A Scalable Message-PassingAlgorithm for Supply Chain Formation                    by Toni Penya-Alba, Meritxell Vinyals,  ...
THE PROB                         LEMAlice              Dave-$2                 $7        Carol         -$5Bob             ...
THE PROB                                              L  EM       Alice                              Dave       -$2       ...
THE PROB                                             L     EMAlice-$2                     Carol                      -$5  ...
THE GOALTo provide a scalable methodfor Supply Chain Formationin markets with highdegrees of competition.
RI BUT IONCO NT     Encoding in a novel graphical model.     Optimized implementation of max-sum.                         ...
factor graph is a graphical model torepresent functions.               f    g                               f(x,y) + g(y,z...
LoopyBeliefPropagation       Michael Winsper             Maria Chli
LOOPY BELIEF PROPAGATIONmap the Supply Chain Formationproblem into a factor graph.apply max-sum over the factor graphto ob...
MAPPING INTO A FACTOR GRAPH  Alice                       Dave  -$2                          $7              Carol         ...
FACTOR GRAPH MAPPINGAlice         Carol    DaveBob                    Eve
FACTOR GRAPH MAPPING             Alice             Carol                        Dave                                exchan...
FACTOR GRAPH MAPPING             Alice           Carol            Dave                             exchanges             B...
FACTOR GRAPH MAPPING     Alice           Carol           Dave-2       exchanges               exchanges                   ...
FACTOR GRAPH MAPPING              Alice                Carol                Dave         -2       exchanges               ...
LBP  memory per     O(G•A 2G+1)    agentbandwidth per    O(G•A G+1)    agent computation     O(G•A 2G+1)time per agent
RB-LBPOur Approach
RB-LBP OUR APPROACHmap problem into a binary factorgraph containing binary variablesand logical constraints.optimized max-...
MAPPING INTO A BINARY FACTOR GRAPH  Alice                     Dave  -$2                        $7               Carol     ...
BINARY FACTOR GRAPH MAPPINGAlice          Carol        DaveBob                         Eve
BINARY FACTOR GRAPH MAPPING      Alice                 Carol               Dave                            activate       ...
BINARY FACTOR GRAPH MAPPING       Alice                Carol                    Dave                             activate ...
BINARY FACTOR GRAPH MAPPING      Alice                  Carol             Dave                      buy               sell...
BINARY FACTOR GRAPH MAPPING     Alice                    Carol                 Dave                   buy                 ...
BINARY FACTOR GRAPH MAPPING            Alice                           Carol                          Dave-2   activate   ...
BINARY FACTOR GRAPH MAPPING             Alice                             Carol                              Dave -2   act...
}Factors as logical constraintsThere is no need to store factors inmemory.                                SimplifiedSingle...
LBP        RB-LBP  memory per     O(G•A 2G+1)   O(G•A)    agentbandwidth per    O(G•A G+1)    O(G•A)    agent computation ...
ExperimentalAnalysis
EXPERIMENTAL SETUPSmall networks [Walsh2003].Large networks [Vinyals2008].Measure memory, communication,time, and quality.
small networks <20 goods <40 agents
SMALL NETWORKSup to 13 times less memory up to 5 times less bandwidth         same solution quality     negligible time di...
large networks     50 goods40-500 agents
LARGE NETWORKSup to 105 times less memoryup to 787 times less bandwidth up to 20 times faster     up to twice bettersoluti...
LARGE NETWORKS  up to 105 timesless memory
FINAL                                    RECA                                           PEncoding in a novel graphical mod...
Coming soon ...
Coming soon ... ... Better valued solutions
ThankYou
Questions?
[Winsper2003] M. Winsper and M. Chli, Decentralised Supply Chain Formation:A Belief Propagation-based Approach, Agent-Medi...
Upcoming SlideShare
Loading in …5
×

A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)

259 views

Published on

Published in: Education, Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
259
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)

  1. 1. A Scalable Message-PassingAlgorithm for Supply Chain Formation by Toni Penya-Alba, Meritxell Vinyals, Jesus Cerquides, and Juan A. Rodriguez-Aguilar for the 26th AAAI Conference
  2. 2. THE PROB LEMAlice Dave-$2 $7 Carol -$5Bob Eve-$3 $8
  3. 3. THE PROB L EM Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8The Supply Chain Formation problem is that of findingthe feasible configuration with maximum value.
  4. 4. THE PROB L EMAlice-$2 Carol -$5 Eve $8 Supply Chain Value = $8 - $5 - $2 = $1
  5. 5. THE GOALTo provide a scalable methodfor Supply Chain Formationin markets with highdegrees of competition.
  6. 6. RI BUT IONCO NT Encoding in a novel graphical model. Optimized implementation of max-sum. BENEFReduced memory, communication and ITScomputation requirements.Higher quality solutions.
  7. 7. factor graph is a graphical model torepresent functions. f g f(x,y) + g(y,z) x y zmax-sum is a message passing algorithm.max-sum can efficiently approximateoptimization problems.
  8. 8. LoopyBeliefPropagation Michael Winsper Maria Chli
  9. 9. LOOPY BELIEF PROPAGATIONmap the Supply Chain Formationproblem into a factor graph.apply max-sum over the factor graphto obtain a solution.
  10. 10. MAPPING INTO A FACTOR GRAPH Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8
  11. 11. FACTOR GRAPH MAPPINGAlice Carol DaveBob Eve
  12. 12. FACTOR GRAPH MAPPING Alice Carol Dave exchanges Bob Eve 0 do nothing 1 buy from Alice, sell to Dave 2 buy from Alice, sell to Eve 3 buy from Bob, sell to Dave 4 buy from Bob, sell to EveAgent variable encodes all of Carol’s possible exchanges.
  13. 13. FACTOR GRAPH MAPPING Alice Carol Dave exchanges Bob Eve -5 inactive 0 otherwise -5Activation factor encodes Carol’s activation cost.
  14. 14. FACTOR GRAPH MAPPING Alice Carol Dave-2 exchanges exchanges 7 exchanges Bob Eve-3 exchanges -5 exchanges 8
  15. 15. FACTOR GRAPH MAPPING Alice Carol Dave -2 exchanges AC CD exchanges 7 exchanges Bob Eve -3 exchanges BC -5 CE exchanges 8Compatibility factors encode compatibility betweenCarol’s states and her neighbors’.
  16. 16. LBP memory per O(G•A 2G+1) agentbandwidth per O(G•A G+1) agent computation O(G•A 2G+1)time per agent
  17. 17. RB-LBPOur Approach
  18. 18. RB-LBP OUR APPROACHmap problem into a binary factorgraph containing binary variablesand logical constraints.optimized max-sum implementation.apply max-sum over the factor graphto obtain a solution.
  19. 19. MAPPING INTO A BINARY FACTOR GRAPH Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8
  20. 20. BINARY FACTOR GRAPH MAPPINGAlice Carol DaveBob Eve
  21. 21. BINARY FACTOR GRAPH MAPPING Alice Carol Dave activate Bob EveActivation variable encodes Carol’s decision to be active.
  22. 22. BINARY FACTOR GRAPH MAPPING Alice Carol Dave activate Bob Eve -5Activation factor encodes Carol’s activation cost.
  23. 23. BINARY FACTOR GRAPH MAPPING Alice Carol Dave buy sell from A to D activate Bob Eve buy from B -5 sell to EOption variables encode Carol’s decision to trade each ofher goods with each of her potential partners.
  24. 24. BINARY FACTOR GRAPH MAPPING Alice Carol Dave buy sell from A to D S activate S Bob Eve buy from B -5 sell to ESelection factors guarantee that only one of theproviders is selected for each good.
  25. 25. BINARY FACTOR GRAPH MAPPING Alice Carol Dave-2 activate S sell to C buy from A sell to D buy from C S activate 7 S activate S Bob Eve-3 activate S sell to C buy from B -5 sell to E buy from C S activate 8
  26. 26. BINARY FACTOR GRAPH MAPPING Alice Carol Dave -2 activate S sell to C = buy from A sell to D = buy from C S activate 7 S activate S Bob Eve -3 activate S sell to C = buy from B -5 sell to E = buy from C S activate 8Equality factors guarantee that Carol takes coherentdecisions with her neighbors’.
  27. 27. }Factors as logical constraintsThere is no need to store factors inmemory. SimplifiedSingle-valued messages messageContain agents’ willingness to calculationcollaborate with each other.
  28. 28. LBP RB-LBP memory per O(G•A 2G+1) O(G•A) agentbandwidth per O(G•A G+1) O(G•A) agent computation O(G•A 2G+1) O(G•A2)time per agent
  29. 29. ExperimentalAnalysis
  30. 30. EXPERIMENTAL SETUPSmall networks [Walsh2003].Large networks [Vinyals2008].Measure memory, communication,time, and quality.
  31. 31. small networks <20 goods <40 agents
  32. 32. SMALL NETWORKSup to 13 times less memory up to 5 times less bandwidth same solution quality negligible time differences
  33. 33. large networks 50 goods40-500 agents
  34. 34. LARGE NETWORKSup to 105 times less memoryup to 787 times less bandwidth up to 20 times faster up to twice bettersolutions
  35. 35. LARGE NETWORKS up to 105 timesless memory
  36. 36. FINAL RECA PEncoding in a novel graphical model.Optimized implementation of max-sum.Reduced memory, communication andcomputation requirements.Higher quality solutions.
  37. 37. Coming soon ...
  38. 38. Coming soon ... ... Better valued solutions
  39. 39. ThankYou
  40. 40. Questions?
  41. 41. [Winsper2003] M. Winsper and M. Chli, Decentralised Supply Chain Formation:A Belief Propagation-based Approach, Agent-Mediated Electronic Commerce,2010.[Walsh2003] W. E. Walsh and M. P. Wellman, Decentralized Supply ChainFormation : A Market Protocol and Competitive Equilibrium Analysis, Journal ofArtificial intelligence Research (JAIR), vol. 19, pp. 513-567, 2003.[Vinyals2008] M. Vinyals, A. Giovannucci, J. Cerquides, P. Meseguer, and J. A.Rodriguez-Aguilar, A test suite for the evaluation of mixed multi-unitcombinatorial auctions, Journal of Algorithms, vol. 63, no. 1-3, pp. 130-150,2008.

×