ATTED Anlytil Tools To Evlute egotition Diiulty Alejndro Bugov & Roert ehes USC - Inortion Sienes Institute ATs PI Meeting Thoe City, April 0, 00
Outline. Approh Overview. SAT enoding o SAP s resoure llotion prole. Experients nd Results. Integrtion Plns
Approh Overview Set o Constrints BIG CSP SAP egotitions Feedk to negotitions CAMERA Anlyze Coplexity & Iprove Solution Doin odeling & onstrints uilt uilt into into SAP SAP SAP Mission Genertor: SAP, give e the next issions to Prole Intere Dyni Enoding {p,p,p 8 } {p,p } s {p s,p 8 } {p } s s s 5 s 6 {p,p 5 } {p,p } s 7 {p,p } x yz xy K issions grph enoding
How n this help SAP? SAP Genertes Missions or the ly dy ATTED Prtitioning to lne lod t tie-slots Mrle-sed SAP egotitions SAP Genertes Missions or the ly dy Mrle-sed SAP egotitions
Coplexity Chrteriztion nd Prtitioning Approh!SAT enoding o the prole!resulting SAT orul ontins prole oplexity inortion!use oplexity esures to quikly estite the xiu nuer o issions tht n e sheduled within tie-slot
Single Tie-Slot Resoure Allotion Prole tht Mrles Solve Resoures Full Full Missions Missions Tsk [vlue] A B C Resoures D E F G H I 0 Broken Broken Missions Missions R Tsk A B [00] C D E F G H I [00] Tsk [00] Resoures R Tsk R R A B C D E F G Tsk H I R R R R R Tsk [600] Tsk R R R Full Full Missions Missions R Tsk R R Broken Broken Missions Missions [900] R [900] Tsk R R Tsk [00] R R R R Tsk R R Tsk R R R Tsk [00] R R R R Tsk R R Tsk R R R
Ipleenting the ATTED Approh to Coplexity Chrteriztion! Interedite prole: Crete SAT enoding o the prole tht voids roken issions! Stright enoding using MASAT won t do it! Approh: Crete SAT enoding tht n hndle these onstrints y inding solution or t lest K issions in ollortion with the Cornell Group Serh or the xiu K or whih solution exists Study the dependeny o K x with the nuer o issions nd resoures to estite sling o the ritil region
SAT Enoding: Vriles resoure resoure vrile vrilea : : True True i i Resoure Resoure A A is is ssigned ssigned to to Tsk Tsk Requireent Requireent ission ission vrile vrile : : True True i i Tsk Tsk is is turned turned on on K x x dditionl dditionl vriles vriles k M k k L L L L to to selet selet t t lest lest K or or the the issions issions k Tsk Tsk Tsk Tsk Tsk Resoures A B C D E F G H I R R R R R R R R R R R R resoure resoure vrile vrile E : : True True i i Resoure Resoure E E is is ssigned ssigned to to Tsk Tsk Requireent Requireent
SAT Enoding: Forul Coposition Tsk Tsk Tsk Tsk Tsk Resoures A B C D E F G H I R R R R R R R R R R R R =... K ross K Cluses to swith on t lest K ission vriles ross i Cluses to prelude resoures eing ssigned to ore thn one tsk Cluses to selet eligile resoures within ission i i=,,.,
At lest K issions orul At lest K issions orul k : k= = exple exple K = L L L K = M K K K K = We wnt to selet t lest K dierent vriles ro this set o x K vriles K = M Link the to the ission vriles
Resoure seletion oruls Assigns Assigns resoures resoures to to no no ore ore thn thn one one requireent requireent ross A = B C A B C A B... A B A B A B Tsk Tsk Tsk Tsk Tsk Resoures A B C D E F G H I R R R R R R R R R R R R Exple: Exple: orul orul or or ission ission Assigns Assigns t t lest lest one one possile possile resoure resoure to to eh eh requireent requireent Cluses Cluses re re only only tive tive when when the the ission ission vrile vrile is is turned turned on on = A A G B B H C A G E C I F B H G C I H I E F
Chrteristis o the Enoding! It works! Atully, pretty well Both or stisiility nd/or optiiztion! Very lrge nuer o luses! WlkSAT solves the extreely st up to the the ritil region! uer o literls per luse vries ro to x,m+
Experients nd Results! Rndoly generted proles hrterized y uer o resoures nd tsks independent Gussin distriutions or: Tsk Vlue uer o Requireents per tsk uer o possile resoures per requireent! Experients with tsks nd resoures or =0, 50, 60 nd 00
SAT oputtionl ost signls xiu nuer o issions Tie ses.e+06.e+05.e+0.e+0 00x00 60x60 50x50 0x0 00x00 SA 60x60 SA 50x50 SA 0x0 SA.E+0.E+0 0 0 0 0 0 50 60 K
Cn predit position o K x ro orul hrteristis.e+07.e+06 = 60 = 00 = 50 = 0 Tie ses.e+05.e+0.e+0.e+0.e+0 tive luses = = 0 5 0 5 0 5 0 Ative Cluses/^ ross + k ross k x = un,, ross, i
How n this help SAP? SAP Genertes Missions or the ly dy k x = un,, ross, i Mrle-sed SAP egotitions We We n n nlytilly nlytilly estite estite the the xiu xiu nuer nuer o o issions issions tht tht its its on on eh eh tie tie slot slot First First deonstrtion deonstrtion o o oplexity oplexity esures esures eing eing used used to to inluene inluene the the negotition negotition proess proess SAP Genertes Missions or the ly dy Mrle-sed SAP egotitions
Good good-enough/soon enough/soon-enough properties Mxiu Vlue.E+05.E+0 00x00 60x60 50x50 0x0 00x00 SA 60x60 SA 50x50 SA 0x0 SA.E+0 0 0 0 0 0 50 60 K
Plns! Integrte the SAT enoding pproh to rel light dt ro SAP! Test predition pilities using rel dt! Intere with Snp s Mrles engine to ounite oplexity esures! Initil deonstrtion o SAP rles with ATTED prtitioning inortion
ED
Sling o the uer o Cluses nd Vriles with prole size.e+0 8.E+0 nuresourevriles totlvriles.0e+05 CrossCluses issioncluses totlcluses.0e+05 6.E+0.E+0.0E+05.E+0 0.E+00 5 5 5 55 65 75 85 95 05 uer o Tsks 0.0E+00 0 0 0 50 60 70 80 90 00 0 uer o Tsks