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GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
GECCO 2010 OBUPM Workshop
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GECCO 2010 OBUPM Workshop

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Stochastic local search in continuous domain

Stochastic local search in continuous domain

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  • 1. Stochastic Local Search in Continuous Domain Petr Pošík posik@labe.felk.cvut.cz Czech Technical University in Prague Faculty of Electrical Engineering Department of Cybernetics Intelligent Data Analysis Group P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 1 / 25
  • 2. Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs Motivation P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 2 / 25
  • 3. Why local search? Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs There’s something about population: P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 3 / 25
  • 4. Why local search? Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs There’s something about population: data set forming a basis for offspring creation P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 3 / 25
  • 5. Why local search? Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs There’s something about population: data set forming a basis for offspring creation allows for searching the space in several places at once P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 3 / 25
  • 6. Why local search? Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs There’s something about population: data set forming a basis for offspring creation allows for searching the space in several places at once (replaced by restarted local search with adaptive neighborhood) P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 3 / 25
  • 7. Why local search? Motivation Why local search? Agenda Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs There’s something about population: data set forming a basis for offspring creation allows for searching the space in several places at once (replaced by restarted local search with adaptive neighborhood) Hypothesis: The data set (population) is very useful when creating (sometimes implicit) global model of the fitness landscape or a local model of the neighborhood. It is often better to have a superb adaptive local search procedure and restart it, than to deal with a complex global search algorithm. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 3 / 25
  • 8. Agenda Motivation Why local search? 1. Adaptation in stochastic local search: Agenda Roles of population and model Introduction Notable examples of Notable examples of local search based on EAs local search based on EA ideas Personal history in the field of real-valued EDAs Personal history in the field of real-valued 2. Features of stochastic local search in continuous domain EDAs Survey of relevant works in the article in proceedings P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 4 / 25
  • 9. Motivation Introduction Relation of local search and EAs (EDAs) Stochastic Local Search Roles of population and model Unifying view Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs Introduction P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 5 / 25
  • 10. Relation of local search and EAs (EDAs) Classification of optimization techniques [Neu04]: incomplete: no safeguards against getting stuck in a local optimum assymptotically complete: reaches global optimum with certainty (or with probability one) if allowed to run indefinitely long, but has no means to know when a global optimum has been found. complete: reaches global optimum with certainty if allowed to run indefinitely long, and knows after finite time if an approximate optimum has been found (within specified tolerances). P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 6 / 25
  • 11. Relation of local search and EAs (EDAs) Classification of optimization techniques [Neu04]: incomplete: no safeguards against getting stuck in a local optimum assymptotically complete: reaches global optimum with certainty (or with probability one) if allowed to run indefinitely long, but has no means to know when a global optimum has been found. complete: reaches global optimum with certainty if allowed to run indefinitely long, and knows after finite time if an approximate optimum has been found (within specified tolerances). Practical point of view: Judging an algorithm based on its behaviour, not on its functional parts. EAs: EDAs:   population   population  data source for offs. creation  data source for offs. creation selection model building crossover model sampling (with explicit model) (with implicit model)    mutation  When can an EA with one of these procedures be described as local search? When the distribution of offspring produced by the respective data source is single-peak (unimodal). [Neu04] Arnold Neumaier. Complete search in continuous global optimization and constraint satisfaction. Acta Numerica, 13:271–369, May 2004. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 6 / 25
  • 12. Stochastic Local Search Motivation Term coined by Holger Hoos and Thomas Stuetzle [HS04]: Introduction Relation of local search and EAs (EDAs) Stochastic Local Search Roles of population and model Unifying view Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs originally used in the combinatorial optimization settings the term nicely describes EDAs with single-peak probability distributions [HS04] Holger H. Hoos and Thomas Stützle. Stochastic Local Search : Foundations & Applications. The Morgan Kaufmann Series in Artificial Intelligence. Morgan Kaufmann, 2004. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 7 / 25
  • 13. Roles of population and model Observation: Algorithm 1: Evol. scheme in discrete domains 1 begin 2 X (0) ← InitializePopulation() 3 f (0) ← Evaluate(X (0) ) 4 g←1 5 while not TerminationCondition() do 6 S ← Select(X ( g−1) , f ( g−1) ) 7 M ← Build(S ) 8 XOffs ← Sample(M) 9 f Offs ← Evaluate (XOffs ) 10 { X ( g) , f ( g) } ← 11 Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 8 / 25
  • 14. Roles of population and model Observation: Algorithm 1: Evol. scheme in discrete domains 1 begin 2 X (0) ← InitializePopulation() 3 f (0) ← Evaluate(X (0) ) 4 g←1 5 while not TerminationCondition() do 6 S ← Select(X ( g−1) , f ( g−1) ) 7 M ← Build(S ) 8 XOffs ← Sample(M) 9 f Offs ← Evaluate (XOffs ) 10 { X ( g) , f ( g) } ← 11 Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 Population is evolved (adapted) Model is used as a single-use processing unit P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 8 / 25
  • 15. Roles of population and model Observation: Algorithm 1: Evol. scheme in discrete domains 1 begin 2 X (0) ← InitializePopulation() 3 f (0) ← Evaluate(X (0) ) 4 g←1 5 while not TerminationCondition() do 6 S ← Select(X ( g−1) , f ( g−1) ) 7 M ← Build(S ) 8 XOffs ← Sample(M) 9 f Offs ← Evaluate (XOffs ) 10 { X ( g) , f ( g) } ← 11 Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 Population is evolved (adapted) Model is used as a single-use processing unit What happens if we use generational repacement and update the model instead of building it from scratch? P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 8 / 25
  • 16. Roles of population and model Observation: Algorithm 1: Evol. scheme in discrete domains Algorithm 2: Evol. scheme in cont. domains 1 begin 1 begin 2 X (0) ← InitializePopulation() 2 M(1) ← InitializeModel() 3 f (0) ← Evaluate(X (0) ) 3 g←1 4 g←1 4 while not TerminationCondition() do 5 while not TerminationCondition() do 5 X ← Sample(M( g) ) 6 S ← Select(X ( g−1) , f ( g−1) ) 6 f ← Evaluate (X) 7 M ← Build(S ) 7 S ← Select(X, f ) 8 XOffs ← Sample(M) 8 M( g+1) ← Update(g, M( g) , X, f , S ) 9 f Offs ← Evaluate (XOffs ) 9 g ← g+1 10 { X ( g) , f ( g) } ← 11 Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 Population is evolved (adapted) Model is used as a single-use processing unit What happens if we use generational repacement and update the model instead of building it from scratch? P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 8 / 25
  • 17. Roles of population and model Observation: Algorithm 1: Evol. scheme in discrete domains Algorithm 2: Evol. scheme in cont. domains 1 begin 1 begin 2 X (0) ← InitializePopulation() 2 M(1) ← InitializeModel() 3 f (0) ← Evaluate(X (0) ) 3 g←1 4 g←1 4 while not TerminationCondition() do 5 while not TerminationCondition() do 5 X ← Sample(M( g) ) 6 S ← Select(X ( g−1) , f ( g−1) ) 6 f ← Evaluate (X) 7 M ← Build(S ) 7 S ← Select(X, f ) 8 XOffs ← Sample(M) 8 M( g+1) ← Update(g, M( g) , X, f , S ) 9 f Offs ← Evaluate (XOffs ) 9 g ← g+1 10 { X ( g) , f ( g) } ← 11 Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) Model is evolved (adapted) 12 g ← g+1 Population is used only as a data set allowing us to gather some information Population is evolved (adapted) about the fitness landscape Model is used as a single-use processing unit What happens if we use generational repacement and update the model instead of building it from scratch? P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 8 / 25
  • 18. Unifying view Motivation Introduction Algorithm 3: General Evolutionary Scheme Relation of local search and EAs (EDAs) 1 begin Stochastic Local Search Roles of population and 2 M(0) ← InitializeModel() model Unifying view 3 X (0) ← Sample(M(0) ) Notable examples of 4 f (0) ← Evaluate(X (0) ) local search based on EA 5 g←1 ideas 6 while not TerminationCondition() do Personal history in the field of real-valued 7 {S , D} ← Select(X ( g−1) , f ( g−1) ) EDAs 8 M( g) ← Update(g, M( g−1) , X ( g−1) , f ( g−1) , S , D ) 9 XOffs ← Sample(M( g) ) 10 f Offs ← Evaluate (XOffs ) 11 { X ( g) , f ( g) } ← Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 9 / 25
  • 19. Unifying view Motivation Introduction Algorithm 3: General Evolutionary Scheme Relation of local search and EAs (EDAs) 1 begin Stochastic Local Search Roles of population and 2 M(0) ← InitializeModel() model Unifying view 3 X (0) ← Sample(M(0) ) Notable examples of 4 f (0) ← Evaluate(X (0) ) local search based on EA 5 g←1 ideas 6 while not TerminationCondition() do Personal history in the field of real-valued 7 {S , D} ← Select(X ( g−1) , f ( g−1) ) EDAs 8 M( g) ← Update(g, M( g−1) , X ( g−1) , f ( g−1) , S , D ) 9 XOffs ← Sample(M( g) ) 10 f Offs ← Evaluate (XOffs ) 11 { X ( g) , f ( g) } ← Replace(X ( g−1) , XOffs , f ( g−1) , f Offs ) 12 g ← g+1 both the population and the model are evolved (adapted) DANGER: using “the same information” over and over to adapt the model (part of the population may stay the same over several generations) P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 9 / 25
  • 20. Motivation Introduction Notable examples of local search based on EA ideas Building-block-wise mutation algorithm Binary local search with linkage identification Building-block hill-climber CMA-ES G3PCX Summary Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 10 / 25
  • 21. Building-block-wise mutation algorithm Motivation Sastry and Goldberg [SG07] Introduction Notable examples of compared BBMA with selecto-recombinative GA on a class of nonuniformly scaled local search based on EA ADFs ideas Building-block-wise mutation algorithm assumed that BB information is known Binary local search with linkage identification showed that Building-block hill-climber $ in noiseless conditions BBMA is faster, while CMA-ES $ in noisy conditions selecto-recombinative GA is faster G3PCX Summary Personal history in the field of real-valued EDAs [SG07] Kumara Sastry and David E. Goldberg. Let’s get ready to rumble redux: crossover versus mutation head to head on exponentially scaled problems. In GECCO ’07: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pages 1380–1387, New York, NY, USA, 2007. ACM. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 11 / 25
  • 22. Binary local search with linkage identification Motivation Vanicek [Van10] Introduction Notable examples of Binary local search (actually BBMA) completed with LIMD local search based on EA ideas Linkage identification by non-monotonicity check [MG99] Building-block-wise mutation algorithm works well on ADFs, fails on hierarchical functions Binary local search with Graph of reliability (function: k*5bitTrap) Graph of reliability (function: k*8bitTrap) linkage identification 5 10 7 10 Building-block hill-climber 6 CMA-ES 4 10 10 G3PCX Summary 5 10 evaluations evaluations Personal history in the 3 10 field of real-valued 4 EDAs 10 2 10 3 LIMD bsf 10 LIMD bsf random random BOA BOA ECGA ECGA 1 2 10 10 0 10 20 30 40 50 60 70 0 20 40 60 80 100 120 dim dim [MG99] Masaharu Munetomo and David E. Goldberg. Linkage identification by non-monotonicity detection for overlapping functions. Evolutionary Computation, 7(4):377–398, 1999. [Van10] Stanislav Vaníˇ ek. Binary local optimizer with linkage learning. Technical report, Czech Technical University in Prague, Prague, c Czech Republic, 2010. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 12 / 25
  • 23. Building-block hill-climber Motivation Iclanzan and Dumitrescu [ID07] Introduction Notable examples of similar to BBMA local search based on EA ideas uses compact genetic codes Building-block-wise mutation algorithm beats hBOA on hierarchical functions (hIFF, hXOR, hTrap) Binary local search with linkage identification Building-block hill-climber CMA-ES G3PCX Summary Personal history in the field of real-valued EDAs [ID07] David Iclanzan and Dan Dumitrescu. Overcoming hierarchical difficulty by hill-climbing the building block structure. In GECCO ’07: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pages 1256–1263, New York, NY, USA, 2007. ACM. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 13 / 25
  • 24. CMA-ES Motivation Hansen and Ostermeier [HO01] Introduction Notable examples of based on evolutionary strategy local search based on EA ideas $ (1 + 1)-ES (mutative, parent-centric) searches neighborhood of 1 point Building-block-wise mutation algorithm $ (1 + λ)-ES (mutative, parent-centric) searches neighborhood of 1 point , Binary local search with linkage identification $ (µ + λ)-ES (mutative, parent-centric) searches neighborhood of several points , Building-block hill-climber $ (µ/ρ + λ)-ES (recombinative, between parent-centric and mean-centric) , CMA-ES G3PCX searches neighborhood of several points Summary $ CMA-ES is actually (µ/µ, λ)-ES (recombinative, mean-centric) searches Personal history in the neighborhood of 1 point field of real-valued EDAs [HO01] Nikolaus Hansen and Andreas Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159–195, 2001. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 14 / 25
  • 25. G3PCX Generalized generation gap by Deb in [Deb05] Algorithm 4: Generalized Generation Gap Input: number of parents µ, number of offspring λ, number of replacement candidates r 1 begin 2 B ← initialize population of size N 3 while not TerminationCondition() do 4 P ← select µ parents from B : select the best population member and µ − 1 other parents uniformly 5 C ← generate λ offspring from the selected parents P using any chosen recombination scheme 6 R ← choose a r members of population B uniformly as candidates for replacement 7 B ← replace R in B by the best r members of R∪C claimed to be more efficient than CMA-ES on three 20D functions P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 15 / 25
  • 26. G3PCX Generalized generation gap by Deb in [Deb05] Parent-centric crossover [DAJ02] PCX with µ = 3 and large λ Algorithm 4: Generalized Generation Gap Input: 2 number of parents µ, 1.5 number of offspring λ, 1 number of replacement candidates r 1 begin 0.5 2 B ← initialize population of size N 3 while not TerminationCondition() do 0 4 P ← select µ parents from B : select the best population member and µ − 1 other parents −0.5 uniformly 5 C ← generate λ offspring from the selected −1 parents P using any chosen recombination −0.5 0 0.5 1 1.5 2 2.5 3 3.5 scheme 6 R ← choose a r members of population B uniformly as candidates for replacement 7 B ← replace R in B by the best r members of R∪C claimed to be more efficient than CMA-ES on three 20D functions P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 15 / 25
  • 27. G3PCX Generalized generation gap by Deb in [Deb05] Parent-centric crossover [DAJ02] PCX with µ = 3 and large λ Algorithm 4: Generalized Generation Gap Input: 2 number of parents µ, 1.5 number of offspring λ, 1 number of replacement candidates r 1 begin 0.5 2 B ← initialize population of size N 3 while not TerminationCondition() do 0 4 P ← select µ parents from B : select the best population member and µ − 1 other parents −0.5 uniformly 5 C ← generate λ offspring from the selected −1 parents P using any chosen recombination −0.5 0 0.5 1 1.5 2 2.5 3 3.5 scheme 6 R ← choose a r members of population B Local-search-intensive variant used: uniformly as candidates for replacement the best pop. member is always selected as a 7 B ← replace R in B by the best r members of parent, and R∪C the best pop. member is always selected as claimed to be more efficient than CMA-ES on the distribution center. three 20D functions [DAJ02] Kalyanmoy Deb, Ashish Anand, and Dhiraj Joshi. A computationally efficient evolutionary algorithm for real-parameter optimization. Technical report, Indian Institute of Technology, April 2002. [Deb05] K. Deb. A population-based algorithm-generator for real-parameter optimization. Soft Computing, 9(4):236–253, April 2005. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 15 / 25
  • 28. Summary Motivation Introduction Notable examples of local search based on EA ideas Building-block-wise mutation algorithm Binary local search with linkage identification Building-block hill-climber CMA-ES G3PCX Summary “By borrowing ideas from EAs and building local search techniques based on them, Personal history in the we can arrive at pretty efficient algorithms, field of real-valued which usually have less parameters to tune.” EDAs P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 16 / 25
  • 29. Motivation Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs Distribution Tree Linear coordinate transformations Non-linear global transformation Estimation of contour lines of the fitness Personal history in the field of real-valued EDAs function Variance enlargement in simple EDA Features of simple EDAs Final summary Thanks for your attention P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 17 / 25
  • 30. Distribution Tree Motivation Distribution Tree-Building Real-valued EA [Poš04] Introduction Griewangk function Rosenbrock function Notable examples of 5 local search based on EA 2 ideas 4 1.5 Personal history in the 3 field of real-valued 1 EDAs 2 Distribution Tree 1 0.5 Linear coordinate transformations 0 0 Non-linear global −1 transformation −0.5 Estimation of contour −2 lines of the fitness −1 function −3 Variance enlargement in −1.5 simple EDA −4 Features of simple EDAs −5 −2 −5 0 5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Final summary Thanks for your attention Identifies hyper-rectangular areas of the search space with significantly different densities. Does not work well if the promising areas are not aligned with the coordinate axes. Need some coordinate transformations? [Poš04] Petr Pošík. Distribution tree–building real-valued evolutionary algorithm. In Parallel Problem Solving From Nature — PPSN VIII, pages 372–381, Berlin, 2004. Springer. ISBN 3-540-23092-0. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 18 / 25
  • 31. Linear coordinate transformations No tranformation vs. PCA vs. ICA [Poš05] PC 1 PC 2 PC 1 PC 2 6 6 5 5 4 4 0 0 2 2 −5 −5 0 0 0 2 4 6 0 2 4 6 −10 0 10 −10 0 10 IC 1 IC 2 IC 1 IC 2 6 6 5 5 4 4 0 0 2 2 −5 −5 0 0 −10 0 10 −10 0 10 0 2 4 6 0 2 4 6 Results are different, but the difference does not Results are different and the difference matters! matter. The global information extracted by linear tranformation procedures often was not useful. Need for non-linear transformation or local transformations? [Poš05] Petr Pošík. On the utility of linear transformations for population-based optimization algorithms. In Preprints of the 16th World Congress of the International Federation of Automatic Control, Prague, 2005. IFAC. CD-ROM. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 19 / 25
  • 32. Non-linear global transformation Motivation Kernel PCA as transformation technique in EDA [Poš04] Introduction Notable examples of local search based on EA Training data points ideas 8 Data points sampled from KPCA Personal history in the field of real-valued 7 EDAs 6 Distribution Tree Linear coordinate 5 transformations Non-linear global transformation 4 Estimation of contour lines of the fitness 3 function Variance enlargement in 2 simple EDA 1 Features of simple EDAs Final summary 0 2 4 6 8 10 Thanks for your attention Works too well: It reproduces the pattern with high fidelity If the population is not centered around the optimum, the EA will miss it Need for efficient population shift? Is the MLE principle suitable for model building in EAs? [Poš04] Petr Pošík. Using kernel principal components analysis in evolutionary algorithms as an efficient multi-parent crossover operator. In IEEE 4th International Conference on Intelligent Systems Design and Applications, pages 25–30, Piscataway, 2004. IEEE. ISBN 963-7154-29-9. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 20 / 25
  • 33. Estimation of contour lines of the fitness function Build a quadratic classifier separating the selected and the discarded individuals [PF07] 1 1 1 0 0 0 −1 −1 −1 −2 −2 −2 −3 −3 −3 −4 −4 −4 −2 −1 0 1 2 3 −2 −1 0 1 2 3 −2 −1 0 1 2 3 Ellipsoid Function Classifier built by modified perceptron 10 10 CMA−ES algorithm or by semidefinite programming Perceptron SDP Works well for pure quadratic functions 5 10 Average BSF Fitness If the selected and discarded individuals are not separable by an ellipsoid, the training 0 10 procedure fails to create a good model Not solved yet −5 10 −10 10 0 1000 2000 3000 4000 5000 6000 Number of Evaluations [PF07] Petr Pošík and Vojtˇ ch Franc. Estimation of fitness landscape contours in EAs. In GECCO ’07: Proceedings of the 9th annual conference on Genetic and evolutionary e computation, pages 562–569, New York, NY, USA, 2007. ACM Press. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 21 / 25
  • 34. Variance enlargement in simple EDA Variance adaptation is often used. Is a constant variance multiplier a viable alternative? [Poš08] Minimal requirements for a successful real-valued EDA $ the model must converge if centered around optimum $ the model must not converge if set on the slope Is there a single value k of multiplier for MLE variance estimate that would ensure the reasonable behaviour just mentioned? Does it depend on the single-peak distribution being used? 1 1 1 10 10 10 0 10 k k k −1 kmax, τ = 0.1 10 kmax, τ = 0.3 0 0 10 10 kmax, τ = 0.5 kmax, τ = 0.7 kmax kmax kmax, τ = 0.9 kmin , τ = 0.1 kmin , τ = 0.1 −2 kmin , τ = 0.1 10 kmin , τ = 0.3 kmin , τ = 0.3 kmin , τ = 0.3 kmin , τ = 0.5 kmin , τ = 0.5 kmin , τ = 0.5 kmin , τ = 0.7 kmin , τ = 0.7 kmin , τ = 0.7 kmin , τ = 0.9 kmin , τ = 0.9 −3 kmin , τ = 0.9 0 1 0 1 10 0 1 10 10 10 10 10 10 dim dim dim For Gaussian and “isotropic Gaussian”, allowable k is hard or impossible to find. For isotropic Cauchy, allowable k seems to always exist. [Poš08] Petr Pošík. Preventing premature convergence in a simple EDA via global step size setting. In Günther Rudolph, editor, Parallel Problem Solving from Nature – PPSN X, volume 5199 of Lecture Notes in Computer Science, pages 549–558. Springer, 2008. P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 22 / 25
  • 35. Features of simple EDAs Motivation Consider a simple EDA using the following sampling mechanism: Introduction Notable examples of local search based on EA zi ∼ P , ideas xi = µ + R × diag(σ ) × (c · zi ). Personal history in the field of real-valued EDAs 1. What kind of base distribution P is used for sampling? Distribution Tree Linear coordinate transformations 2. Is the type of distribution fixed during the whole evolution? Non-linear global transformation Estimation of contour 3. Is the model re-estimated from scratch each generation? Or is it updated lines of the fitness incrementaly? function Variance enlargement in simple EDA 4. Does the model-building phase use selected and/or discarded individuals? Features of simple EDAs Final summary 5. Where do you place the sampling distribution in the next generation? Thanks for your attention 6. When and how much (if at all) should the distribution be enlarged? 7. What should the reference point be? What should the orientation of the distribution be? See the survey of SLS algorithms and their features in the article in proceedings. http://portal.acm.org/citation.cfm?id=1830761.1830830 P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 23 / 25
  • 36. Final summary Motivation Introduction It seems that by borrowing ideas from EC community and incorporating them back Notable examples of into local search methods we can get very efficient algorithms. This seems to be the local search based on EA case especially for continuous domains. ideas Personal history in the In the same time, it is important to study where are the limits of such methods. field of real-valued EDAs Comparison with state-of-the-art techniques. Distribution Tree Linear coordinate transformations Black-box optimization benchmarking workshop Non-linear global http://coco.gforge.inria.fr/doku.php?id=bbob-2010 transformation Estimation of contour lines of the fitness set of benchmark functions (noiseless and noisy, unimodal and multimodal, function well-conditioned and ill-conditioned, structured and unstructured) Variance enlargement in simple EDA expected running time of the algorithm is used as the main measure of Features of simple EDAs performance Final summary Thanks for your set of postprocessing scripts which produce many nice and information-dense attention figures and tables set of latex article templates many algorithms to compare with already benchmarked, their data freely available!!! P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 24 / 25
  • 37. Thanks for your attention Motivation Introduction Notable examples of local search based on EA ideas Personal history in the field of real-valued EDAs Distribution Tree Linear coordinate transformations Non-linear global transformation Estimation of contour lines of the fitness function Variance enlargement in simple EDA Features of simple EDAs Final summary Any questions? Thanks for your attention P. Pošík c GECCO 2010, OBUPM Workshop, Portland, 7.-11.7.2010 25 / 25

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