evolutionary computational inteliigence
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Evolutionary Computational Inteliigence. Lecture 6b: Towards Parameter Control. Ferrante Neri University of Jyväskylä. Motivation 1. An EA has many strategy parameters, e.g. mutation operator and mutation rate crossover operator and crossover rate - PowerPoint PPT PresentationTRANSCRIPT
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Evolutionary Computational Inteliigence
Lecture 6b: Towards Parameter Control
Ferrante Neri
University of Jyväskylä
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Motivation 1
An EA has many strategy parameters, e.g. mutation operator and mutation rate crossover operator and crossover rate selection mechanism and selective pressure (e.g.
tournament size) population size
Good parameter values facilitate good performance
Q1 How to find good parameter values ?
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Motivation 2
EA parameters are rigid (constant during a run)
BUT
an EA is a dynamic, adaptive process
THUS
optimal parameter values may vary during a run
Q2: How to vary parameter values?
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Parameter tuning
Parameter tuning: the traditional way of testing andcomparing different values before the “real” runProblems: users mistakes in settings can be sources of errors
or sub-optimal performance costs much time parameters interact: exhaustive search is not
practicable good values may become bad during the run
(e.g. Population size)
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Parameter Setting: Problems
A wrong parameter setting can lead to an undesirable algorithmic behavious since it can lead to stagnation or premature convergence
Too large population size, stagnation Too small population size, premature convergence In some “moments” of the evolution I would like to
have a large pop size (when I need to explore and prevent premature convergence); in other “moments” I would like to have a small one (when I need to exploit available genotypes)
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Parameter control
Parameter control: setting values on-line, during theactual run, I would like that the algorithm “decides” by
itself how to properly vary parameter setting over the run
Some popular options for pursuing this aim are: predetermined time-varying schedule p = p(t) using feedback from the search process encoding parameters in chromosomes and rely on natural
selection (similar to ES self-adaptation)
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Related Problems
Problems: finding optimal p is hard, finding optimal p(t) is harder still user-defined feedback mechanism, how to ”optimize”? when would natural selection work for strategy parameters?
Provisional answer: In agreement with the No Free Lunch Theorem, optimal control
strategy does not exist. Nevertheless, there are a plenty of interesting proposals that can be very performing in some problems. Some of these strategies are very problem oriented while some others are much more robust and thus applicable in a fairly wide spectrum of optimization problems
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How
Three major types of parameter control:
deterministic: some rule modifies strategy parameter without feedback from the search (based on some counter)
adaptive: feedback rule based on some measure monitoring search progress
self-adaptative: parameter values evolve along with solutions; encoded onto chromosomes they undergo variation and selection
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Global taxonomy
P A R A M E T E R T U N ING(b e fo re th e ru n)
D E T E R M IN IS T IC(t im e de p en de n t)
A D A P T IVE(fe e db a ck fro m sea rch)
S E L F -A D A P T IVE(co d ed in ch ro m o som e s)
P A R A M E T ER C O N T R O L(d u ring th e ru n)
P A R A M E T E R S E T T ING
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The parameter changes may be based on: time or nr. of evaluations (deterministic control) population statistics (adaptive control)
– progress made– population diversity– gene distribution, etc.
relative fitness of individuals creeated with given values (adaptive or self-adaptive control)
Evidence informing the change
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Evidence informing the change
Absolute evidence: predefined event triggers change, e.g. increase pm by 10% if population diversity falls under threshold x
Direction and magnitude of change is fixed Relative evidence: compare values through
solutions created with them, e.g. increase pm if top quality offspring came by high mut. Rates
Direction and magnitude of change is not fixed
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Deterministic Control
It is based on a priori designed scheme which takes into account the variable time
The general idea is that the algorithm at the beginning of the process has different needs compared to the end of it
The main disadvantage of such an approach is that the algorithmic designer is supposed to know beforehand when the changes in parameter setting must be carried out
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Deterministic Control
1st example: the population is enlarged at the end of the optimization process (after a prearranged number of generations)
2nd example (Arabas 1994): assign to each solution a lifetime parameter. Fitter individuals must survive longer. The population is thus variable over a certain number of generations
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Adaptive Control
It is online measured an index to perform the parameter setting of the subsequent generations
Fitness improvements: if the algorithmic response in terms of improvements are relevant, then a parameter is unchanged. When the parameter setting is inefficient then the parameter setting is modified (e.g. mutation rate increased when no improvements are found)
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Adaptive Control
Fitness diversity: in high diversity conditions the algorithm needs to exploit available genotypes, in low diversity conditions the algorithm needs to detect new genotypes and search directions
A measurement of the diversity can be employed for enlarging population size in lo diversity condition and shrinking in high diversity conditions (analogously for mutation rate)
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Adaptive Control
1st example:
min 1, best avg
best
f f
f
1f vpop pop popS S S
max 1m mp p
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Adaptive Control
2nd example
max
1
1
1
avg best
worst best
f vpop pop pop
m m
f f
f f
S S S
p p
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Adaptive Control
3rd example:
max
min 1,
1
1
f
avg
f vpop pop pop
m m
f
S S S
p p
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Self-adaptive control
It encodes the control parameter within the genotype of the solution and it is based on the idea that it should evolve with the population
1 2, ,... , _nx x x ctr par
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Self-adaptive control
If for example the control parameter measures the improvements due to the mutation, it can affect the mutation rate
Another popular option is to employ such a parameter for deciding the replication in the mating pool of the individuals (if the solution looks very promising) in order to have a tailored selection pressure
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Evaluation / Summary
Parameter control offers the possibility to use appropriate values in various stages of the search
Adaptive and self-adaptive parameter control – offer users “liberation” from parameter tuning– delegate parameter setting task to the evolutionary process– the latter implies a double task for an EA: problem solving +
self-calibrating (overhead)
Robustness, insensivity of EA for variations assumed– If no. of parameters is increased by using (self)adaptation– For the “meta-parameters” introduced in methods