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Managing Director / CTO NuTech Solutions GmbH / Inc. Martin-Schmeißer-Weg 15 D – 44227 Dortmund Tel.: +49 (0) 231 72 54 63-10.

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Presentation on theme: "Managing Director / CTO NuTech Solutions GmbH / Inc. Martin-Schmeißer-Weg 15 D – 44227 Dortmund Tel.: +49 (0) 231 72 54 63-10."— Presentation transcript:

1 Managing Director / CTO NuTech Solutions GmbH / Inc. Martin-Schmeißer-Weg 15 D – Dortmund Tel.: +49 (0) Fax: +49 (0) Thomas Bäck UPP 2004 Le Mont Saint Michel, September 15, 2004 Problem Solving by Evolution: One of Nature’s UPPs Full Professor for „Natural Computing“ Leiden Institute for Advanced Computer Science (LIACS) Niels Bohrweg 1 NL-2333 CA Leiden Tel.: +31 (0) Fax: +31 (0)

2 2 PharminformaticsOtherECUPP of CAsApplicationsOverview  Optimization and Evolutionary Computation  Genetic Algorithms, Evolution Strategies, Self-Adaptation  Convergence Velocity Theory  Applications: Some Examples  Applications: Programming of CA  Links to Bio- and Pharminformatics  Drug Design  Classification  Evolutionary DNA-Computing

3 3 PharminformaticsOtherECUPP of CAsApplicationsOverview Natural Computing  Computing Paradigms after Natural Models  NN, EC, Simulated Annealing, Swarm & Ant Algorithms, DNA Computing, Quantum Computing, CA,...  Journals  Journal of Natural Computing (Kluwer).  Theoretical Computer Science C (Elsevier).  Book Series on Natural Computing (Springer).  Leiden Center of Natural Computing (NL).

4 4 PharminformaticsOtherECUPP of CAsApplicationsOverview Unifying Evolutionary Algorithm t := 0; initialize(P(t)); evaluate(P(t)); while not terminate do P‘(t) := mating_selection(P(t)); P‘‘(t) := variation(P‘(t)); evaluate(P‘‘(t)); P(t+1) := environmental_selection(P‘‘(t) Q); t := t+1; od

5 5 PharminformaticsOtherECUPP of CAsApplicationsOverview  Real-valued representation  Normally distributed mutations  Fixed recombination rate (= 1)  Deterministic selection  Creation of offspring surplus  Self-adaptation of strategy parameters: Variance(s), Covariances  Binary representation  Fixed mutation rate p m (= 1/n)  Fixed crossover rate p c  Probabilistic selection  Identical population size  No self-adaptation Genetic Algorithm Evolution Strategies Genetic Algorithms vs. Evolution Strategies

6 6 PharminformaticsOtherECUPP of CAsApplicationsOverview Genetic Algorithms: Mutation  Mutation by bit inversion with probability p m.  p m identical for all bits.  p m small (e.g., p m = 1/n ).

7 7 PharminformaticsOtherECUPP of CAsApplicationsOverview Genetic Algorithms: Crossover  Crossover applied with probability p c.  p c identical for all individuals.  k -point crossover: k points chosen randomly.  Example: 2-point crossover.

8 8 PharminformaticsOtherECUPP of CAsApplicationsOverview Genetic Algorithms: Selection  Fitness proportional:  f fitness  population size  Tournament selection:  Randomly select q << individuals.  Copy best of these q into next generation.  Repeat times.  q is the tournament size (often: q = 2 ).

9 9 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolution Strategies: Mutation  -adaptation by means of –1/5-success rule. –Self-adaptation. Creation of a new solution: Convergence speed:  Ca. 10  n down to 5  n is possible. More complex / powerful strategies: –Individual step sizes  i. –Covariances.

10 10 PharminformaticsOtherECUPP of CAsApplicationsOverview Self-Adaptation:  Motivation: General search algorithm  Geometric convergence: Arbitrarily slow, if s wrongly controlled !  No deterministic / adaptive scheme for arbitrary functions exists.  Self-adaptation: On-line evolution of strategy parameters.  Various schemes:  Schwefel one , n , covariances; Rechenberg MSA.  Ostermeier, Hansen: Derandomized, Covariance Matrix Adaptation.  EP variants (meta EP, Rmeta EP).  Bäck: Application to p in GAs. Step size Direction

11 11 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolution Strategies: Self-Adaptation  Learning while searching: Intelligent Method.  Different algorithmic approaches, e.g: Pure self-adaptation: Mutational step size control MSC: Derandomized step size adaptation Covariance adaptation

12 12 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolution Strategies: Self-Adaptive Mutation n = 2, n  = 1, n  = 0 n = 2, n  = 2, n  = 0 n = 2, n  = 2, n  = 1

13 13 PharminformaticsOtherECUPP of CAsApplicationsOverview Self-Adaptation: Dynamic Sphere  Optimum  :  Transition time proportionate to n.  Optimum  learned by self- adaptation.

14 14 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolution Strategies: Selection (  ) (  )

15 15 PharminformaticsOtherECUPP of CAsApplicationsOverview Possible Selection Operators  (1+1)-strategy: one parent, one offspring.  (1, )-strategies: one parent, offspring. Example: (1,10)-strategy. Derandomized / self-adaptive / mutative step size control.  ( , )-strategies:  >1 parents,  >  offspring Example: (2,15)-strategy. Includes recombination. Can overcome local optima.  (  + )-strategies: elitist strategies.

16 16 PharminformaticsOtherECUPP of CAsApplicationsOverview Vision: Self-adaptive software  Self-adaptation is the ability of an algorithm to iteratively make the solution of a problem more likely.  Software that monitors its performance, improves itself, learns while it interacts with its user(s). [Robertson, Shrobie, Laddaga, 2001]  Self-adaptation in ES: Evolution of solutions and solution search algorithms.

17 17 PharminformaticsOtherECUPP of CAsApplicationsOverview Robust vs. Fast Optimization:  Global convergence with probability one: General, but for practical purposes useless.  Convergence velocity: Local analysis only, specific functions only.

18 18 PharminformaticsOtherECUPP of CAsApplicationsOverview GA Convergence Velocity Analysis:  (1+1)-GA, (1, )-GA, (1+ )-GA.  For counting ones function:  Convergence velocity:  Mutation rate p, q = 1 – p, k max = l – f a.

19 19 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity Analysis:  Optimum mutation rate ?  Absorption times from transition matrix in block form, usingwhere

20 20 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity Analysis:  p too large: Exponential  p too small: Almost constant.  Optimal: O(l ln l). p

21 21 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity Analysis:  (1, )-GA ( k min = -f a ), (1+ )-GA ( k min = 0 ) :

22 22 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity Analysis: (1, )-GA, (1+ )-GA:(1, )-ES, (1+ )-ES: Conclusion: Unifying, search-space independent theory !?

23 23 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity Analysis:  ( , )-GA ( k min = -f a ), (  + )-GA ( k min = 0 ) :  Theory  Experiment

24 24 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity for Bimodal Function:  A generalized Trap Function ( u = number of ones):

25 25 PharminformaticsOtherECUPP of CAsApplicationsOverview Transition Probabilities for Bimodal Function:  Probability to mutate u 1 ones into u 2 ones:  Probability that one step of the algorithm changes parent ( u 1 -> u 2 ):

26 26 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity for Bimodal Function: Convergence velocity: (1+1), z 2 =100, current position varies (5,20,...). (1+ ), z 2 =100, position 20, lambda varies (1,2,...). (1+ ), z 2 =100, position 35, lambda varies (1,2,...). Global max. Jump to local max.

27 27 PharminformaticsOtherECUPP of CAsApplicationsOverview Convergence Velocity for Bimodal Function:  New Algorithm: Several mutation rates.  Expands theory to all counting ones functions (including moving ones).  Optimal lower mutation rate: 1/l.  Currently further analyzed / tested on NP-complete problems.

28 28 PharminformaticsOtherECUPP of CAsApplicationsOverview Optimization Problem:  f : Objective function, can be  Multimodal, with many local optima  Discontinuous  Stochastically perturbed  High-dimensional  Varying over time.  can be heterogenous.  Constraints can be defined over

29 29 PharminformaticsOtherECUPP of CAsApplicationsOverview Optimization Algorithms:  Direct optimization algorithm: Evolutionary Algorithms  First order optimization algorithm: e.g, gradient method  Second order optimization algorithm: e.g., Newton method

30 30 PharminformaticsOtherECUPP of CAsApplicationsOverview Applications: General Aspects Evaluation EA-OptimizerBusiness Process Model Simulation FunctionModel from Data ExperimentSubjectiveFunction(s)

31 31 PharminformaticsOtherECUPP of CAsApplicationsOverview  Dielectric filter design (40-dimensional). Quality improvement by factor 2.  Car safety optimization (10-30 dim.) 10% improvement.  Traffic control (elevators, planes, cars) 3-10% improvement.  Telecommunication  Metal stamping  Nuclear reactors,... Overview of Examples

32 32 PharminformaticsOtherECUPP of CAsApplicationsOverview Unconventional Programming ?  „Normal“ EA application:  EA as Programming Paradigm: EA Other Algorithm Task EA Task

33 33 PharminformaticsOtherECUPP of CAsApplicationsOverview UP of CAs (= Inverse Design of CAs)  1D CAs: Earlier work by Mitchell et al., Koza,...  Transition rule: Assigns each neighborhood configuration a new state.  One rule can be expressed by bits.  There are rules for a binary 1D CA Neighborhood (radius r = 2)

34 34 PharminformaticsOtherECUPP of CAsApplicationsOverview UP of CAs (rule encoding)  Assume r=1: Rule length is 8 bits  Corresponding neighborhoods

35 35 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs: 1D  Time evolution diagram:

36 36 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs: 1D  Majority problem:  Particle-based rules.  Fitness values: 0.76, 0.75, 0.76, 0.73

37 37 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs: 1D Don‘t care about initial state rules Block expanding rules Particle communication based rules

38 38 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs: 1D Majority Records  Gacs, Kurdyumov, Levin 1978 (hand-written):81.6%  Davis 1995 (hand-written):81.8%  Das 1995 (hand-written):82.178%  David, Forrest, Koza 1996 (GP):82.326%

39 39 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of Cas: 2D  Generalization to 2D (nD) CAs ?  Von Neumann vs. Moore neighborhood (r = 1)  Generalization to r > 1 possible (straightforward)  Search space size for a GA: vs

40 40 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs  Learning an AND rule.  Input boxes are defined.  Some evolution plots:

41 41 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs  Learning an XOR rule.  Input boxes are defined.  Some evolution plots:

42 42 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs  Learning the majority task.  84/169 in a), 85/169 in b).  Fitness value: 0.715

43 43 PharminformaticsOtherECUPP of CAsApplicationsOverview Inverse Design of CAs  Learning pattern compression tasks.

44 44 PharminformaticsOtherECUPP of CAsApplicationsOverview Current Drug Targets: GPCR

45 45 PharminformaticsOtherECUPP of CAsApplicationsOverview Goals (in Cooperation with LACDR):  CI Methods:  Automatic knowledge extraction from biological databases.  Automatic optimisation of structures – evolution strategies.  Exploration for  Drug Discovery,  De novo Drug Design. Initialisation Final (optimized)

46 46 PharminformaticsOtherECUPP of CAsApplicationsOverview Clustering GPCRs: New Ways  SOM based on sequence homology, family clusters marked.  Overlay with phylogenetic (sub-)tree. Class A amine dopamine trace amine peptide angiotensin chemokine CC other melanocortin viral (rhod)opsin vertebrate other unclassified Class B corticotropic releasing factor

47 47 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolutionary DNA-Computing (with IMB):  DNA-Molecule = Solution candidate !  Potential Advantage: > candidate solutions in parallel.  Biological operators:  Cutting, Splicing.  Ligating.  Amplification.  Mutation.  Current approaches very limited.  Our approach:  Suitable NP-complete problem.  Modern technology.  Scalability (n > 30).

48 48 PharminformaticsOtherECUPP of CAsApplicationsOverview Evolutionary DNA-Computing:  Example: Maximum Clique Problem  Problem Instance: Graph  Feasible Solution: V‘ such that  Objective Function: Size |V‘| of clique V‘  Optimal Solution:Clique V‘ that maximizes |V‘|.  Example: {2,3,6,7}: Maximum Clique ( ) {4,5,8}: Clique. ( )

49 49 PharminformaticsOtherECUPP of CAsApplicationsOverview DNA-Computing: Classical Approach 1: X := randomly generate DNA strands representing all candidates; 2: Remove the set Y of all non-cliques from X: C = X – Y; 3: Identify with smallest length (largest clique);  Based on filtering out the optimal solution.  Fails for large n (exponential growth).  Applied in the lab for n=6 (Ouyang et el., 1997); limited to n=36 (nanomole operations).

50 50 PharminformaticsOtherECUPP of CAsApplicationsOverview DNA-Computing: Evolutionary Approach 1: Generate an initial random population P, ; 2: while not terminate do 3:P := amplify and mutate P; 4:Remove the set Y of all non-cliques from P: P := P - Y; 5:P‘ := select shortest DNA strands from P; 6: od  Based on evolving an (near-) optimal solution.  Also applicable for large n.  Currently tested in the lab (Leiden, IMB).

51 51 PharminformaticsOtherECUPP of CAsApplicationsOverview Scalability Issues: Maximum Clique: Simulation Results (1, )-GA (best of 10) Problem n = Opt. brock200_ brock200_ brock200_ brock200_ hamming p_hat p_hat  Averages (not shown here) confirm trends.  Theory for large (NOT infinite) population sizes (other than c  ) ?

52 52 PharminformaticsOtherECUPP of CAsApplicationsOverview Questions ? Thank you very much for your time !


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