A savings procedure based construction heuristic for the offshore wind cable layout optimization problem

Transcription

1 A svings proeure se onstrution heuristi for the offshore win le lyout optimiztion prolem Sunney Foter (B.Eng. Mehnil) MS. Cnite in Energy Deprtment of Informtis, University of Bergen, Norwy 2018 Supervisors: Prof. Dg Hugln (UiB) n Ahm Hemmti,PhD. Deep Win Conferene 2018, Tronheim, Norwy

2 Tle of Content INTRODUCTION Offshore Win Cle Lyout (OWCL)Optimiztion Prolem Sttement n Assumptions Constrints: Noe rossing/le rossing, ostles n out-egree Fetures: Prllel les n rnhing MILP moel use for enhmrking heuristi solutions HEURISTIC Bsi ie Pseuooe (Esu-Willims) Ies to tkle le rossing Ies to ientify noe rossing Pseuooe (Ostle-Awre Esu Willims) Experimentl Results n Moifie Algorithm Initil results from the Moifie Esu-Willims (Win frms: Wlney 1, Wlney 2 n Brrow) Prmetriztion n introuing shpe ftor Improve results From onstrution heuristi to Met-Heuristi : Future tivities (Very lrge Neighorhoo serh (VLNS) n GRASP)

3 Tle of Content INTRODUCTION Offshore Win Cle Lyout (OWCL)Optimiztion Prolem Sttement n Assumptions Constrints: Noe rossing/le rossing, ostles n out-egree Fetures: Prllel les n rnhing MILP moel use for enhmrking heuristi solutions HEURISTIC Bsi ie Pseuooe (Esu-Willims) Ies to tkle le rossing Ies to ientify noe rossing Pseuooe (Ostle-Awre Esu Willims) Experimentl Results n Moifie Algorithm Initil results from the Moifie Esu-Willims (Win frms: Wlney 1, Wlney 2 n Brrow) Prmetriztion n introuing shpe ftor Improve results From onstrution heuristi to Met-Heuristi : Future tivities (Very lrge Neighorhoo serh (VLNS) n GRASP)

4 Offshore Win Cle Lyout Optimiztion Offshore win or inter-rry le lyout (OWCL) optimiztion prolem is NP hr prolem There is similrity etween OWCL n pitte miniumum spnning tree (CMST) prolem with unit emn whih hs lso een prove to e NP hr (Ppimitriou, 1978) With inresing numer of turine noes n itionl restrite res in the win frm, ext methos in solving lrge instnes eome ineffiient Due to the ineffiienies of the ext methos in solving lrge instnes, heuristis n e use to ttin goo n fesile solutions Constrution, improvement n hyri heuristis re lssil heuristis exploring limite serh spe s oppose to lrge serh spe in metheuristis, ut using some unique strtegies n e use to ttin smll optimlity gp even with lssil pprohes

5 Offshore win les Export les Turine noes Susttion Export les Inter-rry les Eh noe must e onnete to one of the susttion Imge Soure: Buer et l, 2014

6 Prolem Sttement n Assumption Prolem : Input: 1. Lotion of the turines n susttions 2. Lotion of the restrite res n ostles in the se-e 3. Cle pity (mximum power flow or numer of turines llowe on single le) Output: Minimum le length lyout suh tht there is unique pth from eh turine to one of the susttion Constrints: 1. Cle rossing/noe rossing not llowe 2. Cle pity must e stisfie 3. Outegree of eh turine is one (no splitting of power les) Assumption: Cle ost is iretly proportionl to the length of the les n oesnot epen on ny other prmeter. This is similr to pitte minimum spnning tree prolem (NP hr ) with some itionl onstrints

7 Prolem Sttement n Assumption Prolem : Input: 1. Lotion of the turines n susttions 2. Lotion of the restrite res n ostles in the se-e 3. Cle pity (mximum power flow or numer of turines llowe on single le) Output: Minimum le length lyout suh tht there is unique pth from eh turine to one of the susttion Constrints: 1. Cle rossing/noe rossing not llowe 2. Cle pity must e stisfie 3. Outegree of eh turine is one (no splitting of power les) Assumption: Cpity = 4 Cle ost is iretly proportionl to the length of the les n oesnot epen on ny other prmeter. This is similr to pitte minimum spnning tree prolem (NP hr ) with some itionl onstrints

8 Constrint 1: Cle rossing n Noe rossing Noe rossing Cle rossing Imge Soure: Fishetti et l 2016 Noe rossing free The min resons ehin suh onstrint re: 1. Nee for expensive rige struture 2. Therml interferene etween the two les results in reuing the le pity 3. In se of filure of one of the le oth the les re ffete while repring

9 Constrint 2: Power les nnot e splitte Allowe Not Allowe The out-egree of eh turine noe must e one. However, inegree n e more whih is refere to s rnhing.

10 Constrint 3: Restrite res Diret links re sometimes not possile ue to restrite res in the se-e Numer of steiner noes is esign prmeter n n e more thn the extreme points of the onvex hull Steiner noes\optionl noes Turine noes Susttion noe Convex hull roun the ostle Cles Restrite re We re mking n ssumption tht ny onve n onvex restrite re n e represente y onvex hull without ompromising on optimlity

11 Constrint 3: Restrite res Diret links re sometimes not possile ue to restrite res in the se-e Numer of steiner noes is esign prmeter n n e more thn the extreme points of the onvex hull Steiner noes\optionl noes Turine noes Susttion noe Convex hull roun the ostle Cles Restrite re We re mking n ssumption tht ny onve n onvex restrite re n e represente y onvex hull without ompromising on optimlity

12 Allowe: Brnhing n prllel les Both rnhing n prllel les provie flexiility to the finl lyout n my le to reution in the totl le length No-Brnhing Brnhing Soure: Buer et l Soure: Klein et l 2017 Prllel le Imge Soure: Klein et l 2017

13 Tle of Content INTRODUCTION Offshore Win Cle Lyout (OWCL)Optimiztion Prolem Sttement n Assumptions Constrints: Noe rossing/le rossing, ostles n out-egree Fetures: Prllel les n rnhing MILP moel use for enhmrking heuristi solutions HEURISTIC Bsi ie Pseuooe (Esu-Willims) Ies to tkle le rossing Ies to ientify noe rossing Pseuooe (Ostle-Awre Esu Willims) Experimentl Results n Moifie Algorithm Initil results from the Moifie Esu-Willims (Win frms: Wlney 1, Wlney 2 n Brrow) Prmetriztion n introuing shpe ftor Improve results From onstrution heuristi to Met-Heuristi : Future tivities (Very lrge Neighorhoo serh (VLNS) n GRASP)

14 Bsi ie ehin the heuristi Esu-Willims heuristi is well known heuristi for the pitte minimum spnning tree prolem. Strt with ostly, fesile str lyout In eh itertion remove one link onneting the non-root noe with the root noe (susttion noe) resulting in ost sving. Finl output of the Esu- Willims Heuristi Fesile lyout Cpity = 3 Although CMST n le lyout prolems re quite similr ut there re itionl onstrints whih re to e stisfie in the offshore win le lyout prolem

15 Bsi ie ehin the heuristi Esu-Willims heuristi is well known heuristi for the pitte minimum spnning tree prolem. Strt with ostly, fesile str lyout In eh itertion remove one link onneting the non-root noe with the root noe (susttion noe) resulting in ost sving. Finl output of the Esu- Willims Heuristi Cn t use Esu-Willims heuristi lone! Fesile lyout Cpity = 3 Although CMST n le lyout prolems re quite similr ut there re itionl onstrints whih re to e stisfie in the offshore win le lyout prolem

16 Pseuooe of Esu-Willims heuristi V: set of verties A: 0: root noe : ost of the rs K: le pity R i : reution fution vlue of noe i X i : onnete omponent ontining noe i

17 Pseuooe of Esu-Willims heuristi V: set of verties A: 0: root noe : ost of the rs K: le pity R i : reution fution vlue of noe i X i : onnete omponent ontining noe i Reution funtion vlue (R i )t eh non-root noe is the ifferene of the ost of the entrl link with the root noe n ost of forming link with the nerest fesile onnete omponent (stisfying the le pity limittion)

18 Ie to tkle le rossing Non- rossing proeure n Dijkstr re use susequently to ientify shortest fesile pth etween two noes i 0 n i n Continues until shortest fesile (non-rossing ) pth is foun etween i 0 n i n So, the si ie is tht one we hve ientifie the two turine noes to e onnete using the mx reution funtion vlue, we try to use the ove ie to fin the shortest nonrossing pth etween them

19 Ostle-Awre Esu Willims Heuristi(1/2) L : stores line segments relte to the ostles PointArry: stores oorintes of ll the noes L2: stores the rs/line segments forme uring the proeure IntersetionArry: stores oth L2 n L While loop #1: ontinues unless ll the reution vlues eome zero While loop #2: ontinues unless the noe with highest reution vlues gets linke with nother noe

20 Ostle-Awre Esu Willims Heuristi(1/2) L : stores line segments relte to the ostles PointArry: stores oorintes of ll the noes L2: stores the rs/line segments forme uring the proeure IntersetionArry: stores oth L2 n L While loop #1: ontinues unless ll the reution vlues eome zero While loop #2: ontinues unless the noe with highest reution vlues gets linke with nother noe We hve selete noe i 0 hving the mximum reution funtion vlue n its nerest noe i n. Now, in pre-proessing stge the shortest fesile pth etween them is serhe whih my or my not e iret r

21 Ostle-Awre Esu Willims Heuristi(2/2) Pre-proessing stge

22 Non-Crossing proeure s output i Flse iv ii v iii Flse vi

23 Non-Crossing proeure s output i Flse iv ii v Note: Non-rossing proeure lwys ssesses pir of line segments (one from IntersetionArry n one of the ege in the shortest pth given y Dijkstr) iii Flse vi

24 Chllnge: Non-Crossing proeure is unle to ientify noe rossing i Flse iv e O ii v f iii Flse vi

25 Chllnge: Non-Crossing proeure is unle to ientify noe rossing i Flse iv intersetion ii v e 0 f iii Flse vi

26 Chllnge: Non-Crossing proeure is unle to ientify noe rossing i Flse iv ii v e Noe rossing 0 f iii Flse vi

27 Chllnge: Non-Crossing proeure is unle to ientify noe rossing i Flse iv ii v e 0 f iii Flse vi

28 Solution(1/4): A new line segments suh tht noe rossings re etete y Non-rossing proeure i Flse iv ii v e 0 f iii Flse vi

29 Solution(2/4): A new line segments suh tht noe rossings re etete y Non-rossing proeure i Flse iv ii v e 0 f iii Flse vi

30 Solution(3/4): A new line segments suh tht noe rossings re etete y Non-rossing proeure i Flse iv ii v e f Noe rossing etete 0 iii Flse vi

31 Solution(4/4): A new line segments suh tht noe rossings re etete y Non-rossing proeure i Flse iv Fesile Connetion ii v e 0 f iii Flse vi

32 Solution(1/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post prtitioning step

33 Solution(1/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post prtitioning step Dijkstr

34 Solution(2/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post joining step Convex hull of the onnete omponent Dijkstr Grhm sn

35 Solution(2/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post joining step Dijkstr Grhm sn

36 Solution(2/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post joining step Dijkstr Grhm sn Clique formtion

37 Solution(2/2): Where to the line segments? Prtitioning of turine noes in ifferent onnete omponents Output from 1st prt of the lgorithm Post joining step Dijkstr Grhm sn Clique formtion Fesile Connetion Assumption: All the noes re in the onvex hull of their own onnete omponent n not in the onvex hull of others

38 Tle of Content INTRODUCTION Offshore Win Cle Lyout (OWCL)Optimiztion Prolem Sttement n Assumptions Constrints: Noe rossing/le rossing, ostles n out-egree Fetures: Prllel les n rnhing MILP moel use for enhmrking heuristi solutions HEURISTIC Bsi ie Pseuooe (Esu-Willims) Ies to tkle le rossing Ies to ientify noe rossing Pseuooe (Ostle-Awre Esu Willims) Experimentl Results n Moifie Algorithm Initil results from the Moifie Esu-Willims (Win frms: Wlney 1, Wlney 2 n Brrow) Prmetriztion n introuing shpe ftor Improve results From onstrution heuristi to Met-Heuristi : Future tivities (Very lrge Neighorhoo serh (VLNS) n GRASP)

39 Experimentl Results-1 Existing Moel: We hve ompre our results to the optiml solutions ttine from n existing MILP moel evelope y our ollegue Arne Klein, UiB,Norwy The moel presente in [Klein n Hugln, 2017] is implemente using CPLEX 12 Python 3.4 API. All the experiments were rrie out on fst omputer - Intel Xenon with 72 logil ores n 256GB RAM The experiments were rrie out for Wlney 1, Wlney 2, Brrow win frms n for ifferent le pities Develope Heuristi : All the experiments involving the heuristis (Ostle Awre Esu-Willims) in this work re rrie out on personl omputer using 2.5 GHz Intel Core i5 proessor n 4GB RAM Progrmming lnguge use is Jv n without use of ny ommeril solver The mition of the first version of the ostle-wre heuristi is to fin goo, fesile solutions with less optimlity gp [ost(heuristi)/ost(optiml solution)]

40 Experimentl Results-2 K= le pity, Alg2 = Ostle-Awre Esu Willims Wlney 1 finl lyout for K=6

41 Experimentl Results-3 Wlney 2 finl lyout for K=6 There is lrge optimlity gp for Wlney 2 The prtitioning of the turine noes les to extremely long pths onneting onnete omponents to the susttion For exmple, the onnete omponent ontining noes 45, 46, 47, 48, 49, 39 is linke with the susttion using long pth 45->38->27->51

42 Experimentl Results-3 Wlney 2 finl lyout for K=6 There is lrge optimlity gp for Wlney 2 The prtitioning of the turine noes les to extremely long pths onneting onnete omponents to the susttion For exmple, the onnete omponent ontining noes 45, 46, 47, 48, 49, 39 is linke with the susttion using long pth 45->38->27->51

43 Ies/Ativities to reue the opt. gp Moifying the reution funtion n the lgorithm suh tht ril topologies re enourge n thus, long pths to the susttion re voie Using multi-exhnge lrge neighourhoo serh for fining the lolly optiml solution

44 Introuing weight prmeter in reution funtion

45 Introuing weight prmeter in reution funtion As the vlue of weight prmeter W inreses, turine noes loser to the susttion will e preferre.

46 Results from ext, ostle wre Esu Willims n lgorithm with weight prmeter

47 Improve result for Wlney 2 Wlney 2 (Moifie Esu Willims Algorithm- Prmetri) Wlney 2 (Moifie Esu Willims Algorithm)

48 Chnge in le length with weight prmeter

49 Ies/Ativities to reue the opt. gp Moifying the reution funtion n the lgorithm suh tht ril topologies re enourge n thus, long pths to the susttion re voie Using multi-exhnge lrge neighourhoo serh for fining the lolly optiml solution

50 Questions? Thnk You! Projet is supporte y Horln fylkeskommune.