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MULTIMODAL OPTIMIZATION MIKE PREUSS. Multimodal Optimization 1 - PowerPoint PPT Presentation

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MULTIMODAL OPTIMIZATION MIKE PREUSS. Multimodal Optimization 1 2014-09-14 Mike Preuss 2014-09-14 Mike Preuss. WHAT ARE WE DEALING WITH? Multimodal Optimization 2 2014-09-14 Mike Preuss. SOME GENERAL NOTES more questions t han

  1. MULTIMODAL OPTIMIZATION MIKE PREUSS. Multimodal Optimization 1 2014-09-14 Mike Preuss 2014-09-14 Mike Preuss.

  2. WHAT ARE WE DEALING WITH? Multimodal Optimization 2 2014-09-14 Mike Preuss.

  3. SOME GENERAL NOTES  more questions t han answers in Mult imodal Opt imizat ion (MMO)  field not well defined  basic t erms not well defined  similarit ies t o Mult i-Obj ect ive Opt imizat ion (MOO)  huge bulk of lit erat ure  Evolut ionary Comput at ion (EC) people focus on EC approaches  consider t his as “ request for comment s”  suggest ions for fut ure work appreciated  bet t er: you st art t o do int erest ing MMO st uff Multimodal Optimization 3 2014-09-14 Mike Preuss.

  4. OUTLINE  why mult imodal opt imizat ion (MMO)?  abst ract ion: niching and a model EA  different scenarios and t heir measures  t axonomy of met hods  result s/ compet it ion/ soft ware  t he fut ure Multimodal Optimization 4 2014-09-14 Mike Preuss.

  5. why multimodal optimization (MMO)? Multimodal Optimization 5 2014-09-14 Mike Preuss.

  6. ATTEMPTING A DEFINITION In a mult imodal opt imizat ion t ask, t he main purpose is t o f ind mult iple opt imal solut ions (global and local), so t hat t he user can have a bet t er knowledge about dif f erent opt imal solut ions in t he search space and as and when needed, t he current solut ion may be swit ched t o anot her suit able opt imum solut ion. Deb, Saha: Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm, ECJ, 2012 main t asks:  alt ernat ive solut ions  problem knowledge Multimodal Optimization 6 2014-09-14 Mike Preuss.

  7. SEPARATION PROCESS OPTIMIZATION REAL-WORLD EXAMPLES  many solutions invalid, looks like Rastrigin problem Henrich, Bouvy, Kausch, Lucas, Preuss, Rudolph, Roosen. Economic optimization of non- sharp separation sequences by means of evolutionary algorithms. In Comput ers & Chemical Engineering , Volume 32, Issue 7, pp. 1411-1432. Elsevier, 2008. Multimodal Optimization 8 2014-09-14 Mike Preuss.

  8. LINEAR-JET OPTIMIZATION REAL-WORLD EXAMPLES Rudolph, Preuss, Quadflieg. Two-layered surrogate modeling for tuning metaheuristics. In ENBIS / EMS E Conference Design and Analysis of Comput er Experiment s, 2009 Multimodal Optimization 9 2014-09-14 Mike Preuss.

  9. CAMERA POSITIONING REAL-WORLD EXAMPLES Preuss, Burelli, Y annakakis. Diversified Virtual Camera Composition. In EvoApplications 2012, pp. 265-274. S pringer, 2012 Multimodal Optimization 10 2014-09-14 Mike Preuss.

  10. MAIN RESEARCH QUESTIONS  in which sit uat ions are MMO met hods act ually bet t er t han “ usual” EC opt imizat ion algorit hms?  problems  performance measures  ext ernal condit ions, e.g. runt ime  among different MMO met hods, which one shall we choose?  what are t he limit s for furt her improvement ? assumption : successful MMO needs dist ribut ion of solut ions int o different basins of at t raction, t his resembles t he niching idea Multimodal Optimization 11 2014-09-14 Mike Preuss.

  11. abstraction: niching and a model EA Multimodal Optimization 12 2014-09-14 Mike Preuss.

  12. NICHING “ Niching in EAs is a t wo-st ep procedure t hat a) concurrent ly or subsequent ly dist ribut es individuals ont o dist inct basins of at t ract ion and b) facilit at es approximat ion of t he corresponding (local) opt imizers.” (Preuss, BIOMA 2006) Multimodal Optimization 13 2014-09-14 Mike Preuss.

  13. NICHING/SPECIATION Multimodal Optimization 14 2014-09-14 Mike Preuss.

  14. OPTIMIZATION PHASES Redundancy for repeat ed local search and b basins (Beasley 1993) : Multimodal Optimization 15 2014-09-14 Mike Preuss.

  15. BASIN IDENTIFICATION/BASIN RECOGNITION Multimodal Optimization 16 2014-09-14 Mike Preuss.

  16. BASIN IDENTIFICATION Multimodal Optimization 17 2014-09-14 Mike Preuss.

  17. BASIN RECOGNITION Multimodal Optimization 18 2014-09-14 Mike Preuss.

  18. PROBABILISTIC IDENTIFICATION/RECOGNITION  basin ident ificat ion relies on det ect ing if t wo solut ions are locat ed in t he same basin (binary)  basin recognit ion: is t he basin of a cert ain solut ion known?  no perfect knowledge: probabilist ic approach  t hese express sensit ivit y (we do not have informat ion about unvisit ed areas) Multimodal Optimization 19 2014-09-14 Mike Preuss.

  19. SIMULATION  quest ion: how many local searches necessary t o find t he global opt imum (t 2), or  or t o visit all basins at least once (t 3)? Multimodal Optimization 20 2014-09-14 Mike Preuss.

  20. COUPON COLLECTOR‘S PROBLEM (CCP) given a set of 8 collect or’s cards, and we randomly get 3,  how many it erat ions unt il we get one specific card? (2.67)  or obt ain all exist ing cards? (6.58 it erat ions) Multimodal Optimization 21 2014-09-14 Mike Preuss.

  21. EXACT RESULTS P(BI) = 1, P(BR) = 0  under t he assumpt ion of equal probabilit ies (for single cards/ basins), t his can be comput ed  formula of (S tadj e. The collector’s problem with group drawings. Advances in Applied Probability, 22(4):866– 882, 1990):  b = cards/ basins per drawing,  c = number of cards/ basins  n = desired element s of desired set , l = desired set size Multimodal Optimization 22 2014-09-14 Mike Preuss.

  22. EXACT RESULTS Multimodal Optimization 23 2014-09-14 Mike Preuss.

  23. THIS IS SHOCKING!  under t he equal basin size assumpt ion, obt aining t he global opt imum (t 2) needs on average b local searches!  so basin ident ificat ion does not make sense? but :  what about basin recognit ion?  equal basin sizes not realist ic  we cannot know if we have reached t 2  sit uat ion changes if we want mult iple solut ions Multimodal Optimization 24 2014-09-14 Mike Preuss.

  24. SUMMARIZING THE SIMPLE CASES  we leave out perfect BR, no BI, seems unreasonable  even under ideal circumst ances, not much gain for t 2  but BI/ BR help for t 3:  rat ionale for mult imodal opt imizat ion  more complex cases (unequal basin sizes, PBI/ PBR not 0 or 1) have to be simulat ed Multimodal Optimization 25 2014-09-14 Mike Preuss.

  25. SIMULATION: EQUAL BASIN SIZES P(BI) = 0, P(BR) = 0 Multimodal Optimization 26 2014-09-14 Mike Preuss.

  26. SIMULATION: EQUAL BASIN SIZES P(BI) = 0.5, P(BR) = 0 Multimodal Optimization 27 2014-09-14 Mike Preuss.

  27. SIMULATION: EQUAL BASIN SIZES P(BI) = 1, P(BR) = 0 (t his is t he t heoret ically t ract able case, t he difference comes from inst ant st opping when reaching t 2) Multimodal Optimization 28 2014-09-14 Mike Preuss.

  28. SIMULATION: EQUAL BASIN SIZES P(BI) = 0.5, P(BR) = 0.5 Multimodal Optimization 29 2014-09-14 Mike Preuss.

  29. UNEQUAL BASIN SIZES?  why should we care?  because size differences grow exponent ially in dimensions  10D wit h 2:1 per dim makes a volume difference of 1024:1  however, basin ident ificat ion/ basin recognit ion may be very difficult wit h large size differences  we simulat e abst ract 1:10 size difference Multimodal Optimization 30 2014-09-14 Mike Preuss.

  30. SIMULATION: UNEQUAL BASIN SIZES P(BI) = 0, P(BR) = 0 Multimodal Optimization 31 2014-09-14 Mike Preuss.

  31. SIMULATION: UNEQUAL BASIN SIZES P(BI) = 0.5, P(BR) = 0 Multimodal Optimization 32 2014-09-14 Mike Preuss.

  32. SIMULATION: UNEQUAL BASIN SIZES P(BI) = 1, P(BR) = 0 Multimodal Optimization 33 2014-09-14 Mike Preuss.

  33. SIMULATION: UNEQUAL BASIN SIZES P(BI) = 0.5, P(BR) = 0.5 Multimodal Optimization 34 2014-09-14 Mike Preuss.

  34. MODEL EA FINDINGS  t here are limit s t o possible improvement s  for equal basin sizes, t2 cannot really be improved  t 3 can be improved a lot  for unequal basin sizes, t 2 and t 3 are improved by BI/ BR  basin recognit ion (needs archive) is more import ant t han basin ident ificat ion Multimodal Optimization 35 2014-09-14 Mike Preuss.

  35. different scenarios and their measures Multimodal Optimization 36 2014-09-14 Mike Preuss.

  36. MULTIMODAL OPTIMIZATION SCENARIOS one-global: looking for t he global opt imum only all-global: find all preimages of t he global opt imum  t he problems of t he CEC 2013 niching compet it ion belong here all-known: find all preimages of known opt ima, (local or global) good-subset : locat e a small subset of preimages of all opt ima t hat is well dist ribut ed over t he search space Multimodal Optimization 37 2014-09-14 Mike Preuss.

  37. ONE-GLOBAL  t he BBOB (black-box opt imizat ion benchmark) est ablished t he expect ed runt ime (ERT)  MMO not really well suit ed t o one-global scenario  t his could also be applied t o ot her scenarios, need t o redefine t arget s Multimodal Optimization 38 2014-09-14 Mike Preuss.

  38. MEASURING PROCESS 2 main component s:  subset select ion  measuring Multimodal Optimization 39 2014-09-14 Mike Preuss.

  39. MEASURES most ly used current ly in lit erat ure (also for CEC’ 2013):  peak rat io (PR), but t his is problemat ic Multimodal Optimization 40 2014-09-14 Mike Preuss.

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