Managing Director / CTO NuTech Solutions GmbH / Inc. Martin-Schmeißer-Weg 15 D – 44227 Dortmund [email protected]Tel.: +49 (0) 231 72 54 63-10 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 [email protected]Tel.: +31 (0) 71 527 7108 Fax: +31 (0) 71 527 6985
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Managing Director / CTO NuTech Solutions GmbH / Inc. Martin-Schmeißer-Weg 15 D – 44227 Dortmund [email protected] Tel.: +49 (0) 231 72 54 63-10.
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Managing Director / CTONuTech Solutions GmbH / Inc.
Pharminformatics OtherEC UPP 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.
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Pharminformatics OtherEC UPP 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.
1))(Pr( *lim
tPxt
)))(())1((( maxmax tPftPfE
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Pharminformatics OtherEC UPP 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, kmax = l – fa.
l
iiaaf
1
)(
jfljfl
ij
aifif
i
aa
a
a
k
k
a
a
a
a
qpj
flqp
i
fkp
kafamfkp
kpk
10
0)11(
)(
))())((Pr()(
)(max
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity Analysis:
Optimum mutation rate ?
Absorption times from transition matrix
in block form, using where
llafp
1
)1)((2
1*
QR
IP
0
Tj
iji ntE )(
1)()( QInN ij
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity Analysis:
p too large:
Exponential
p too small:
Almost constant.
Optimal: O(l ln l) .
p
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity Analysis:
(1,)-GA (kmin = -fa), (1+)-GA (kmin = 0) :
ikk
ikk
i
fl
kk
ppi
ka
''
1)1(
min,
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity Analysis:
(1,)-GA, (1+)-GA: (1,)-ES, (1+)-ES:
Conclusion: Unifying, search-space independent theory !?
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity Analysis:
(,)-GA (kmin = -fa), (+)-GA (kmin = 0) :
Theory
Experiment
)(1
1)(
min,
kpkafl
kk
jkk
ikk
jikk
ji
ppp
j
i
ikp
'1
'1
'
0
1
1
)1(
1)(
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity for Bimodal Function:
A generalized Trap Function (u = number of ones):
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Transition Probabilities for Bimodal Function:
Probability to mutate u1 ones into u2 ones:
Probability that one step of the algorithm changes parent (u1 -> u2):
)())()(()( 10
212120
21 uupuupuupuupi
iii
i
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Convergence Velocity for Bimodal Function:Convergence velocity:
)'())()'(()()()'(,'
uupufufuufufDu
(1+1), z2=100, current position varies (5,20,...).
(1+), z2=100, position 20, lambda varies (1,2,...).
(1+), z2=100, position 35, lambda varies (1,2,...).
Global max. Jump to local max.
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Pharminformatics OtherEC UPP 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.
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Pharminformatics OtherEC UPP 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
min)(,: xfMf
nMMMM ...21
)(, xfM
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Pharminformatics OtherEC UPP 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 )(xf
)(),( xfxf
)(),(),( 2 xfxfxf
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Applications: General Aspects
Evaluation
EA-Optimizer
Business Process Model
Simulation
215
1
i
iii
i scale
desiredcalculatedweightquality
Function Model from Data
Experiment SubjectiveFunction(s)
...)( yfi
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Pharminformatics OtherEC UPP 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
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Unconventional Programming ?
„Normal“ EA application:
EA as Programming Paradigm:
EAEA Other AlgorithmOther Algorithm TaskTask
EAEA TaskTask
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Pharminformatics OtherEC UPP 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.
1 0 0 0 0 1 1 0 1 0 1 0 1 0 0
Neighborhood(radius r = 2)
1,01,0: 12 r
122 r
1222r
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
UP of CAs (rule encoding)
Assume r=1: Rule length is 8 bits
Corresponding neighborhoods
1 0 0 0 0 1 1 0
000 001 010 011 100 101 110 111
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs: 1D
Time evolution diagram:
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs: 1D
Majority problem:
Particle-based rules.
Fitness values:
0.76, 0.75, 0.76, 0.73
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs: 1D
Don‘t care about initial state rules
Block expanding rules
Particle communication based rules
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Pharminformatics OtherEC UPP 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%
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Pharminformatics OtherEC UPP 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.
10
0
1
1 10
0
1
1
0
0
1
1
52 92
522922
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs
Learning an AND rule.
Input boxes are defined.
Some evolution plots:
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs
Learning an XOR rule.
Input boxes are defined.
Some evolution plots:
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs
Learning the majority task.
84/169 in a), 85/169 in b).
Fitness value: 0.715
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Inverse Design of CAs
Learning pattern compression tasks.
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Pharminformatics OtherEC UPP of CAsApplicationsOverview
Current Drug Targets:
2%2%
11%
5% 7%
45%
28%
receptors enzymeshormones & factors DNAnuclear receptors ion channelsunknown
GPCR
http://www.gpcr.org/
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Pharminformatics OtherEC UPP 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)
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Pharminformatics OtherEC UPP 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 unclassifiedClass B corticotropic releasing factor
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Pharminformatics OtherEC UPP of CAsApplicationsOverview