A summary of recent contributions in the PROMETHEE methods (from members of the SMG unit)

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1 A summry of recent contributions in the PROMETHEE methods (from members of the SMG unit) Prof. Y. De Smet CoDE-SMG, Université libre de Bruxelles (Belgium) Interntionl MCDA workshop on PROMETHEE: Reserch nd cse studies

2 Outline Brief reminder bout PROMETHEE nd GAIA Min topics developed since 2007 (SMG); Softwre implementtions Preference elicittion Sorting nd clustering Visul representtions (ppliction to GIS) Rnk reversl Directions for future reserch 2

3 PROMETHEE in nutshell (1) A finite set of lterntives: A={ 1, 2,.., n } A set of criteri: F={f 1,f 2,..,f q } W.l.g. these criteri hve to be mximized Step 1: computtion of unicriterion preferences degrees 3 )], ( [ ), ( ) ( ) ( ), ( :, j i k k j i k j k i k j i k j i d P f f d A

4 PROMETHEE in nutshell (2) Step 2: Computtion of preference degrees: Step 3: Computtion of flow scores: 4 ), (. ), ( :, 1 j i k q k k j i j i w A ) ( ) ( ) ( ), ( 1 1 ) ( ), ( 1 1 ) ( i i i A b i i A b i i b n b n A + ( i ), A ( i ), A ( i ) More formlly:

5 GAIA in nutshell (1) We hve: ( ) 1 q q 1 w. (, b) w. ( b, ) Where i k k i k k i n1ba k 1 n1ba k 1 q q 1 w. (, b) ( b, ) w. ( ) k k i k i k k i k 1 n 1 ba k 1 k ( i ) k ( i, b) k ( b, i ) ba In other words, every lterntive cn be represented by vector: i [ ( i ), 2 ( ),.., ( 1 i k i )] 5

6 GAIA in nutshell (2) D vlue i [ ( i ), 2( i ),.., ( )] 1 k i 3 q dimensions 2 dimensions Principl component nlysis 6

7 Softwre implementtions

8 Softwre implementtions Hyez, Q., De Smet, Y. nd Bonney, J. D-Sight: new decision mking softwre to ddress multi-criteri problems Interntionl Journl of Decision Support Systems Technologies, 4(4), 1-23 (2012) Long story: PROMCALC, DECISION LAB 2000 Spin-off project funded by the Wlloon Region ( ) D-SIGHT desktop D-SIGHT web Session C 2 nd presenttion Innoviris wrd in 2012 «Jeune entreprise innovnte» But lso Decision Deck, Smrt Picker, Visul Promethee, 8

9 D-SIGHT Projects Ares of Expertise D-Sight hs been developing specific expertise in certin industries over the pst yers. We re proud of hving excellent customers, which help us developing nd improving our softwre solutions. Environmentl Anlysis Projects Prioritiztion Vendor Selection Acdemi: 50 universities in 27 countries

10 Preference elicittion

11 Contributions: Eppe, S., De Smet, Y., Stützle, T. «A bi-objective optimiztion model to eliciting decision mker s preferences for the PROMETHEE II method» Proceedings of ADT (2011), (2011) Eppe, S. et De Smet, Y. «Studying the impct of informtion structure in the PROMETHEE II preference elicition process : simultion bsed pproch», 14th Interntionl Conference on Informtion Processing nd Mngement of Uncertinty in Knowledge-Bsed Systems, IPMU 2012, Ctni, Itly, July 9-13, 2012, LNAI Proceedings, , 2012 Eppe, S. nd De Smet, Y. An dpttive questioning procedure for eleciting PROMETHEE II s weight prmeters to pper in the Interntionl Journl of Multicriteri Decision Mking (2013) Eppe, S. nd De Smet, Y. Approximting PROMETHEE II s net flow scores by piecewise liner vlue functions to pper in the Europen Journl of Opertionl Reserch (2013) 11

12 Generl ide (1) w*,q*,p* PAC, WSR,ASR P2 P2 w,q,p Set of comptible prmeters! R* R Set of comptible rnkings! Worst Kendll s Tu 12

13 Generl ide (2) w*,q*,p* PAC, WSR,ASR P2 P2 w,q,p Set of comptible prmeters! R* W R Set of comptible rnkings! W C w*,q*,p* 13

14 Eppe, S., De Smet, Y., Stützle, T. (2011) «A bi-objective optimiztion model to eliciting decision mker s preferences for the PROMETHEE II method» Proceedings of ADT (2011), Min ide: qulity nd robustness Distinctive feture: the DM my communicte mistkes (n=100,q=2) NSGA-II 14

15 Eppe, S., De Smet, Y. (2012) «Studying the impct of informtion structure in the PROMETHEE II preference elicittion process: A simultion bsed pproch» 14th Interntionl Conference on Informtion Processing nd Mngement of Uncertinty in Knowledge-Bsed Systems, IPMU 2012, Ctni, Itly, July 9-13, 2012, LNAI Proceedings, , 2012 Min ide: quntify informtion infrstructure 15

16 Eppe, S., De Smet, Y. (2012) «Studying the impct of informtion structure in the PROMETHEE II preference elicittion process: A simultion bsed pproch» 14th Interntionl Conference on Informtion Processing nd Mngement of Uncertinty in Knowledge-Bsed Systems, IPMU 2012, Ctni, Itly, July 9-13, 2012, LNAI Proceedings, ,

17 Eppe, S., De Smet, Y. (2012) «Studying the impct of informtion structure in the PROMETHEE II preference elicittion process: A simultion bsed pproch» 14th Interntionl Conference on Informtion Processing nd Mngement of Uncertinty in Knowledge-Bsed Systems, IPMU 2012, Ctni, Itly, July 9-13, 2012, LNAI Proceedings, ,

18 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking Min ide: to overcome the limittions of the previous pproch; pirwise comprisons hve to be «wellchosen» q-evl 18

19 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking 19

20 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking 20

21 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking 21

22 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking 22

23 Eppe, S., De Smet, Y. «An dpttive questioning procedure for eliciting PROMETHEE II s weight prmeters» to pper in the Interntionl of Multicriteri decision mking 23

24 Sorting nd clustering

25 Contributions De Smet, Y. et Gilbrt, F. «A clss definition method for country risk problem», IS-MG 2001/13 Figueir, J., De Smet, Y. et Brns, J.P. «MCDA methods for sorting nd clustering problems : Promethee TRI nd Promethee CLUSTER», IS-MG 2004/02 Nemery, Ph. nd Lmbory, C.: "FlowSort : A flow-bsed sorting method with limiting nd centrl profiles", TOP 16, De Smet, Y. P2CLUST: n extension of PROMETHEE II for ordred clustering to pper in the proceedings of the 2013 IEEE Interntionl Conference on Industril Engineering nd Engineering Mngement, Bngkok, Thïlnd, (2013) 25

26 Flowsort min ide Let us consider set of limit (or centrl profiles) R = r 1, r 2,.., r K+1 R i = R i Ech ctions i is sorted ccording to its reltive position bsed with respect to the profiles ccording to Ri ( i ) Complete or prtil sorting Ide behind P2CLUST Session A1 1 st presenttion 26

27 PROMETHEE nd GIS (Krim Lidouh PhD) Session B2 4 th presenttion 27

28 Decision Clocs Lidouh, K., De Smet, Y. et Zimányi, E. «GAIA Mp : A Tool for Visul Rnking Anlysis in Sptil Multicriteri Problems» in Proceedings of the 13th Interntionl Conference on Informtion Visuliztion 2009, Brcelon IEEE Computer Society, ,

29 Lidouh, K., De Smet, Y. nd Zimányi, E. An Adpttion of the GAIA Visuliztion Method for Crtogrphy, in the proceedings of the 2011 IEEE Symposium on Computtionl Intelligence in Multicriteri Decision- Mking, Frnce, 29-35, 2011

30 Rnk reversl Session A1 5 th presenttion

31 Rnk reversl (1) Rnk reversl AHP: Belton nd Ger (1983), Sty nd Vrgs (1984), Trintphyllou (2001), Wng nd Elhg (2006), Wijnmlen nd Wedley (2009) ELECTRE: Wng nd Trintphyllou (2005) PROMETHEE: De Keyser nd Peeters (1996) The concept of rnk reversl is not fully formlized (dd copy of n lterntive, deletion of non discriminting criterion, deletion of n lterntive, ) A direct consequence of Arrow s theorem Positive results: Dominnce Non discriminting criterion 31

32 Contributions Mreschl, B., De Smet, Y. nd Nemery, P. Rnk Reversl in the PROMETHEE II Method : Some New Results, proceedings of de IEEE 2008 Interntionl Conference on Industril Engineering nd Engineering Mngement, Singpore, (2008) Rolnd, J., De Smet, Y. nd Verly, C. Rnk reversl s source of uncertinty nd mnipultion in the PROMETHEE II rnking : first investigtion to pper in the proceedings of the IPMU 2012 conference (LNAI) Verly, C. nd De Smet, Y. Some considertions bout rnk reversl occurrences in the PROMETHEE methods ccepted for publiction in the Interntionl Journl of Multicriteri Decision Mking. 32

33 More generl result (1) Nottions:, No RR if No RR (for ny ction removed) if 33

34 More generl result (2) RR cn only occur if refined threshold (depends on the smple nd (,b)) rough threshold (constnt) Generliztion: when k ctions re removed No RR if Mreschl, B., De Smet, Y. nd Nemery, P. «Rnk Reversl in the PROMETHEE II Method : Some New Results», proceedings of de IEEE 2008 Interntionl Conference on Industril Engineering nd Engineering Mngement, Singpore, (2008):

35 More generl result (3) Sttisticl results reltive to the «rough threshold» (for q = 2, DA=Unif) Conclusion: The number of RR occurences is relly smll. 35

36 More generl result (4) 2/9 36

37 Relted works for PROMETHEE I No rnk reversl will hppen between i nd j if 1 ( i) ( j) n 1 1 ( i) ( j) n 1 37

38 Rnk reversl = risk of mnipultion Joint work with Julien Rolnd nd Céline Verly (to pper in the proceedings of the IPMU 2012 conference) Aim: to quntify the likelihood of mnipultion in simplified version of the PROMETHEE II rnking: Usul preference function nd equl weights Copelnd scores More formly: A given decision mker hs perfect informtion on the evlution tble; He my propose new lterntives in order to mke lterntive i the first one; Question: how mny lterntives re necessry? 38

39 Liner mthemticl progrm 39

40 Results for 10 lterntives nd 3 criteri 40

41 Comprison with the bound 41

42 Current pplictions 3D Integrted circuits (PhD A.V. Don) Session B1 4 th presenttion Sustinble security in rod design (PhD R. Srrzin) Session A2 2 nd presenttion 1. Plnning 2. Pre-design (drft) 3. Design (detiled) 4. Construction + 5. Opening & Exploittion 42

43 Future/current reserches Rnk reversl: exct conditions; Mngement of missing vlues; Synergies with Dt Envelopement Anlysis; (PhD Bgherikvrin) Session A2 2 nd presenttion Extension of PROMETHEE to temporl evlutions; (PhD I. Benmr). 43

44 Thnk you for your ttention ;-) 44