Research Article Dynamic Relay Satellite Scheduling Based on ABC-TOPSIS Algorithm

Transcription

1 Mathematcal Problems n Engneerng Volume 2016, Artcle ID , 11 pages Research Artcle Dynamc Relay Satellte Schedulng Based on ABC-TOPSIS Algorthm Shufeng Zhuang, 1 Zhendong Yn, 1 Zhlu Wu, 1 and Xaoguang Chen 1,2 1 School of Electroncs and Informaton Engneerng, Harbn Insttute of Technology, Harbn , Chna 2 Insttute of Telecommuncaton Satellte, Chna Academy of Space Technology, Bejng , Chna Correspondence should be addressed to Zhlu Wu; wuzhlu@ht.edu.cn Receved 22 June 2016; Revsed 1 October 2016; Accepted 16 October 2016 Academc Edtor: Erk Cuevas Copyrght 2016 Shufeng Zhuang 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. Trackng and Data Relay Satellte System (TDRSS) s a space-based telemetry, trackng, and command system, whch represents a research feld of the nternatonal communcaton. The ssue of the dynamc relay satellte schedulng, whch focuses on assgnng tme resource to user tasks, has been an mportant concern n the TDRSS system. In ths paper, the focus of study s on the dynamc relay satellte schedulng, whose detaled process conssts of two steps: the ntal relay satellte schedulng and the selecton of dynamc schedulng schemes. To solve the dynamc schedulng problem, a new schedulng algorthm ABC-TOPSIS s proposed, whch combnes artfcal bee colony (ABC) and technque for order preference by smlarty to deal soluton (TOPSIS). The artfcal bee colony algorthm s performed to solve the ntal relay satellte schedulng. In addton, the technque for order preference by smlarty to deal soluton s adopted for the selecton of dynamc schedulng schemes. Plenty of smulaton results are presented. The smulaton results demonstrate that the proposed method provdes better performance n solvng the dynamc relay satellte schedulng problem n the TDRSS system. 1. Introducton Trackng and Data Relay Satellte System (TDRSS) s a system whch can provde servce of data relayng, contnuous trackng, and TT&C (telemetry, trackng, and command) for the spacecrafts of LEO (Low Earth Orbt) and MEO (Mddle Earth Orbt) and also between spacecrafts and ground statons. As a space-based telemetry, trackng, and command system, the TDRSS represents a research feld of the nternatonal communcaton feld. To keep pace wth the development of earth observaton, mltary reconnassance, and deep space exploraton n the feld of aeronautcs and astronautcs, the data transmsson of the relay satellte presents the characterstcs of large capacty, hgh speed, and relay tasks dversfcaton [1]. It s n turn necessary to mprove the tme resource utlzaton of the relay satellte for processng tasks. Thedynamcrelaysatellteschedulngsthatthetaskplan managementcenteroftherelaysatellteallocatesthetme resource of the relay satellte for dfferent user tasks scentfcally, accordng to the prorty and duraton of user tasks. Thusnthelmtedtmeresource,thehghprortysumof the scheduled tasks can be acheved. The ssue of the dynamc relay satellte schedulng, whch focuses on assgnng tme resource to user tasks, has been an mportant concern n the TDRSS system [2]. Dfferent from the statc schedulng, even f the ntal schedulng scheme has been generated, the tasksfromusersatelltesmaybechangednthedynamc schedulng. Therefore, the ntal schedulng scheme cannot satsfythenewtasksrequests.inthscase,theschedulng alternatves need to be regenerated and a new approprate scheme should be selected to replace the ntal schedulng scheme.theselectedschementhedynamcschedulngs output as the fnal dynamc relay satellte schedulng scheme. In summary, the detaled process of the dynamc relay satellte schedulng conssts of two steps: the ntal relay satellte schedulng and the selecton of dynamc schedulng schemes. The ntal relay satellte schedulng problem s a NP-hard optmzaton problem wth the constrants of tasks attrbute, tme resource, and the vsual tme wndows between relay satellte and user satelltes, and ths motvates us to take swarm ntellgence algorthms nto account.

2 2 Mathematcal Problems n Engneerng As a branch of natural nspred algorthms, the theory of swarm ntellgence s proposed and becomes a hot spot to solve the optmzaton problems n varous areas [3]. The essence of swarm ntellgence algorthms focuses on the natural phenomena of bologcal groups. And up to now, a varety of swarm ntellgence algorthms for dfferent bologcal groups have been presented, such as genetc algorthm (GA), smulated annealng (SA), ant colony optmzaton (ACO), partcle swarm optmzaton (PSO), and artfcal bee colony (ABC) algorthm [4, 5]. Among them, the artfcal bee colony (ABC) algorthm s an ntellgence-optmzed algorthm dervng from the llumnaton of bees foot-seekng behavor. Due to ts less parameters and strong robustness, theabcalgorthmswdelyusednvarousareas[6].for example, n [7], the ABC algorthm s successfully appled to solve the classcal optmzaton problem: the travelng salesman problem. Moreover, the ABC algorthm has been appled n other aspects, such as flow shop schedulng problem [8, 9], dynamc job shop schedulng problem [10], clusterng approach [11, 12], sgnal processng [13], and mage processng [14, 15]. For the relay satellte schedulng problem, genetc algorthm s appled to generate the schedulng scheme n [16]. However, tasks prorty has not been consdered. After that the ACO algorthm for satellte control resource schedulng problem s presented n [17], but not for the relay satellte system. In [18], the ACO algorthm s used to solve the relay satellte schedulng problem, and the performances of ACO, GA, and SA algorthm are provded. In the relevant research, the ABC algorthm has not been mentoned and appled for relay satellte schedulng. After the completon of the ntal relay satellte schedulng, the ntal schedulng scheme may not be mplemented mmedately. And the tasks set s lkely to change, whch causesthevaratonoftherelaysatellteschedulngscheme. In ths case, the dynamc schedulng scheme needs to replace the ntal schedulng scheme. The goal of the dynamc schedulng s to select a new modfed scheme, whch not only has the hgh prorty sum of the scheduled tasks, but also has the mnmum schemes varaton n comparson wth the ntal schedulng scheme. Therefore, the selecton of dynamc schedulng schemes can be treated as a multple attrbute decson makng (MADM) problem. The technque for order preference by smlarty to deal soluton (TOPSIS) s an effcent method n dealng wth MADM problems [19 21]. The crtcal prncple of TOPSIS s to rank the alternatves accordng to the dstance between alternatves to deal soluton [22, 23]. The alternatve wth the mnmum dstance from the postve deal soluton and the maxmum dstance from the negatve deal soluton s chosen as the best alternatve. For the last several years, themethodoftopsisswdelyapplednvarousfelds, such as manufacturng [24], mltary [25], product desgn [26], resource allocaton, and resource selecton [27, 28]. As a helpful decson rule, the TOPSIS method s sutable for solvng the selecton problem of the dynamc schedulng schemes. In ths paper, the research content focuses on the dynamc relay satellte schedulng n the TDRSS system. In detal, a new effcent schedulng algorthm ABC-TOPSIS based on artfcal bee colony (ABC) and technque for order preference by smlarty to deal soluton (TOPSIS) s frst proposed, n order to solve the dynamc relay satellte schedulng. Frst, the artfcal bee colony (ABC) algorthm s utlzed to solve the ntal relay satellte schedulng. Then by the quantzaton of the schemes varaton between ntal schedulng scheme and dynamc schedulng scheme, the selecton of dynamc schedulng schemes s converted from multple objectve decson makng (MODM) problem nto multple attrbute decson makng (MADM) problem. Thus, TOPSIS s appled to solve the selecton of dynamc schedulng schemes when the tasks set proposed by user satelltes has changed. The rest of ths paper s organzed as follows. In Secton 2, the dynamc relay satellte schedulng system s ntroduced. The ABC-TOPSIS algorthm s developed to solve the dynamc relay satellte schedulng n Secton 3. In Secton 4, the performance of the proposed ABC-TOPSIS algorthm s shown. The conclusons are drawn n Secton Dynamc Relay Satellte Schedulng System In the dynamc relay satellte schedulng system, the relay satellte receves tasks requests from dfferent user satelltes, ncludng low-orbt magng satellte, electronc satellte, and measurement satellte. Wthout consderng the contents of the tasks, the man dfferences between the tasks are the duraton and the prorty. The purpose of the relay satellte schedulng s to allocate the tme resource of the relay satellte reasonably and to generate the schedulng scheme whch meets the expected target. The specfc mplementaton process conssts of two parts: the ntal relay satellte schedulng and the selecton of dynamc schedulng schemes. The dynamc relay satellte schedulng system dagram s shown n Fgure 1. The ntal relay satellte schedulng generates the daly work plan of the relay satellte. Frstly, the tasks proposed by user satelltes are preprocessed to calculate the avalable tme wndows and to assgn the prorty. Then, the ntal relay satellte schedulng model s establshed based on the constrant condtons and the tme resource nformaton. Fnally, the ntal relay schedulng model s solved by the specfc schedulng algorthm. Thus the schedulng scheme can be derved and delvered to perform. Snce the relay satellte s not always ready to schedule tasks, after the generaton of the ntal relay satellte schedulng scheme, the ntal schedulng scheme cannot be mplemented mmedately. In ths perod, the tasks set would be changed dynamcally: some tasks have been canceled, and some new tasks have been added. In ths case, the varaton of the tasks set leads to the changes n the ntal relay satellte schedulng. In vew of the changes of the tasks requests, a new correspondng dynamc relay satellte schedulng scheme needs to be generated. The dynamc schedulng scheme not only ams at makng full use of the tme resource of the relay satellte and maxmzng the scheduled tasks prorty sum as the ntal schedulng scheme, but also mnmzes the varaton between the ntal scheme and the dynamc scheme.

3 Mathematcal Problems n Engneerng 3 Intal relay satellte schedulng Intal schedulng scheme Implementaton Tasks from dfferent user satelltes Tasks preprocessng Tme resource of relay satellte Selecton of dynamc schedulng scheme Dynamc schedulng scheme Fgure 1: Dynamc relay satellte schedulng system dagram. Theprocessofthedynamcrelaysatellteschedulngs summarzed n two steps, whch are the ntal relay satellte schedulng and the selecton of dynamc schedulng schemes. Fgure 2 shows the flow chat of the dynamc relay satellte schedulng based on the proposed ABC-TOPSIS algorthm. 3. Schedulng Strategy Based on ABC-TOPSIS Algorthm 3.1. Mathematcal Model of Intal Relay Satellte Schedulng Problem. In the ntal relay satellte schedulng problem, the relay satellte has the msson of handng the tasks proposed by the user satelltes. The key object s to allocate the tme resourceoftherelaysatellteforusertasksandachevethe maxmum prorty sum. Snce the relay satellte s not always vsble to user satelltes, the sgnfcant constrant s that there are tme wndows between the relay satellte and user satelltes.thetasksmustbecompletedonlywthnthegven vsual tme wndows. In order to establsh the mathematcal model of the ntal relay satellte schedulng problem, some model parameters are declared as follows Model Parameters. ThesetofthetasksssettoR = r 1,r 2,...,r n },wheren s the number of tasks that need to be scheduled. The set of the prorty of the tasks s expressed as P = p 1,p 2,...,p n } and the set of the duraton of the tasks s D = d 1,d 2,...,d n }.ThesetC = c 1,c 2,...,c n } represents the task contrbuton, whch s the functon of task prorty p and task duraton d. Also the task decson varables are denoted by the set X = x 1,x 2,...,x n },wherex 0, 1}, = 1,2,...,n.Thedecsonvarablex =1represents that the task r has been scheduled by the relay satellte, and x =0 means that the task r has not been scheduled. In addton, the vsual tme wndows and tme resource of the relay satellte are declared. The tme nterval set [SE] = [s 1,e1 ], [s2,e2 ],...,[sk,ek ]} presents the set of vsual tme wndows of the relay satellte whch serve the task r,where k sthenumberofvsualtmewndows,s τ s the start tme, and e τ s the end tme. The tme resource of the relay satellte s denoted by the tme nterval [T S,T E ],wheret S s the start tme and T E s the end tme Objectve Functon. The objectve of the ntal relay satellteschedulngstoobtananoptmaltasksservce scheme, whch, n other words, means the maxmzaton of the sum of the contrbuton of the scheduled tasks. The objectve functon of the ntal relay satellte schedulng can be descrbed as where max n =1 x = 1, r s scheduled 0, unless, c =F(p,d ), c 1. d x c, (1) Constrants. The constrants of the ntal relay satellte task schedulng are gven as follows. (2) T s T T E, T s T +d T E (3) T s τ (1 τ k) f x =1 (4) T +d e τ (1 τ k) f x =1. (5) For r [r 1,r n ], r j [r 1,r n ], =j T T j +d j or T +d T j, where T s the start executon tme of the task r. Constrants (3), (4), and (5) bound the tme perod for the tasks. Constrant (3) represents that tasks whose duraton, more than the length of the relay satellte tme resource, cannot be scheduled. Constrant (4) and constrant (5) mply that the tasks must be scheduled only wthn the gven vsual tme wndows. Constrant (6) means that, at the same tme, the relaysatelltecanonlyhandleonetask.thetmeresources (6)

4 4 Mathematcal Problems n Engneerng Start Analyze ntal schedulng parameters Establsh mathematcal model of ntal schedulng scheme Intal schedulng based on ABC algorthm Intal relay satellte schedulng Feedback tasks mplementaton nformaton to user satelltes Yes Is tasks set changed? Regenerate schedulng alternatves by ABC algorthm No Select dynamc scheme from alternatves by TOPSIS algorthm to replace ntal scheme Implement schedulng scheme Selecton of dynamc schedulng scheme Stop Fgure 2: Flow chat of the dynamc relay satellte schedulng based on the proposed ABC-TOPSIS algorthm. ncapable of beng shared by multple tasks at the same tme. If the current task s not yet completed, new tasks cannot be executed. As expressed n Secton 3.1.1, the task contrbuton varable s the functon of task prorty p and task duraton d. To smplfy the model solvng process, t s assumed that the constructon of the feasble soluton s based on the tme sequence. After the end of the current task, the new task wll be scheduled mmedately for executon. Therefore, the tmeresourceoftherelaysatelltecanbefullyutlzed.inths case, the task contrbuton varable s only related to the task prorty. Then the objectve functon (1) s smplfed as max n =1 x p. (7) 3.2. Intal Relay Satellte Schedulng Based on ABC Algorthm. Snce the optmzaton problem n (7) s generally a NP-hard combnatoral problem, ths requres an effcent optmzaton algorthm for the ntal relay satellte schedulng. In ths secton, the artfcal bee colony algorthm s appled to solve therelaysatellteschedulngproblem. The artfcal bee colony (ABC) algorthm s an ntellgence-optmzed algorthm dervng from the llumnaton of bees foot-seekng behavor. There are three knds of roles n the bee swarm ntellgence model, whch are scout bees, onlooker bees, and employed bees. In the begnnng, wthout pror knowledge, all bees are dentfed as scout bees wth the behavor of the random search around hves. The rchness of the food sources s compared and the relatvely rch food source s selected as the searchng routes of employed bees

5 Mathematcal Problems n Engneerng 5 [29].Thentheemployedbeestakechargeofsearchngfood around the food sources n ther memory; after that, they share the food amount nformaton wth the onlooker bees by dancng n the nearby hve. Then the onlooker bees would select employed bees to follow accordng to the nformaton provded by employed bees [30]. The artfcal bee colony algorthm for the ntal relay satellte schedulng problem can be descrbed as follows. (1) Defne the transton probablty of scout bees and onlooker bees P(r,k,t),whchmeanstheprobabltythat the task r s scheduled n the kth vsual tme wndow at the moment t. The transton probablty of scout bees can be expressed as P(r,k,t) [p ] α [1/d ] β = r allow(k,t) [p ] α [1/d ], β r allow (k, t) 0, r allow (k, t), where p s the prorty of the task r and d stheduratonof the task r. α and β are the weght factors. The set allow (k, t) represents the allowed tasks set for schedulng. Accordng to (8), the task wth hgher prorty and shorter duraton has hgherprobabltytobescheduled. The transton probablty of onlooker bees s wrtten as P(r,k,t) [p ] α [1/d ] β [φ] γ = r allow(k,t) [p ] α [1/d ] β [φ], γ r allow (k, t) 0, r allow (k, t), where φ represents the leadng factor, whch s the leadng nformaton generated by employed bees. The correspondng weght s denoted as γ. (2) In the ABC algorthm, pseudo-random proporton rule s adopted, whch can be descrbed as follows: (a) generate a unformly dstrbuted random number q n the nterval [0, 1], (b) f q q 0 (q 0 s a fxed parameter value), then r = arg max P(r,k,t), (10) r allow(k,t) (c) f q>q 0, then choose the task accordng to P(r,k,t). (3) In each teraton, the optmal soluton s set as the poston of employed bees. Then, the employed bees release the leadng nformaton to attract the onlooker bees. After each teraton, the leadng factor s updated. The updated rules can be descrbed as (8) (9) φ (j+1) =φ (j) +q g C cur, (11) where j s the current teraton. q g represents the leadng factor update ncrease coeffcent. And C cur s the normalzed ftness, whch s defned as follows. C cur = ft max SN n=1 ft, (12) n where ft n s the ftness of the nth soluton. The calculaton equaton s expressed as 1+f n, f n >0 ft n = 1 1+abs (f n ), f n <0. (13) In (13), f n s the optmal soluton tll current teraton n the ABC algorthm for the objectve functon (7). (4) In order to avod the excessve accumulaton of leadng factor, the leadng factor range s lmted to [φ mn, φ max ]. φ (j), φ mn φ (j) φ max φ (j+1) = φ max, φ (j) >φ max φ mn, φ (j) <φ mn. (14) The ABC algorthm s termnated when t reaches the maxmum number of teratons [12] and the schedulng scheme wth the maxmum prorty sum s the fnal output result for the ntal relay satellte schedulng problem. As s seen from the above, n the ABC algorthm, the scout bees search the soluton space-based on the constrant condtons, whch ensures the randomness and avods fallng nto the local optmal soluton. The employed bees correspond to the optmalsolutontllcurrentteraton.theykeeptheelte feature and mantan attracton to the onlooker bees. The onlooker bees select employed bees to follow accordng to the leadng nformaton. The prospect of the mechansm s to mport postve feedback and guarantee the convergence of the algorthm. Through the coordnaton of three knds of bees, the ABC algorthm acheves the effectve optmzaton ablty of randomness and convergence Selecton of Dynamc Schedulng Schemes Based on TOPSIS Algorthm. After the generaton of the ntal relay satellte schedulng scheme, t wats for the mplementaton of the relay satellte. Generally, the ntal relay satellte schedulng scheme would not be made any adjustments. However, n fact, snce the varaton of the user satelltes requrements,someofthetasksthathavebeenproposedmay be canceled. Or n addton, some new tasks are nserted, especally some hgh prorty tasks. The change of the tasks has a drect mpact on the set of the tasks R. Whatsmore, the parameter sets of the tasks prorty P and tasks duraton D also change, respectvely. In ths case, the ntal schedulng scheme cannot be performed completely. In consderaton of the changes of the tasks requests, t s necessary to make the dynamc adjustment and to generate a new correspondng dynamc relay satellte schedulng scheme based on the ntal schedulng scheme. Under the dynamc condton, the adjustment of the ntal schedulng scheme must follow certan prncples. No matter how the tasks set changes, one of the major objectvesstoachevethehghtasksprortysum.theother objectve s to mnmze the varaton between ntal scheme and dynamc scheme. Once the ntal schedulng scheme s

6 6 Mathematcal Problems n Engneerng generated, the user satelltes wll receve the tasks mplementaton plan from the relay satellte. And the tasks, whch are scheduled, enter the state of pendng executon. Then the user satelltes may make the correspondng work arrangements for tasks. Therefore a large-scale dynamc adjustment s bound to affect the user satelltes future decson. Basedontheaboveanalyss,thedynamcschedulng problem s a multple objectve decson makng (MODM) problem.oneobjectveofthedynamcschedulngsto allocatethetmeresourceoftherelaysatellteforusertasks and acheve the maxmum prorty sum. The other s to select a new dynamc schedulng scheme, whch has the mnmal change to the ntal schedulng scheme. In order to facltate solvng the multple objectve decson makng problem of the dynamc relay satellte schedulng, frstly t s essental to quantze the schemes varaton between the ntal schedulng scheme and the dynamc schedulng scheme. Assume that the tasks set scheduled n the ntal schedulng scheme s denoted as R n, whle the tasks set scheduled n the dynamc schedulng scheme s expressed as R dyn.thevarablechange(r) ndcates whether the task r changes between the ntal schedulng scheme and the dynamc schedulng scheme. The varable Change(r) s defned as the followng equaton. Change (r) = 0, r R n and r R dyn (15) 1, r R n and r R dyn. Thus, the schemes varaton between the ntal schedulngschemeandthedynamcschedulngschemecanbe wrtten as VAR = Change (r) (16) r R n The solvng process of the dynamc schedulng problem s to select a new modfed scheme, whch has the mnmum schemes varaton n comparson wth the ntal schedulng scheme. The detaled steps are gven as follows. (1) When the change of the tasks set happens after ntal schedulng, reorganze the model parameters of the sets, and use the ABC algorthm to generate several new dynamc schedulng schemes as Secton 3.2. The dynamc schedulng schemes set s denoted as S = s 1,s 2,...,s a },wherea s the number of the new dynamc schedulng schemes. The scheduled tasks prorty sum set of the dynamc schedulng schemes s wrtten as P(s) =p(s 1 ), p(s 2 ),...,p(s a )}. (2) Compare the new dynamc schedulng schemes wth the ntal schedulng scheme, and calculate the schemes varatons for all newly generated schedulng schemes wth reference to the ntal schedulng scheme, accordng to (15) and (16). And the schemes varatons set s represented as VAR(s) =var(s 1 ), var(s 2 ),...,var(s a )}. (3) After the completon of step (1) andstep(2), the dynamc schedulng problem s transformed from multple objectve decson makng (MODM) problem nto multple attrbute decson makng (MADM) problem. The MADM problem of the dynamc schedulng can be denoted as DR [P (s), VAR (s)]. s S (17) The dynamc schedulng problem can be depcted as the use of the decson rule DR to choose a best schedulng scheme from the set S, n accordance wth the attrbute P(s) and VAR(s). In ths paper, the TOPSIS (Technque for Order Preference by Smlarty to an Ideal Soluton) algorthm s adopted as the decson rule DR for the dynamc schedulng, whch s descrbed as follows. (a) Construct normalzed decson matrx Z j = f j a =1 f2 j, (18) where 1,2...,a} and j 1,2}. f j s the jth attrbute value of the scheme. f 1 =p(s ),andf 2 = var(s ). (b) Construct the weghted normalzed decson matrx Z j =w j Z j, (19) where w j s the weght value of the jth attrbute. The value w j represents the mportance of each attrbute. (c) Determne the postve deal soluton (PIS) and negatve deal soluton (NIS) PIS =(max NIS =(mn Z j j=1),(mn Z j j=2)} Z j j=1),(max Z j j=2)}. (20) (d) Calculate the separaton measures of each alternatves from the PIS and NIS C PIS C NIS = = 2 j=1 2 j=1 (Z j PIS j ) 2 (Z j NIS j ) 2. (21) (e) Calculate the relatve closeness of the th schedulng scheme wth respect to the deal soluton C = (C PIS C NIS +C NIS ). (22) The set of the dynamc schedulng schemes can now be ranked accordng to the descendng order of C.Byusng the value C, we can get the apprasal ranks for each scheme. The maxmum value of C corresponds to the best dynamc schedulng scheme. 4. Smulaton Results In ths secton, the performances of the proposed dynamc schedulng method ABC-TOPSIS are shown n the followng smulaton results. Assume a system wth a relay satellte and 10 user satelltes. Each user satellte has 3 tasks requests. Thus thenumberoftaskss30.thetotaltmeresourceoftherelay satellte s set to 100 mnutes. The relay satellte arranges two

7 Mathematcal Problems n Engneerng 7 Table 1: Schedulng parameters. User satellte Tme wndows of relay satellte/mnute Duraton of each task/mnutes Prorty of each task Satellte 1 [1030][7095] [1196] [466] Satellte 2 [1535][5080] [1387] [1358] Satellte 3 [1232][6096] [1045] [2148] Satellte 4 [5 25][55 70] [7 6 10] [5 9 10] Satellte 5 [1736][4062] [1164] [1164] Satellte 6 [850][5570] [858] [777] Satellte 7 [3055][8093] [1085] [985] Satellte 8 [2243][6688] [996] [6159] Satellte 9 [20 50][80 99] [7 12 9] [5 12 7] Satellte 10 [1838][4578] [1058] [1038] Satellte Tme (mnute) Fgure 3: Schedulng result based on ABC algorthm. vsual tme wndows for each user satellte. The tasks prorty and duraton are set between 1 and 15. Table 1 shows the ntal schedulng parameters. Fgure 3 shows a generated ntal schedulng scheme wth the ABC algorthm. In the ABC algorthm for the ntal relay satellte schedulng, the number of bees s set to 100, and the maxmumnumberofteratonss50.q 0 =0.9,q g =0.1,the weght factors α, β, andγ are set to 1.5. The leadng factor range values φ mn and φ max are equal to 0.5 and 8, respectvely. In Fgure 3, the yellow lnes represent the vsual tme wndows between relay satellte and user satelltes. In addton, the black lnes are the scheduled tasks. The length of the black lnes corresponds the duraton of tasks. The detaled tasks scheduledsequencesshownntable2.itcanbeseenthat thetmeresourceoftherelaysatelltesfullyutlzedwththe constrants of tme wndows. Moreover, the ntal schedulng scheme acheves the optmal soluton wth the prorty sum of scheduled tasks equalng to 122. Table 3 compares the performances between ABC, ACO, SA, and GA algorthms for the ntal schedulng. The total teraton tmes of four algorthms are all set to 50. Accordng to Table 3, the ABC and ACO algorthms obtan the optmal prorty sum, whle the SA and GA algorthms fall nto the local optmal soluton. The ACO and GA algorthms take larger teraton tmes to converge, wth respect to the ABC and SA algorthm. Therefore, wth the comprehensve comparson of the convergence and optmzaton ablty, the ABC algorthm turns to be more effectve than other three algorthms. Ths s manly due to the reasons that, n the ABC algorthm, scout bees, onlooker bees, and employed bees perform own dutes effcently. The scout bees search the soluton space randomly based on the constrant condtons, whch ensures the randomness and avods fallng nto the local optmal soluton. The employed bees keep the elte feature and mantan attracton to the onlooker bees, whch guarantee the convergence of the algorthm. In addton, n order to compare the performances of ABC, ACO, SA, and GA algorthms more fully, the smulaton experments are carred on for four relay satellte schedulng cases, whch are lsted as follows. Schedulng Case 1. Tme resource of the relay satellte s set to 100 mnutes, the number of user satelltes s arranged to 10, thenumberoftmewndowss20,andthenumberoftasks s 30. Schedulng Case 2. Tmeresourceoftherelaysatelltessetto 100 mnutes, the number of user satelltes s arranged to 15, the number of tme wndows s 30, and the number of tasks s 45. Schedulng Case 3. Tme resource of the relay satellte s set to 150 mnutes, the number of user satelltes s arranged to 15, the number of tme wndows s 45, and the number of tasks s 45. Schedulng Case 4. Tmeresourceoftherelaysatelltessetto 150 mnutes, the number of user satelltes ncreases to 15, the number of tme wndows s 45, and the number of tasks s 60. Tables 4 7 compare the performances between ABC, ACO, SA, and GA n dfferent schedulng stuatons. From Tables 4 7, t s clear that the algorthms of SA and GA fall nto local optmal soluton and obtan a relatvely low prorty sum, whle the ABC and ACO algorthms both acheve a hgh prorty sum. Then by comparson of average and standard devaton values of prorty sum, ABC appears to be more stable and effcent than ACO.

8 8 Mathematcal Problems n Engneerng Table 2: Scheduled tasks. Scheduled task User satellte Prorty Duraton/mnute R 3 Satellte 4 10 [5 15] R 2 Satellte 3 14 [15 19] R 3 Satellte 2 8 [19 26] R 2 Satellte 6 7 [26 31] R 3 Satellte 8 9 [31 37] R 2 Satellte 7 8 [37 45] R 2 Satellte 5 6 [45 51] R 1 Satellte [51 61] R 2 Satellte 4 9 [61 67] R 3 Satellte 3 8 [67 72] R 3 Satellte 1 6 [72 78] R 2 Satellte 8 15 [78 87] R 2 Satellte 9 12 [87 99] Table 3: Performance of ABC, ACO, SA, and GA algorthms. Algorthm Optmal prorty sum Iteraton tmes for convergence GA SA ACO ABC Table 7: Algorthms performance n schedulng case 4. Algorthms ABC ACO SA GA Optmal prorty sum Worst prorty sum Average of prorty sum Standard devaton of prorty sum Table 4: Algorthms performance n schedulng case 1. Algorthms ABC ACO SA GA Optmal prorty sum Worst prorty sum Average of prorty sum Standard devaton of prorty sum Table 5: Algorthms performance n schedulng case 2. Algorthms ABC ACO SA GA Optmal prorty sum Worst prorty sum Average of prorty sum Standard devaton of prorty sum Table 6: Algorthms performance n schedulng case 3. Schemes prorty sum Schemes varaton Fgure 4: Schemes prorty sum versus scheme varaton Algorthms ABC ACO SA GA Optmal prorty sum Worst prorty sum Average of prorty sum Standard devaton of prorty sum After the generaton of the ntal schedulng scheme, the tasks set would be changed dynamcally: some tasks have been canceled, and some new tasks have been added. In ths case, the varaton of the tasks set leads to the change n the ntal relay satellte schedulng. Once the change of the tasks set happens after ntal schedulng, reorganze the model parametersofthesets,andusetheabcalgorthmtogenerate several new dynamc schedulng schemes. In the followng smulaton, the number of alternatves of the new dynamc schedulng s 50. Fgure 4 shows the selecton results of the dynamc schedulng schemes by the ABC-TOPSIS method. Assume the varaton of tasks requrements s that 2 new tasks are nserted.theprortesof2newtasksare5and15,whle theduratonsare3mnutesand6mnutes,respectvely. The weght value of each attrbute w j s set to 0.5 equally.

9 Mathematcal Problems n Engneerng 9 Schemes varaton ABC-TOPSIS ABC-SAW Varaton of the tasks set Fgure 5: Schemes varaton versus varaton of the tasks set. Schemes prorty sum ABC-TOPSIS ABC-SAW Varaton of the tasks set Fgure 6: Schemes prorty sum versus varaton of the tasks set. The total 50 alternatves are presented n a scatter plot n accordance wth the schemes varaton and schemes prorty sum. In addton, the value near the scatter n Fgure 4 represents the number of alternatves. In Fgure 4, the best selecton alternatve by ABC-TOPSIS s marked n red, and theworstselectonalternatvebyabc-topsissmarkedn blue. Therefore, the schemes varaton value VAR n (16) of the best dynamc scheme s only 1, whch s a small change between ntal scheme and dynamc scheme. Meanwhle, the best scheme acheves the hgh tasks prorty sum of 132. Thebestalternatvesthendentfedasthefnaldynamc schedulng scheme. Fgures 5 and 6, respectvely, show the schemes varaton VAR and the schemes prorty sum between the ntal schedulng scheme and the dynamc schedulng scheme versus the varaton of the tasks set. When the varaton value of the tasks set s n,tmeansthatn tasks are canceled from the ntal tasks set. Meanwhle, when the varaton value of the tasks set s n, tmeansthatn tasks are nserted nto the ntal tasks set. In the smulaton, the varaton of the tasks sets from 3 to7.abc-sawsthemethodthatcombnes artfcal bee colony (ABC) and smple addtve weghtng (SAW). From Fgures 5 and 6, t can be seen that the ABC- TOPSIS method obtans the smaller schemes varaton and a lttle bt lower prorty sum n comparson wth ABC-SAW. The ABC-TOPSIS method provdes better performance n obtanng the small schemes varaton, whle the ABC-SAW method has more emphass on the hgh prorty sum. Thedynamcrelaysatellteschedulngstreatedasa multple attrbute decson makng (MADM) problem. The two attrbutes are the schemes varaton and prorty sum. In order to compare the performances of ABC-TOPSIS and ABC-SAW clearly, a comprehensve evaluaton value CE s ntroduced, whch s defned as follows. CE = abs (VAR 0 ) abs (PS 0 ) VAR 0 = VAR TS PS 0 = PS V PS, (23) where TS s the number of scheduled tasks n the ntal schedulng scheme. PS s the prorty sum of scheduled tasks n the ntal schedulng scheme. PS V s the schemes prorty sum varaton between the ntal schedulng scheme and the dynamc schedulng scheme. Snce the value CE takes nto account the relatve values of schemes varaton and prorty sum, t s able to effectvely evaluate the performance of ABC- TOPSIS and ABC-SAW. The method wth lower CE would provde better performance n solvng the dynamc relay satellte schedulng problem. Fgure 7 compares the evaluaton ndex CE of ABC- TOPSISandABC-SAW.TheABC-TOPSISmethodproposed n ths paper acheves the relatvely lower CE than ABC-SAW, whch proves that the ABC-TOPSIS has better performance n solvng the dynamc schedulng problem. The ABC- SAW method uses weghtng addton operaton for dfferent attrbutes, whch leads to the result that t s senstve to the large attrbute value. In the dynamc schedulng problem, the value of the tasks prorty sum s larger than the value of the schemes varaton. Thus, the ABC-SAW would select the dynamcschemewthhghprortysum.andthescheme varaton attrbute receved less attenton. 5. Concluson In ths paper, an effcent method ABC-TOPSIS for the dynamcrelaysatellteschedulngsproposed.thedetaled processofthedynamcrelaysatellteschedulngconssts of two steps: the ntal relay satellte schedulng and the selecton of dynamc schedulng schemes. In the frst step,

10 10 Mathematcal Problems n Engneerng CE ABC-TOPSIS ABC-SAW Varaton of the tasks set Fgure 7: CE versus varaton of the tasks set. the ntal relay satellte schedulng mathematcal model s establshed as a NP-hard combnatoral problem. The artfcal bee colony (ABC) algorthm s appled to solve the ntal schedulng problem and to generate the ntal schedulng scheme wth hgh tasks prorty sum. In the second step, the selecton of dynamc schedulng schemes s consdered as a multple attrbute decson makng (MADM) problem, whch ams at achevng the hgh tasks prorty sum and the small varaton between ntal scheme and dynamc scheme. Therefore, the technque for order preference by smlarty to deal soluton (TOPSIS) s performed for the selecton of dynamc schedulng schemes. The smulaton results show that, n contrast wth the other approach, the ABC-TOPSIS s an effectve and reasonable dynamc schedulng method. Competng Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments The research n ths artcle s supported by the Natonal Natural Scence Foundaton of Chna (Grant nos and ). References [1] S.Rojanasoonthon,J.F.Bard,andS.D.Reddy, Algorthmsfor parallel machne schedulng: a case study of the trackng and data relay satellte system, JournaloftheOperatonalResearch Socety,vol.54,no.8,pp ,2003. [2] S. Rojanasoonthon, Parallel Machne Schedulng wth Tme Wndows, Graduate School of the Unversty of Texas, Austn, Tex, USA, [3] M. Basu, Artfcal bee colony optmzaton for mult-area economc dspatch, Internatonal Electrcal Power and Energy Systems,vol.49,no.1,pp ,2013. [4] D. Karaboga and B. Basturk, On the performance of artfcal bee colony (ABC) algorthm, Appled Soft Computng, vol.8, no. 1, pp , [5] M. El-Abd, Performance assessment of foragng algorthms vs. evolutonary algorthms, Informaton Scences, vol. 182, no. 1, pp , [6] W.-L. Xang and M.-Q. An, An effcent and robust artfcal bee colony algorthm for numercal optmzaton, Computers and Operatons Research,vol.40,no.5,pp ,2013. [7] L. P. Wong, M. Y. H. Low, and C. S. Chong, Bee Colony Optmzaton wth Local Search for Travelng Salesman Problem, Sngapore Nanyang Technologcal Unversty, [8] J.-Q. L, Q.-K. Pan, and F.-T. Wang, A hybrd varable neghborhood search for solvng the hybrd flow shop schedulng problem, Appled Soft Computng,vol.24, no.1,pp , [9] J.-Q. L, Q.-K. Pan, and P.-Y. Duan, An mproved artfcal bee colony algorthm for solvng hybrd flexble flowshop wth dynamc operaton skppng, IEEE Transactons on Cybernetcs, vol.46,no.6,pp ,2016. [10] S.Nguyen,M.Zhang,M.Johnston,andK.C.Tan, Automatc programmng va terated local search for dynamc job shop schedulng, IEEE Transactons on Cybernetcs,vol.45,no.1,pp. 1 14, [11] C. S. Zhang, D. T. Ouyang, and J. X. Nng, An artfcal bee colony approach for clusterng, Expert Systems wth Applcatons,vol.37,no.7,pp ,2010. [12] D. Karaboga and C. Ozturk, A novel clusterng approach: Artfcal Bee Colony (ABC) algorthm, Appled Soft Computng, vol. 11, no. 1, pp , [13]S.L.Sabat,S.K.Udgata,andA.Abraham, Artfcalbee colony algorthm for small sgnal model parameter extracton of MESFET, Engneerng Applcatons of Artfcal Intellgence, vol.23,no.5,pp ,2010. [14]M.Ma,J.Lang,M.Guo,Y.Fan,andY.Yn, SARmage segmentaton based on artfcal bee colony algorthm, Appled Soft Computng, vol. 11, no. 8, pp , [15] F. G. Mohammad and M. S. Abadeh, Image steganalyss usng a bee colony based feature selecton algorthm, Engneerng Applcatons of Artfcal Intellgence, vol.31,no.1,pp.35 43, [16] Z.L.L,X.Meng,S.Q.Lu,S.L.Zhang,andW.Zheng, Genetc algorthm for TDRS communcaton schedulng wth resource constrants, n Proceedngs of the Internatonal Symposum on Intellgent Informaton Technology Applcaton Workshops (IITAW 08), pp , Shangha, Chna, December [17] Z.Na,F.Z.Ren,andK.L.Jun, Newpheromonetralupdatng method of ACO for satellte control resource schedulng problem, n Proceedngs of the IEEE Congress on Evolutonary Computaton (CEC 10),pp.1 6,July2010. [18] Z. S. Gu, Research on the Relay Satellte Dynamc Schedulng Problem Modelng and Optmzaton Technology, Natonal Unversty of Defense Technology, [19] A. A. Naen, S. Homayoun, and M. Saadatseresht, Improvng the dynamc clusterng of hyperspectral data based on the ntegraton of swarm optmzaton and decson analyss, IEEE JournalofSelectedTopcsnAppledEarthObservatonsand Remote Sensng,vol.7,no.6,pp ,2014. [20] Z. Yue, Extenson of TOPSIS to determne weght of decson maker for group decson makng problems wth uncertan nformaton, Expert Systems wth Applcatons, vol. 39,no. 7, pp , 2012.

11 Mathematcal Problems n Engneerng 11 [21] Z. Yue, Approach to group decson makng based on determnng the weghts of experts by usng projecton method, Appled Mathematcal Modellng, vol.36,no.7,pp , [22] S.-M. Chen and J.-A. Hong, Fuzzy multple attrbutes group decson-makng based on rankng nterval type-2 fuzzy sets and the TOPSIS method, IEEE Transactons on Systems, Man, and Cybernetcs: Systems,vol.44,no.12,pp ,2014. [23] N. G. Pateraks, A. Mazza, S. F. Santos et al., Mult-objectve reconfguraton of radal dstrbuton systems usng relablty ndces, IEEE Transactons on Power Systems,vol.31,no.2,pp , [24] Y. T. İç, An expermental desgn approach usng TOPSIS method for the selecton of computer-ntegrated manufacturng technologes, Robotcs and Computer-Integrated Manufacturng,vol.28,no.2,pp ,2012. [25] M. Dağdevren, S. Yavuz, and N. Kılınç, Weapon selecton usng the AHP and TOPSIS methods under fuzzy envronment, Expert Systems wth Applcatons, vol. 36, no. 4, pp , [26] H. Shdpour, M. Shahrokh, and A. Bernard, A mult-objectve programmng approach, ntegrated nto the TOPSIS method, n order to optmze product desgn; In three-dmensonal concurrent engneerng, Computers and Industral Engneerng, vol.64,no.4,pp ,2013. [27] A. Kelemens, K. Ergazaks, and D. Askouns, Support managers selecton usng an extenson of fuzzy TOPSIS, Expert Systems wth Applcatons,vol.38,no.3,pp ,2011. [28] D. Mohamad and R. M. Jaml, A preference analyss model for selectng tourst destnatons based on motvatonal factors: a case study n kedah, malaysa, Proceda-Socal and Behavoral Scences,vol.65,pp.20 25,2012. [29] X.F.Dng,G.L.Lu,M.Du,H.Guo,C.Duan,andH.Qan, Effcency mprovement of overall PMSM-nverter system basedonartfcalbeecolonyalgorthmunderfullpowerrange, IEEE Transactons on Magnetcs,vol.52,no.7,pp.1 4,2016. [30] M. D. L, H. Zhao, X. W. Weng, and H. Q. Huang, Artfcal bee colony algorthm wth comprehensve search mechansm for numercal optmzaton, Systems Engneerng and Electroncs,vol.26,no.3,pp ,2015.

12 Advances n Operatons Research Advances n Decson Scences Appled Mathematcs Algebra Probablty and Statstcs The Scentfc World Journal Internatonal Dfferental Equatons Submt your manuscrpts at Internatonal Advances n Combnatorcs Mathematcal Physcs Complex Analyss Internatonal Mathematcs and Mathematcal Scences Mathematcal Problems n Engneerng Mathematcs Dscrete Mathematcs Dscrete Dynamcs n Nature and Socety Functon Spaces Abstract and Appled Analyss Internatonal Stochastc Analyss Optmzaton