TELK OMNIKA, V ol.16, No .6, December 2018, pp . 2747–2755 ISSN: 1693-6930, accredited First Gr ade b y K emenr istekdikti, Decree No: 21/E/KPT/2018 DOI: 10.12928/TELK OMNIKA.v16i6.9691 2747 Reinf or ced Island Model Genetic Algorithm to Solve Univer sity Cour se Timetab ling Alfian Akbar Gozali, Shig eru Fujim ura * Gr aduate School of IPS , W aseda Univ ersity 2-7 Hibikino , W akamatsu, Kitakyushu, Fukuoka 808-0135, J apan * Corresponding author , e-mail: alfian@tass .telk om univ ersity .ac.id Abstract The Univ ersity Course Timetab ling Prob lem (UCTP) is a scheduling prob lem of assigning teaching e v ent in cer tain time and room b y consider ing the constr aints of univ ersity stak eholders such as students , lecturers , depar tments , etc. This prob lem become s complicated f or univ ersities which ha v e immense n umber of students and lecturers . Theref ore , a scalab le and reliab le timetab ling solv er is needed. Ho w e v er , current solv ers and gener ic solution f ailed to meet se v er al specific UCTP . Moreo v er , some univ ersit ies implement student sectioning prob lem with individual student specific constr aints . This research introduces the Reinf orced Asynchronous Island Model Genetic Algor ithm (RIMGA) to optimiz e the r esource usage of the computer . RIMGA will configure the sla v e that has completed its process to helping other machines that ha v e y et to complete theirs . This research sho ws that RIMGA not only impro v es time perf or mance in the computational e x ecution process , it also off ers g reater oppor tunity to escape the local optim um tr ap than pre vious model. K e yw or ds: univ ersity course timetab ling prob lem, island model, genetic algor ithm Cop yright c 2018 Univer sitas Ahmad Dahlan. All rights reser ved. 1. Intr oduction The Univ ersity Course Timetab ling Prob lem (UCTP) is a scheduling prob lem of assigning teaching e v ent in cer tain time and room b y consider ing the constr aints of univ ersity stak eholders such as students , lecturers , depar tments , etc. The constr aints could be hard (encour aged to be fulfilled) or soft (better to be fulfilled) constr aints . Timetab ling itself is conside red an NP-Hard prob lem [4]. Some univ ersities such as T elk om Univ ersity [5] ha v e a large population of students and lecturers , and so their constr aints are also g reat as a result. This condition could mak e the prob lem e v en more complicated. In addition, the student body in T elk om Univ ersity has increased from 6,570 students in 2010 to 21,698 in 2016. The n umber is a result of the merging of f our univ ersities: T elk om Institute of T echnology , T elk om P olytechnic , T elk om Institute of Management and T elk om School of Ar ts . The univ ersity timetab ling solv er m ust, as a result, meet a ne w specification: scalability . One of the most recent researches is the application of genetic algor ithms (GAs), which is inspired b y the theor y of e v olution. This method has been used to solv e man y actual UCTP cases . There are se v er al GA models such as inf or med GA [10], par allel GA [2], NSG A II [11, 9], Adaptiv e Real Cod ed GA [13], Hybr id Fuzzy and GA [6], Quantum Ev olutionar y Computing [1], and distr ib uted model GA [14] that ha v e been proposed. This research u sed the distr ib uted model GA, or what is kno wn usually as Island Model GA [14], out of all these models . W e ha v e chosen this model f or its high scalability . F or the univ ersity course timetab ling itself , Gozali et al. introduced Asynchronous Island Model GA (AIMGA) [5]. This model succeeded in solving actual UCTP cases in the T elk om Univ ersity Sch ool of Engineer ing with a satisfying result. Ho w e v er , when it w as r un under v ar ious computer specifications , f aster computers w ere idle aft er ha ving completed their tasks while the slo w er ones w ere still r unning. This idling prob lem left an oppor tunity to be e xploited f or more efficient perf or mance . Receiv ed Ma y 21, 2018; Re vised No v ember 2, 2018; Accepted No v ember 23, 2018 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 1693-6930 2748 Theref ore , w e are going to introduce the Reinf orced AIMGA (RIMGA) to impro v e time perf or mance in the computational e x ecution process . At the same time , w e also off er g reater oppor tunity to escape the local optim um tr ap than the con v entional AIMGA. T ak en together , the contr ib utions of this w or k are (1) introducing RIMGA as a br and ne w mechanism to complement common AIMGA, (2) designing the T elk om Univ ersity UCTP , and (3) analyzing RIMGA perf or mance in handling T elk om UCTP . This paper consists of se v en sections . The remainder of this paper is organiz ed as f ollo ws . Section 2 talks about the mechanism of proposed method, RIMGA and its par ameters , handles AIMGA’ s idling prob lem. Section 3 introduces the research method which is split into tw o subsections: designing T elk om UCTP and its RIMGA implementation. Section 4 sho ws ho w w e conducted the e xper iment, results , and its discussion. The last b ut not the least, section 5 tak es place as the conclusion of this w or k. 2. The Pr oposed Method 2.1. Reinf or ced State The AIMGA could solv e the synchronous model w aiting prob lem, b ut in reality , it is f ound that there is still an oppor tunity to increase the AIMGA efficiency . There is almost no prob lem if the specification of the computers is not too diff erent. If , ho w e v er , the y are actually under a v er y diff erent specification, there will be sla v es that complete their tasks f aster than other sla v es . Such a condition will mak e the f aster sla v es idle while the slo w er ones are still r unning their tasks . The RIMGA w as introduced in this paper to increase the AIMGA efficiency . The main idea of th e RIMGA is ho w the idle island (computer) can be utiliz ed fur ther to help another r unning island. The idle island as an island that has reached its stop condition has to find another island which is still r unning. The idle island will reinf orce that island to complete its process more quic kly . Figure 1 illustr ates the diff erence betw een the asynchronous and the RIMGA. Figure 1. The diff erence of tw o island GA Models The AIMGA isolates each computer to r un separ ately so that each computer can complete its task without w aiting f or other computers to complete theirs . The reinf orced model tr ies to utiliz e the idle time (g r a y cell) of sla v e 2 from the asynchronous one . After sla v e 2 has completed its task, it w ould help sla v e 1 to finish its task (gener ation 3). As sho wn in the Master Island state diag r am in Figure 2-master state , the RIMGA implements the reinf orced function. It tr ies to find an island that has not completed its task to be helped b y the island that has . This attempt aims to maximiz e the productivity of the model b y optimizing the utility of the idle island that has completed its task. Figure 2-sla v e state sho ws that the RIMGA star ts when there is an island that has completed all its process . The master will e v aluate and choose which of th e islands that has not completed Reinf orced Island Model Genetic Algor ithm to Solv e Univ ersity ... (Alfian Akbar Gozali) Evaluation Warning : The document was created with Spire.PDF for Python.
2749 ISSN: 1693-6930 Figure 2. Master-Sla v e Island State diag r am its task to be helped b y the island that has . There are se v er al consider ations in pic king the island to be helped and ho w to gener ate its population. Such consider ations are presented as reinf orced par ameters . 2.2. Reinf or ced P arameter s Reinf orced par ameters are par ameters that control ho w the reinf orced state beha v es . The master island will use the reinf orced par ameters to control ho w the islands that ha v e completed their tasks to help those th at ha v e not. There are three reinf orced par ameters: the island state , island pr ior ity , and individual pic king method. The reinf orced par ameters are defined as f ollo ws . The set of (sla v e) islands is e xpressed b y S . The set of islands that ha v e completed their tasks is represented b y F , those that h a v e not b y U , and those that are helped b y H. Let F S , U S , and H S where F = U . The reinf orced par ameters are e xpressed as f p j p = f tr ue; f al se gg such that p 1 is the island state , p 2 the island pr ior ity , and p 3 the individual pic king method. The first par ameter is the island state . The island state is a condition to deter mine whether an island that is being helped b y another island or not. This par ameter will deter mine whether the reinf orcement direction is div e rgent (balance f or all islands that ha v e not completed their tasks) or con v ergent (islands that ha v e , one b y one). An island that is helped b y another island e xpressed as H i . R ( a; b ) is a function that deter mines whether island a m ust help island b or not. R ( a; b ) will retur n tr ue if p 1 is tr ue and island b has not been helped b y another island y et. If R ( a; b ) = tr ue , island a helps island b and the state of island b will be changed to being helped. hel p ( a; b ) is a procedure in which island a helps island b . R ( f : 8 F ; u : 8 U ) = ( tr ue; if ( p 1 = tr ue ) \ ( u = 2 H ) f al se; other w ise if ( R ( f ; u ) = tr ue ) ) hel p ( f ; u ) ; u   h (1) The second par ameter is island priority . It has tw o choices: those could be based on the least n umber of iter ations or on the poorest (largest) fitness . These choices ref er to the f actors are the most impor tant , the n umber of iter ations or fitness v alue . If the least n umber of iter ations w ere activ ated ( p 2 = tr ue ), the island that has completed its task will find and help another island which has the least n umber of iter ations . Otherwise , if the poorest fitness w ere activ ated ( p 2 = f al se ), the island that has completed its task will find and help another island that has the lo w est fitness v alue . Let iter ation(s) retur n the current iter ation of island s and fitness retur n the best current TELK OMNIKA V ol. 16, No . 6, December 2018 : 2747 2755 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 1693-6930 2750 fitness of island s . s = ( ar g min ( iter ation ( u : 8 U )) ; if ( p 1 = tr ue ) ar g min ( f itness ( u : 8 U )) ; other w ise (2) The third par ameter is individual pic king method . This par ameter deter mines the w a y of pic king individuals from an island that going to be helped (reinf orced). There are tw o w a ys of pic king individuals . Th e first ( p 3 = tr ue ) is b y pic king the best individual from helped island and duplicating it into as man y as the individual n umbers of a population. The second ( p 3 = f al se ) is b y pic king the best population from helped island or usually the last population fr om it. The second w a y has the consequence of the best individual b uc k et in the master ha ving to be changed into the best population b uc k et. In other w ords , the master island m ust k eep the best population from e v er y island r ather than the best individual. 3. Resear c h Method 3.1. UCTP in T elk om Univer sity The UCTP in T elk om Univ ersity is a student-le v el timetab ling (student sectioning) prob lem. As ref erenced from T omas Muller et al., Student sectioning is the prob lem of assigning students to classes of a subject while respecting individual st udent requests along with additional constr aints . F or e xample , a student cannot attend tw o classes which o v er lap in time[7]. Theref ore , the fulfillment of each of the students’ pref erence is encour aged as w ell. This approach has been implemented in pre vious researches [10, 5] in T elk om Univ ersit y and other univ ersities such as Purdue [8] and W ater loo Univ ersity [3]. Lik e an y other UCTP , T elk om Univ ersity is a minim um optimization prob lem. The objectiv e is to minimiz e all the predefined constr aint violation f or each of the teaching e v ents . Such that a teaching e v ent is an e v ent of a lecturer l in a room r at time t class c f or a set of students S . Which is defined b y f ollo wing notation: e = ( l ; r ; t; c; S ) (3) With ref erence from pre vious researchers [10, 5, 2], this research used tw o types of constr aints , the hard and the soft constr aints . Hard constr aint (HC) is a constr aint that m ust be satisfied. Soft constr aint (SC) ought more to be satisfied to impro v e the quality of the timetab ling. As the constr aints are w or king in the same UCTP cases , the types of HCs and SCs used f or this research are e xactly the same as the pre vious research conducted b y Suy anto [10] and Gozali [5]. Let i = 1 :: 5 be hard constr aints and i = 6 :: 12 be soft constr aints . As hard constr aints m ust be f ar bigger r ather than soft constr aints , the objectiv e function becomes: Minimiz e V = 5 X i =1 M V i + 12 X i =6 V i (4) where V is a violation v alue f or each i constr aint. The symbol M means a v er y big n umber so that M V i is m uch larger than V i . With regard to the T elk om Univ ersity UCTP in this research, the HC v alues are set m uch higher than SC so that the GA will pr ior itiz e poor fitness more because of HC . By treating the SCs this , the y became the f ocus after all HCs ha v e been satisfied. The penalty v alue of SCs is designed to be propor tional to its influence . F or e xample , as a lectur ing e v ent has a lecturer and around 50 students , the r atio of lecturer SC to student SC should be 1:50. 3.2. RIMGA f or UCTP Directed chromosome will be used f or the chromosome representation. Directed chromosome mimics the real-w or ld representation which, in this case , is the univ ersity timetab ling representation. Reinf orced Island Model Genetic Algor ithm to Solv e Univ ersity ... (Alfian Akbar Gozali) Evaluation Warning : The document was created with Spire.PDF for Python.
2751 ISSN: 1693-6930 Thus , the chromosome , as sho wn in Figure 3, is the representation (mapping) from the real-w or ld timetab le . Figure 3. Directed chromosome Fur ther more , since the AIMGA model w as der iv ed from the single model, the AIMGA core (individual reproduction and e v aluation of fitness) w as the same as the single model. The AIMGA implemented Inf or med GA core , which applied local search and only used directed m utation o v er crosso v er [10]. Der iv ed from pre vious researchers [5, 10], this r esearch also uses tw o stages of the inf or med GA, class-le v el timetab ling (stage 1) and student-le v el timetab ling (stage 2). The significant diff erence betw een these tw o stages lies in stage 1 which e xcludes student constr aints . That is because the student e v aluation time process took m uch longer time due to a large n umber of students . The ne xt stage will include student constr aints . Directed m utation which is an additional w a y to impro v e the process efficiency of the GA w as also used. 4. Result and Discussion This research e xper iment has three goals: to implement the AIMGA concept into the T elk om Univ ersity UCTP , analyz e RIMGA par ameters , and compare the RIMGA with the ordinar y AIMGA. W e conduct the first three e xper iments with the regard of implementing and analyzing RIMGA par ameters , while the last e xper iment is f or compar ing with con v entional AIMGA. Dataset used in this research w as T elk om Univ ersity Engineer ing School, a f aculty in T elk om Univ ersity , at odd semester f or enrollment y ears 2011/2012. This f aculty had char acter istics as e xplained in T ab le 1. T ab le 1. Inf or med GA Scheme No Attrib utes V alue 1 Classes 813 2 Rooms 80 3 Students 6570 4 A v er age n umber of classes per students 6.481 5 A v er age n umber of meetings per class 2.752 6 Lecturers 316 7 A v er age classes per lecturers 2.582 4.1. Result and Discussion This section e xplains the test scenar io which aims to test three reinf orced state par ameters: the island state , island pr ior ity and individual pic king method. Each test will be r un thr ice with 5 islands [5] in sequence . This n umber is considered sufficient because there are already statistically significant diff erences b y using the 3 test results . The specifications of the computer used f or this test are tw o computers with Core i5 and 4GB memor y , one computer with Core2Duo (2.8 GHz) TELK OMNIKA V ol. 16, No . 6, December 2018 : 2747 2755 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 1693-6930 2752 and 2 GB memor y , and tw o computers with Core2Duo (2.6 GHz) an d 1 GB memor y b ut from diff erent man uf acturers . W e use fitness and e x ecution time as the e v aluation par ameters . 4.1.1. Island State T est T ab le 2 sho ws the results f or the island state test. F rom this tab le , ignor ing the island state is better than consider ing the island state . By ignor in g the island state , more than one f aster sla v e can help the slo w est sla v e so that the slo w est sla v e can reach its stopping cr iter ia sooner . The result is in line with the computer specifications of the islands that are v er y diff erent. Theref ore , balancing the process b y consider ing the island state is not as eff ectiv e as ignor ing it. Thus , the ne xt test scenar io used the ignor ing of the island state configur ation. T ab le 2. Island State T est Result T est Number Ignoring island state Considering island state Best Dur ation Best Dur ation Fitness (hh:mm:ss) Fitness (hh:mm:ss) 1 11520 16:55:59 11900 18:48:36 2 11950 16:52:33 11480 18:53:38 3 11840 16:30:32 11940 18:48:41 A vera g e 11770 16:46:21 11773 18:50:18 4.1.2. Island Priority T est T ab le 3 sho ws the test result f or this scenar io . It indicates that f or the dur ation of e x ecution and best fitness , and the least n umber of iter ations ga v e better result r ather than the poorest fitness . The dur ation inter v al betw een them is just around 9 min utes . The slo w er sla v e with the least n umber of iter ations is requires more help so f ar . This condition sho ws that the GA perf or mance depends more on the current gener ation than fitness . Thus , k eeping the slo w er island with f e w er gener ations w ould be better than poor fitness . The result, which places the current gener ation abo v e fitness , means that population in each island is ab le to k eep their div ersity . It is easier f or the island to a v oid the local optim um tr ap due to its div ersity . F or this case , theref ore , adding gener ations is better than increasing fitness . Finally , according to the result, the ne xt test will use the least n umber of iter ations . T ab le 3. Island Pr ior ity T est Result T est Number The least iteration n umber s The w or st fitness Best Dur ation Best Dur ation Fitness (hh:mm:ss) Fitness (hh:mm:ss) 1 11520 16:55:59 13310 17:20:29 2 11950 16:52:33 12410 16:51:01 3 11840 16:30:32 12130 16:34:14 A vera g e 11770 16:46:21 12616 16:55:15 Reinf orced Island Model Genetic Algor ithm to Solv e Univ ersity ... (Alfian Akbar Gozali) Evaluation Warning : The document was created with Spire.PDF for Python.
2753 ISSN: 1693-6930 4.1.3. Individual Pic king Method T est The test result f or individual pic king method test is sho wn in T ab le 4. It is sho wn in this tab le that the best population cop y is super ior to the b est individual duplication in fitness v alue . By consuming about 21 more min utes in e x ecution time , the best population cop y produced a fitness v alue 11,650. This w as better than the 12,430 from the best individual duplication. T ab le 4. Individual Pic king Method T est Result T est Number The best population cop y The best individual duplication Best Dur ation Best Dur ation Fitness (hh:mm:ss) Fitness (hh:mm:ss) 1 11520 16:55:59 12750 16:32:50 2 11950 16:52:33 12440 16:15:05 3 11840 16:30:32 12100 16:28:54 A vera g e 11770 16:46:21 12430 16:25:36 Pic king the best population is better r ather than cop ying the best individual into a population mean f or this case , the gener ation trend still tends to tr ap in a local optim um. Thus , pic king a whole best population and contin uing the process with it will help the island that did not complete its task to increase its div ersity . This par ameter , which is similar to the Island Pr ior ity T est e xplanation, is also e xper imental. The T empor al-Salient Scheme [12] could be implemented to direct the solutions this prob lem. Ho w e v er , lik e the pre vious e xample , the research uses island order instead of the T empor al-Salient Scheme f or the sak e of time efficiency . 4.1.4. Comparison T est of RIMGA The last e xper iment is to compare the perf or mance of the AIMGA and the RIMGA. The goal of this process is to analyz e ho w f ar the RIMGA could beat the AIMGA in perf or mance . The test w as r un in tw o phase: maxim um fitness and time constr aint. Maxim um fitness constr aint test w as done to compare their time perf or mance to r each same fitness and vice v ersa. Done in the same w a y as the pre vious test, this test w as done in three consecutiv e times to obtain the a v er age . T ab le 5-Dur ation sho ws the test result with same maxim um fitness . The ter minate condition of this tr ial is fitness=10000. T ab le 5 indicates that AIMGA e x ecution time w as almost t wice of the RIMGA. T ab le 5. Maxim um Fitness Limitation T est Result Model Duration (hh:mm:ss) Fitness RIMGA 16:55:59 9980 AIMGA 24:00:00 9980 T ab le 5-Fitness sho ws the result of the 24-hour test. When both r an f or 24 hours , there w as no significant diff erence betw een the RIMGA and the AIMGA in gener al. W e can theref ore conclude that, o v er all, the implementation of the Reinf orced function impro v es the AIMGA perf or mance in obtaining a good result. In addition, the result will be the same if the y still ha v e the same GA core . TELK OMNIKA V ol. 16, No . 6, December 2018 : 2747 2755 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 1693-6930 2754 5. Conc lusions This resear c h has sho wn that the AIMGA can solv e the T elk om Univ ersity UCTP with acceptab le accur acy represented b y the GA fitness v alue . Fur ther more , b y implementing the RIMGA, the timetab ling result accur acy increases in perf or mance to ne xt le v el. This ne w approach can obtain the same result as the AIMGA in a f aster (about twice) e x ecution time with a some what similar eff ect when the y r un under the same time constr aint. Thus , the reinf orced state is an e xcellent choice if w e w ant to obtain good results more quic kly . The optim um configur ation par ameters of the RIMGA f or T elk om UCTP are Island State: ignored, Island Pr ior ity: the least iter ation n umbers , and Individual Pic king: the best population cop y . Although this study f ocuses on the T elk om Univ ersity UCTP , the findings ma y w ell ha v e a bear ing on other UCTPs with similar char acter istics as the T elk om Univ ersity UCTP . T ak en together , this research confir ms that the RIMGA can solv e the UCTP with scalability issues . This study also contr ib utes additional e vidences that encour age the use o f the reinf orced function in the AIMGA. The results of the e xper iment could ser v e as the basis f or future researchers in settin g its par ameters . In addition, fur ther studies still need to be conducted f or the RIMGA f or better real-w or ld implementation. Fur ther studies on its netw or k cost is also necessar y to in v estigate its real computational time and cost. The RIMGA also still needs to be implemented in a simpler prob lem to study the correct consider ations in the par ameter adjustment. Ac kno wledgments Indonesia Endo wment Fund f or Education (LPDP), a scholarship from Ministr y of Finance , Repub lic of Indonesia, suppor ts this w or k. W e conduct this research while at Gr aduate School of Inf or mation, Production, and Systems , W aseda Univ ersity , J apan. Ref erences [1] N. K. Ar y ani, A. Soepr ijanto , I. M. Y . Negar a, and M. Sy ai’in. Economic dispatch using quantum e v olutionar y algor ithm in electr ical po w er system in v olving distr ib uted gener ators . Inter national Jour nal of Electr ical and Computer Engineer ing , 7(5):2365 2373, Oct. 2017. [2] K. Banczyk, T . Boinski, and H. Kr a wczyk. P ar allelisation of genetic algor ithms f or solving univ ersity timetab ling prob lems . In Inter national Symposium on P ar allel Computing in Electr ical Engineer ing (P ARELEC’06) , pages 325–330, Sept 2006. [3] M. W . Car ter . A comprehensiv e course timetab ling and student scheduling system at the univ ersity of w ater loo . In E. Bur k e and W . Erben, editors , Pr actice and Theor y of A utomated Timetab ling III: Third Inter national Conf erence , P A T A T 2000 K onstanz, Ger man y , A ugust 16–18, 2000 Selected P apers , pages 64–82, Ber lin, Heidelberg, 2001. Spr inger Ber lin Heidelberg. [4] M. Gare y and D . S . Johnson. Computer and Intr actability . W .H. F reeman and Compan y , Ne w Y or k, 1979. [5] A. A. Gozali, J . Tir ta w angsa, and T . A. Basuki. Asynchronous Island Model Genetic Algor ithm f or Univ ersity Course Timetab ling. In Proceedings of the 10th Inter national Conf erence on the Pr actice and Theor y of A utomated Timetab ling , pages 179–187, Y or k, 2014. P A T A T . [6] Q. K otimah, W . F . Mahm udy , and V . N. Wija y anin g r um. Optimization of fuzzy tsukamoto membership function using genetic algor ithm to deter mine the r iv er w ater . Inter national Jour nal of Electr ical and Computer Engineer ing , 7(5):2838 2846, Oct. 2017. [7] T . Muller and K. Murr a y . Comprehensiv e approach to student sectioning. Annals of Oper ations Research , 181:249–269, 2010. [8] K. Murr a y , T . Muller , and H. Rudo v a. Modeling and Solution of a Comple x Univ ersity Course Timetab ling Prob lem. In E. K. Bur k e and H. Rudo v ´ a, editors , Pr actice and Theor y of A utomated Timetab ling VI , n umber 3867 in Lecture Notes in Computer Science , pages 189–209. Spr inger Ber lin Heidelberg, A ug. 2006. DOI: 10.1007/978-3-540-77345-0 13. [9] A. W . Pr atama, A. Buono , R. Hida y at, and H. Harsa. Estimating par ameter of nonlinear bias correction method using nsga-ii in daily precipitation data. TELK OMNIKA , 16(1):241 249, Reinf orced Island Model Genetic Algor ithm to Solv e Univ ersity ... (Alfian Akbar Gozali) Evaluation Warning : The document was created with Spire.PDF for Python.
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