberger, 2015), amel auto.arma, s emploed ths research. Reerrg the automated ucto, the ucto wll coduct a search over possble model wth the order costrats provded wll retur the best ARIMA model based o the lowest AICc crtero. Accordg to the best ARIMA model depeds o the chage o the prevous observato update. hereore, the ARIMA model s used to st or ARIMA (p, d, q) ths research. he crtero used to select the proper model s AICc as show Equatos (2) (3). 2k k 1 AICc AIC (2) k 1 L AIC 2k 2l (3) where k are sample sze parameters, respectvel. L s the maxmum value o the lkelhood ucto or the model he support vector regresso model he support vector mache model (Meer, Dmtradou, Hork, Wegessel, & Lesch, 2014) s oe o computatoal tellgece models, whch s supervsed learg model s usuall exploted classcato. Regardg regresso aalss, he SVR model s a exteso model o support vector mache cocerg regresso problems geerates a regresso ucto b applg a set o hgh dmesoal lear ucto olear ucto b usg kerel uctos. I addto, the SVR models are able to be a useul tool or solvg complex problems ukow uctoal relatoshp as well. he model ormulato o SVR or regresso problems s show as Equato (4) * x Kx, x b (4) 1 where α α are the so-called Lagrage multplers, b s a scalar threshold, K x, x s kerel ucto. he kerel uctos are the most used or SVR models, whch are deed as ollows: Fgure 2. Data preparato o prevous dataset. I order to explore the most tted SVR model, the best SVR model s selected based o the lowest mea square error. Moreover, the approprate parameter estmato s searched b usg grd search he deretal evoluto optmzato he deretal evoluto (DE) (Arda, Mulle, Peterso, & Ulrch, 2013) s a populato based stochastc search heurstc troduced b Stor Prce (1997) as a global optmzato algorthm o cotuous umercal mmzato problems.he algorthm o deretal evoluto s preseted Fgure Hbrdzato o SVR DE he ma objectve o the hbrd model s to developed complex models emphaszg o parameter selecto optmzato techque. he proposed model uses capablt o SVR models to model the predctve ucto whlst the DE algorthm s used to d the best parameters o SVR model order to guaratee the best SVR model based o a gve search space. he algorthm o the developed model s preseted as ollows: For m equal to 2 to a termato crtero do - he kerel ucto s selected to ormulate the model ormulato o SVR to predct the uture data as Equato (4). - he DE provdes tal parameters wth regard to dmesoal eatures o the kerel ucto as preseted Equato (5).,,..., 1,2,3 N, 1,,, 2,, 3,, d,,,..., (5) Lear: Kx x x x,, Polomal: p K x, x x x r 2 Radal bass: Kx, x exp x x, Sgmod: Kx, x tah x x r where, r, p are kerel parameters. I ths research, the SVR models are used to orecast tme seres data b rearragg prevous observatos to m colums o prevous observatos, amel SVR (m). he rst m 1 colums the last colum are used as put data target data, respectvel. he data preparato o prevous dataset beore emplog the SVR models s preseted as Fgure 2. Fgure 3. DEalgorthm.

4 . Sujjavrasup / Sogklaakar J. Sc. echol. 41 (6), , where s a vector o kerel ucto parameters, d s dmesoal parameters o the kerel ucto, s the umber o geerato, N s the sze o populato. - Utl a termato crtero s met repeat as ollows: For each aget the populato does: For t equal to 70% o the prevous observatos to the observato beore the last observato do - Rearrage the prevous observatos to m colums o the prevous observatos. Ed t m t2 t1 m m1 m2 t - For the rst m 1 colums o the matrx o the prevous observatos are used as put data whlst the last colum o the matrx o the prevous observatos s adopted as target data. - Use the parameters o the kerel ucto as Equato (6). ˆt t1 t2 t3 tm1,,,..., : (6) where s the predcto ucto determed b the support vector regresso; value at tme perod t; ŷ t t s the actual s the predcted value at tme perod t; s a set o the kerel ucto parameters; m s teger that represets the umber o colums. - he SVR model uses the parameters to ormulate the tted predcto ucto. - he tted SVR model s exploted to orecast the uture data. - Calculate MAPE - A tal mutat parameter vector r 2, at rom as Equato (7). v, 0. v,, best,, r, 8 0 r1, r2, where s created b selectg three members o the populato,, (7), best, r 0, r 1, are the -th vector o the populato at the curret geerato the best dvdual vector wth the best tess, respectvel. s the umber o geeratos; r 0, r 1, r 2 are roml chose umbers wth the populato sze; 1,2,3,..., N - he crossover operator geerates a tral vector u, as Equato (8) u, v j,, j,, r j, otherwse 0.5 or j I r (8) Ed where 1,2,3,..., N; j 1,2,3,..., d r j, U, r umber o geeratos. - he deretal evoluto uses a greed selecto operator as Equato (9)., 1, ~ 0,1 u,, u, otherwse, where, s the MAPE o the tral vector u I s a rom teger rom,2,...,d, 1. s the (9) equal to MAPE o the target vector. s the umber o geeratos; 1,2,3,..., N Ed - Choose the aget rom the populato that has the lowest MAPE retur t as the best oud parameters o kerel ucto.

5 1298. Sujjavrasup / Sogklaakar J. Sc. echol. 41 (6), , Cross-valdato All orecastg models are evaluated ther orecast accurac b usg seve tme seres datasets o petroleum cosumpto each cotet, whch are obtaed rom U.S. Eerg Iormato Admstrato. Each dataset o the petroleum cosumptos s separated to two subsets as trag dataset test dataset. For trag dataset, 70% o each tme seres data o petroleum cosumpto s used to ormulate the tted model to orecast oe step ahead. he rest o each tme seres data o petroleum cosumpto s used to evaluate those orecast models as the hold out set, whch s 11 old cross valdato. Ater the actual data s realzed, the t s cluded to trag dataset to ormulate predct oe step ahead utl the last data o hold out set. For exstg measures o accurac (Hdma & Koehler, 2006), the most commol used measures are MAE MAPE. he MAE s recommeded to evaluate orecast accurac o same scale o data sets due to scale-depedet measure. Meawhle, the MAPE s also recommeded to evaluate orecast accurac s the prmar measure the M- competto. A advatage o MAPE measure s percetage error that has advatage o beg scale-depedet. hus, t s requetl used to compare orecast perormace across deret data sets rather tha MAE as scale-depedet measure. Eve though, there are argumets agast o usg MAPE some stuatos (.e., meagul zero, heaver pealt o postve errors tha o egatve errors), t ma stll be preerred or reasos o smplct to expla. Wth regard to reduce the dsadvatages o MAPE, smape s developed proposed to address the problems. I order to evaluate the orecast perormaces, three accurac measures used ths research are MAE, MAPE, smape cross-valdato. All mathematcal expressos o the accurac measures are preseted Equato (10) to (12). ŷ 1 MAE (10) ŷ 1 MAPE 100 (11) 2 ŷ ŷ 1 smape 100 (12) 3. Results Dscusso For a superor ablt o the most proper model wth regard to petroleum cosumpto, all orecastg models are evaluated b usg several crtera uder ma stuatos. Frst, all orecastg models are compared based o the three measures o orecast accurac. Secod, descrptve statstcal aalss s descrbed b usg box plots based o MAPE to dspla measures o cetral tedec. he last, both aalss o varace test post hoc test are aalzed to det sgcatl derece betwee the orecast models. he summar o all orecastg models based o three measures o orecast accurac s demostrated able 1. I able 1, the proposed model provdes hgher accurac tha both tradtoal sgle models. hs dg revealed that the developed model ma be a meagul model to deal wth these problems. Moreover, the expermetal results dcated that the utlzato o optmzato techque ca overcome the tradtoal SVR model all cases. Meawhle the SVR model outperorms ARIMA model approxmatel 82% o all cases. Cosequetl, ths evdece supports that the techque ca ehace orecast accurac reduces the rsk o usg mproper parameters o SVR model. he most approprate models o SVR regardg petroleum cosumpto are descrbed able 2. Furthermore, the box plot s used to dspla descrptve statstcs o each orecast model based o MAPE as preseted Fgure 4. able 2. Data Most approprate models o SVR regardg petroleum cosumpto. SVR model Kerel ucto Cost parameter amma Arca SVR(4) Lear NA Asa Oceaa SVR(2) Radal bass Cetral South SVR(3) Lear NA Amerca Eurasa SVR(2) Radal bass Europe SVR(4) Lear NA Mddle East SVR(5) Radal bass North Amerca SVR(2) Radal bass able 1. Summar o all orecastg models based o three measures o orecast accurac. Data ARIMA SVR SVR-DE MAE MAPE smape MAE MAPE smape MAE MAPE smape Arca Asa Oceaa Cetral South Amerca Eurasa Europe Mddle East North Amerca

6 . Sujjavrasup / Sogklaakar J. Sc. echol. 41 (6), , able 3. Summar o aalss o varace test based o MAPE. D Sum square Mea square P-value Forecastg model (treatmet) Dataset (block) Resduals Fgure 5. Summar o multple comparsos based o MAPE. Fgure 4. Vsual data dspla o box plot based o MAPE. Reerecg Fgure 4, the proposed model demostrated that t provdes both the lowest mea meda o MAPE compared to other cdate orecastg models. Moreover, both mea meda o SVR model are also lower tha ARIMA model. I order to det sgcatl derece o orecast perormaces, the romzed block desg s ex-ploted to vestgate the dg. However, the ormalt test o MAPE has to be perormed b usg Shapro-Wlk test beore applg the aalss o varace test. ve results o ormalt test, p-values o Shapro-Wlk test are more tha 0.05, whch dcated that MAPE o each orecastg model comes rom a ormall dstrbuted populato at 0.05 sg-cace levels. Subsequetl, the summar o aalss o va-race test based o MAPE s preseted able 3. As gve results able 3, ths evdece dcated that at least oe predcto perormace o orecastg model s sgcatl deret rom oe other at the 0.05 sgcace level. However, the datasets are ot sgcatl deret rom oe other at 0.05 sgcace level. For parwse comparsos o meas, the uke s Hoestl Sgcat Derece s used to det sgcatl derece. he summar o multple comparsos s demostrated Fgure5. As results o multple comparsos, the orecastg perormace o proposed model s sgcatl deret rom both ARIMA SVR models. O the other h, the SVR model s ot sgcatl deret rom ARIMA model. 4. Coclusos Accordg to all evdeces, the revealed that the proposed model has superor ablt provdes hgher accurac tha other compared models at 0.05 sgcace levels. Cosequetl, t ca support to coclude that the optmzato techque cocerg parameter selecto o SVR model s able to mprove orecast accurac compared wth cdate models. I other words, the techque o optmal parameter selecto ca reduce the rsk o usg mproper parameters o SVR models. hus, the developed model ca overcome the lmtato o each other regardg datasets o petroleum cosumpto ca be a promsg tool to predct aual petroleum cosumpto. Reereces Al-Musalh, M. S., Deo, R. C., Adamowsk, J. F., & L, Y. (2018). Short-term electrct dem orecastg wth MARS, SVR ARIMA models usg aggregated dem data Queesl, Australa. Advaced Egeerg Iormatcs, 35, Arda, D., Mulle, K. M., Peterso, B.., & Ulrch, J. (2013). DE-optm: Deretal Evoluto R. Chroma, H., Kha, A., Abubakar, A. I., Saad, Y., Hamza, M. F., Shub, L.,... Herawa,. (2016). A ew approach or orecastg OPEC petroleum cosumpto based o eural etwork tra b usg lower pollato algorthm. Appled Sot Computg, 48, de Olvera, E. M., & Olvera, F. L. C. (2018). Forecastg md-log term electrc eerg cosumpto through baggg ARIMA expoetal smoothg methods. Eerg, 144, Edger, V. Ş., &Akar, S. (2007). ARIMA orecastg o prmar eerg dem b uel urke. Eerg Polc, 35(3), Hu, Z., Bao, Y., Chog, R., & Xog,. (2015). Md-term terval load orecastg usg mult-output support vector regresso wth a memetc algorthm or eature selecto. Eerg, 84, Hussa, A., Rahma, M., & Memo, J. A. (2016). Forecastg electrct cosumpto Paksta: the wa orward. Eerg Polc, 90, Hdma, R. J., Athaasopoulos,., Razbash, S., Schmdt, D., Zhou, Z., Kha, Y.,... Wag, E. (2015). Forecast: Forecastg uctos or tme seres lear models. R package verso, 6(6), 7. Hdma, R. J., & Koehler, A. B. (2006). Aother look at measures o orecast accurac. Iteratoal Joural o Forecastg, 22(4), Jado, S. S., war, R., Sharma, H., & Basal, J. C. (2017). Hbrd artcal bee colo algorthm wth deretal evoluto. Appled Sot Computg, 58, Jag, H., & Dog, Y. (2017). lobal horzotal radato orecast usg orward regresso o a quadratc kerel support vector mache: Case stud o the bet Autoomous Rego Cha. Eerg, 133. do: /j.eerg

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