Efficiency Enhancement In Estimation of
Distribution Algorithms

Kumara Sastry

Illinois Genetic Algorithms Laboratory
Dep...
Competent Genetic Algorithms

Inve ‘on 72 ‘ ' , . ' ' ‘
DSM_(7Q's) 55' ( )   "3’ 50'‘
(OIuIInIzImona‘Theory|  I’ HI ‘*— GA...
Estimation of Distribution Algorithms: 
lntractability To Tractability

«to Competent genetic algorithms: 

+ Solve hard p...
Efficiency Enhancement:  Tractability To Practicality

~: o Even sub-quadratic evaluations can be daunting

9 Large number...
Outline

«: » Decomposition of efficiency-enhancement techniques

o: « Efficiency enhancement in EAs
e Parallelization
at ...
Rationale For Decomposition:  Trade-Offs

«to Quality-Duration trade—off

«I Longer run duration,  with high quality solut...
Decomposition of Efficiency Enhancement Techniques

«: ~ Four part harmony of efficiency-enhancement
techniques (EETs)

0 ...
Parallelization

«z» Distribute one or more EA components among multiple
processors

oz» EAs are easy to parallelize
<9» P...
Hybridization

oz» Couple domain-specific and local-search techniques
with GAs

«.  Faster convergence,  Repair,  Initiali...
Evaluation Relaxation

»: » Replace an accurate,  but costly function evaluation
with approximate,  but cheap function eva...
Time Continuation

Large population,  single-convergence epoch Vs small
population,  multiple epochs. 

4» Given fixed com...
Tractability to Practicality: 
Combining Different Facets of EETs

»: » If each efficiency enhancement is independent
4. S...
Efficiency Enhancement in EDAs

»: » EETs in EDAs as opposed to simple EAs
2- Effective use of information in the probabil...
Tight Integration of Probabilistic Models and EETs

»: » Illustrate with two examples

»: » Evaluation relaxation in EDAs
...
Inducing Surrogate Form Using Probabilistic Models

»: » Sub-structure identification

+ Use linkage-learning techniques i...
Efficiency Enhancement via Substructural Surrogates

Identify key substructures using EDAs

infer the surrogate structure ...
Substructural Surrogates in BOA

»: » Speed-Up:  Ratio of # function evaluations without
efficiency enhancement to that wi...
Inducing Neighborhood Operators Using
Probabilistic Models

~: » Inducing good neighborhoods
o Sample of candidate solutio...
Deterministic Problems:  Mutation
Noisy Problems:  Crossover

oz» Deterministic fitness:  ozo Noisy fitness:  Recombinatio...
Adaptive Time Continuation in EDAs:  Noisy Fitness

oz» As noise increases,  switch from mutation-dominated
search to cros...
Efficiency Enhancement of Model Building

oz» Parallelization of model building [Ocenasek et al,  2003;
Munetomo et al 200...
Speedup via Sporadic Model Building

oz» Model-building speed-up increases with problem size
ozo Evaluation slowdown incre...
Road to Supermultiplicative Speedups: 
Combining Competent GAs with Different Facets of EETs

oz» Mulltiplicative speedup ...
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Efficiency Enhancement of Estimation of Distribution Algorithms

  1. 1. Efficiency Enhancement In Estimation of Distribution Algorithms Kumara Sastry Illinois Genetic Algorithms Laboratory Department of Industrial & Enterprise Systems Engineering University of Illinois at Urbana-Champaign httg: //www—illiga| .ge. uiuc. edu ksast uiuc. edu Supported by AFOSR F49620-03-1-0129. NSF/ DMR at MCC Dt-‘IR-03-76550
  2. 2. Competent Genetic Algorithms Inve ‘on 72 ‘ ' , . ' ' ‘ DSM_(7Q's) 55' ( ) "3’ 50'‘ (OIuIInIzImona‘Theory| I’ HI ‘*— GA(unlform) ' 9“ 1 I ' Dc-sign 3c—: »:mposl'. lor / ’ PMX (85) ‘I-my r Eil_*3~1§9‘ljI I mGA’(89) 1 fmGA (93) / N . PB| L(&) Exponentia|9Polynomia| Scalability ‘B , ,{v' Number of Evaluations O gemGA(98) LLGA(9§-97) / UMDM95) ‘-cGl'(97) | L| NC(98) LIMDl98) / eCGA(98) 5°f‘(93) | I , 4 I / ~Bgw2°°m —{l [Eefl. afl1_2,0_O_5_J-I ‘ ’ / z ' I - ’ Ill b l BOA 8- hBOA 2001 DSMDGMQOOS) mu 0 leave ( J 25 Prgglem Size 100 200 Low Cost! High Cost! High Error Low gm, » La | I I I I I [GoIdbe, g(2002). Unarticulated Articulated Dimensional Facetwise Equations Des, -an of/ nnol/ at/ ’0n_] Wisdom QL'I/ Ialiéatlive Models Models Of Motion 0 e s
  3. 3. Estimation of Distribution Algorithms: lntractability To Tractability «to Competent genetic algorithms: + Solve hard problems quickly, reliably, and accurately [Goldberg, 2002; Pelikan, 2005] = l< Decomposable and Hierarchical problems I lntractability 9 tractability + Polynomial (usually sub-quadratic) scalability + Even sub-quadratic scalability may be daunting 4: Complex search problems * 1000 variables, 10 seconds/ evaluation 9 ~120 days!
  4. 4. Efficiency Enhancement: Tractability To Practicality ~: o Even sub-quadratic evaluations can be daunting 9 Large number of variables o Expensive evaluation o Limited computational resource o Large order sub-problems in decomposition «: « Need Efficiency-Enhancement Techniques o Tractability 9 Practicality o Premium on principled design methodology that yields greatest speed-up
  5. 5. Outline «: » Decomposition of efficiency-enhancement techniques o: « Efficiency enhancement in EAs e Parallelization at Evaluation relaxation + Time Continuation «tr Hybridization «to Efficiency enhancement in EDAs o: Other efficiencies for practical use of EDAs [http: //medal. cs. umsl. edu/ files/ EE for EDAs. pdf, http: //gal31.ge. uiuc. edu/ kumara/2005/11/24/principled-efficiency- enhancement-technigues/ |
  6. 6. Rationale For Decomposition: Trade-Offs «to Quality-Duration trade—off «I Longer run duration, with high quality solution Vs. shorter run duration with lower quality solution «zo Accuracy-Cost trade—off I Accurate, but costly evaluation Vs. less accurate, but cheaper evaluation oz. Time Budgeting tradeoffs «tr Single large population run Vs. multiple small population runs [Goldberg (2002). Design of / nnovat/ '0n. ]
  7. 7. Decomposition of Efficiency Enhancement Techniques «: ~ Four part harmony of efficiency-enhancement techniques (EETs) 0 Parallelization | Cantt'J-Paz, 2000; Ocenasek etal, 2003; Munetomo et al 2005] 0 Hybridization [Moscata, 1989; Davis, 1991; Hart, 1994; Goldberg & Voessner 1999; Krasnogor, 2002; Sinha 2003; Pelikan, Sastry& Goldberg, 2006] 9 Time utilization | Goldberg, 1999; Srivastava 2002; Sastg & Goldberg, 2004; Lima, et al 2005; Lima et al 2006] o Evaluation relaxation [Miller, 1997; Sastry, 2002; Albert, 2002; Jin, 2003; Sastgg, Pelikan & Goldberg, 2004; Pelikan 8. Sastry, 2004; Sastry, Lima, Goldberg, 2006]
  8. 8. Parallelization «z» Distribute one or more EA components among multiple processors oz» EAs are easy to parallelize <9» Population-based methods 4» Fitness does not depend on other individuals oz» Four types of parallel EAs [Cantu-Paz, 2000] + Single-population master-slaves 4» Multiple populations 9 Fine grained 4- Hierarchical combinations [Adamidis, 1994; Cantu-Paz, 1998; Lin etal, 1994; Alba & Troya, 1999]
  9. 9. Hybridization oz» Couple domain-specific and local-search techniques with GAs «. Faster convergence, Repair, Initialization, Solution refinement, Robustness, etc. , «to A necessary component of industrial strength GAs ~: ~ Theoretical understanding is limited: 4. Division of labor: Spatial & temporal 4- Effect of local search on sampling . . Optimal duration of local search [Bosworth et al, 1972, Moscata, 1989; Davis, 1991; Orvash 8. Davis, 1993; Ibaraki, 1997; Fleurent & Ferland, 1994; Ramsey 8. Grefenstette, 1993; Hartman 8. Rieger, 2001; Lima etal, 2005; Hart, 1994; Goldberg 8. Voessner, 1999; Krasnogor, 2002; Sinha 2003
  10. 10. Evaluation Relaxation »: » Replace an accurate, but costly function evaluation with approximate, but cheap function evaluations »: » Approximation introduces error in evaluation »: » Error comes in two flavors: Variance and Bias . : Variance can be handled spatially -: Bias has to be handled temporally »: » Source of approximation: .» Exogenous + Endogenous + Exogenous and Endogenous [Miller 1997; Sastry, 2002; Albert, 2002; Jin, 2003; Sastry, Pelikan 8. Goldberg, 2004; Pelikan & Sastry, 2004; Sastry, Lima, & Goldberg, 2006]
  11. 11. Time Continuation Large population, single-convergence epoch Vs small population, multiple epochs. 4» Given fixed computational resources >l< Pop size x run duration x # epochs Continuation operator 9*‘. <1) G. ) 2 '2 U) U) C. ‘ I: 2 9 0-1 0-! "3 C3 3 E: 3 D. 94 O O 0-. D- Generations Generations Continuation operator: Selectively perturb incorrectly set subsolutions | Goldberg, 1999; Srivastava 2002; Vrajitoru, 2000; Luke, 2001; Sastry 8 Goldberg, 2004; Lima et al, 2005; Lima et al 2006]
  12. 12. Tractability to Practicality: Combining Different Facets of EETs »: » If each efficiency enhancement is independent 4. Speed-up of each EET would hold v Total speed-up is multiplicative not additive! >l= Moderate speed-ups are also substantial Master-slave parallel GA on 100 cpus: 100.00 Speed-up from hybridization: 1.30 Speed-up from continuation: 1.20 Speed-up from evaluation relaxation: 1.25 Total Speed-up: 100*1.3*1.2*1.5 195.00 Computing power of additional 95 processors!
  13. 13. Efficiency Enhancement in EDAs »: » EETs in EDAs as opposed to simple EAs 2- Effective use of information in the probabilistic models + Calls for tight integration of models and surrogate design »: » Efficiency enhancement of probabilistic model building 4. Model building can be expensive as well 4» Speedup model building process »: « Efficient EDA implementations . . Program and memory efficiencies
  14. 14. Tight Integration of Probabilistic Models and EETs »: » Illustrate with two examples »: » Evaluation relaxation in EDAs -. . Inducing surrogate form using probabilistic models »: » Adaptive time continuation in EDAs «I. Inducing neighborhood operators for local search using probabilistic models
  15. 15. Inducing Surrogate Form Using Probabilistic Models »: » Sub-structure identification + Use linkage-learning techniques including EDAs . .. E. g., eCGA »: » Surrogate form induced from the probabilistic model -I» Example model: [1 3] [2] [4] -. ~ Surrogate: fs = C0 + 01961 + 03333 + C1,3Iv1i1?3 + 02962 + 041134 «z» Coefficients of Surrogates: Subsolution qualities + Can use linear regression methods
  16. 16. Efficiency Enhancement via Substructural Surrogates Identify key substructures using EDAs infer the surrogate structure from the substructure! model Use least squares method to estimate the coefficients of the surrogate 3 +6:/ Wd), =o_01 Only 1-3% individuals +~: ,/<«ga>2=o.1 need expensive evaluation 1 i i Endogenous surrogate Speedup 2 3 A on noisy problems o Simple surrogates don’t give any speedup 0,4 0i6 0:8 [Sastry et 3| Proportion of inheritance, pi
  17. 17. Substructural Surrogates in BOA »: » Speed-Up: Ratio of # function evaluations without efficiency enhancement to that with it. »: o Only 1-15% individuals need evaluation »: » Speed-Up: 30-53 g n~<1—. ».> 1<1+. ».> 1-5 '0 50-bit oneMax ‘ ‘ i> ‘ 125 Th " 3 18:? ?? Fitness modeling ‘ — eo-i rap . — Theory in vh U1 0 1C0-bi’. 0neMax 0 10 4-Trap 1 2 Speed~Upn 8 _‘. Speed-up, nmh G 3 8 8 8 .3 G c 01 02 03 04 05 0'5 07 ca proportion of Inheritance. D. 01 V 0.4 0,6 lpenkan & Sastry’ 2004] ‘ Proportion of inheritance, pi A
  18. 18. Inducing Neighborhood Operators Using Probabilistic Models ~: » Inducing good neighborhoods o Sample of candidate solutions o Use linkage-learning procedures . ... .. 3.. .; . ... .. developed for selectorecombinative GAs »: » Neighborhood: Space vs. Sub-space BB #3 BB #3 »: » Search: Hillclimbing vs. Random o Consider linkage partitions an Arbitrary left-to-right order 9 Choose the best schemata an Among the 2*‘ possible ones
  19. 19. Deterministic Problems: Mutation Noisy Problems: Crossover oz» Deterministic fitness: ozo Noisy fitness: Recombination Mutation is more efficient is more efficient 17 = 'rzfc. Jl! ; log 71?. ) I '”. ft'-X0 m-k Tran _s 0) —Theory 0 k=4.d= O.25 ---- Theory 0 k=5,d=02 _. ‘P .3 N Speed-Up, amp <5 | Sastry 8. Goldberg, 2004] 5 16 20 so so Number of building blocks, m
  20. 20. Adaptive Time Continuation in EDAs: Noisy Fitness oz» As noise increases, switch from mutation-dominated search to crossover-dominated search mode ‘l05r'I -9- eCGA -I3 - eCMA . a O . l.. ... ... . .. C) 5 5.’ C .15 C .9 . . m 2 In > 0 c .9 ‘G c 2 . . o E E D Z . . . l 1o , 1o"_ . , 10; 2 a N0|$€'t0'$|9l‘| a| 73110.0;/ (0/dl‘ Noise—to—signal ratio. oNf(crr"d)‘ [Lima et al 2005; Lima et al 2006]
  21. 21. Efficiency Enhancement of Model Building oz» Parallelization of model building [Ocenasek et al, 2003; Munetomo et al 2005] oz» Prior knowledge utilization [Ba| uja, 2002] oz» Model relaxation techniques . ; Example: Sporadic model building [Pelikan et al 2006] »o Learn structure of probabilistic models intermittently * Remaining generations use structure from previous iteration >l= Parameters are always updated Save time in most expensive part of model building
  22. 22. Speedup via Sporadic Model Building oz» Model-building speed-up increases with problem size ozo Evaluation slowdown increases with problem size ozo Speedup in CPU time increases with problem size —e—Speedup of structure—building + Slowdown of evaluation , I-6-CPU speedu with SMB l A 01 O) A 01 (IO U1 (D Q C E 8 G. 0 E '5 :2 o. 0 '5 9 E (I) Speedup or Slowdown 1 00 200 400 800 300 400 Problem size Problem size [Pelikan, Sastry 8. Goldberg, 2006]
  23. 23. Road to Supermultiplicative Speedups: Combining Competent GAs with Different Facets of EETs oz» Mulltiplicative speedup is substantial Master-slave parallel GA on 100 cpus: 100.00 Speed-up from hybridization: 1.30 Speed-up from continuation: 1.20 Speed-up from evaluation relaxation: 1.25 Total Speed-up: 100*1.3*1.2*1.5 195.00 oz» Tight integration of probabilistic models of EDAs with design of EETs yield significantly higher speedups -4» 1.25 to 53 for an evaluation-relaxation scheme z Evidence of supermultiplicative speedups! 4» Can explain with facetwse models

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