Download Lecture 7

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 and
comparing different values before the “real” run
Problems:
 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
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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)
Parameter control
Parameter control: setting values on-line, during the
actual 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:
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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)
Related Problems
Problems:
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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:
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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
How
Three major types of parameter control:
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deterministic: some rule modifies strategy parameter
without feedback from the search (based on some counter)
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adaptive: feedback rule based on some measure
monitoring search progress
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self-adaptative: parameter values evolve along with
solutions; encoded onto chromosomes they undergo
variation and selection
Global taxonomy
PARAMETER SETTING
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PARAMETER TUNING
PARAMETER CONTROL
(before the run)
(during the run)
DETERMINISTIC
ADAPTIVE
SELF-ADAPTIVE
(time dependent)
(feedback from search)
(coded in chromosomes)
Evidence informing the change
The parameter changes may be based on:
 time or nr. of evaluations (deterministic control)
 population statistics (adaptive control)
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–
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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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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
Deterministic Control
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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
Deterministic Control
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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
Adaptive Control
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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)
Adaptive Control
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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)
Adaptive Control
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1st example:

  min 1,

f best  f avg 

fbest

f
v
S pop  S pop
 S pop
1   
pm  pmmax 1  
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Adaptive Control
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2nd example
  1
f avg  fbest
f worst  fbest
f
v
S pop  S pop
 S pop
1  
pm  pmmax 1  
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Adaptive Control
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3rd example:
  f 
  min 1,

f
 avg 
f
v
S pop  S pop
 S pop
1  
pm  pmmax 1  
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Self-adaptive control
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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
 x1 , x2 ,...xn , ctr _ par 
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Self-adaptive control
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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
Evaluation / Summary
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Parameter control offers the possibility to use
appropriate values in various stages of the search
Adaptive and self-adaptive parameter control
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Robustness, insensivity of EA for variations assumed
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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)
If no. of parameters is increased by using (self)adaptation
For the “meta-parameters” introduced in methods