Something about Building Block Hypothesis

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23 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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Something about Building Block
Hypothesis

Ying
-
Shiuan You

Taiwan Evolutionary Intelligence LAB

2009/10/31

Adaptive Capacity


Some population based search algorithm called
“adaptive.”


The avg. fitness of the populations “grows” as generation.



This feature of GA is called “adaptive capacity.”


Building Block Hypothesis is currently dominant
explanation.

2

The Schema Theorem


If
m
(
H
,
t
+1) >
m
(
H
,
t
)
, the schema
H

grows.


Lower
-
bound estimation of schema growth.


Consider only destructive forces.



Minimal, sequential, superior (ms
2
) schemata grow.


Identifies building blocks of a good solution.


Holland (1975),
Adaptation in Natural and Artificial Systems
, The MIT Press

Building Block Hypothesis


Goldberg’s words, “… we construct better and better
strings from the best partial solutions of past
samplings”(Goldberg, 1989, p. 41)



“…a genetic algorithm seek near optimal
performance through the juxtaposition of short, low
-
order, high
-
performance schemas”(Goldberg, 1989)

4

Goldberg, David E (1989),
Genetic Algorithms in Search, Optimization and Machine
Learning,

Kluwer Academic Publishers, Boston, MA.

Two Landscape Features of BBH


The presence of short, low
-
order, highly fit schemas,
i.e. building block.



The presence of “stepping stone” solutions which
combine BBs to create even higher fitness schemas.

5

Stephanie Forrest & Melanie Mitchell (1993),
Relative building
-
block fitness and
building
-
block hypothesis
.

Nearly Decomposable Problems


We do not want to solve every problem.



OneMax



NIAH



Too simple: simple heuristic, hill climbing


Too difficult: enumeration


Nearly decomposable problems

Tain
-
Li Yu’s slide on 2006 GA course

Fully Deception


Low
-
order estimates
mislead GA.



x* =
111
: f
111

> f
i
, i ≠
111
.



Require complementary
schemata better than
competitors.

Tain
-
Li Yu’s slide on 2006 GA course

Trap Function


Ackley, 1985.


Local searcher would go to the wrong optima.



In general:

to be deceptive.

Goldberg & Deb (1993). Analyzing Deception in Trap Functions.

Tain
-
Li Yu’s slide on 2006 GA course

Theories Develop on m
-
k decomposable


Convergence Time (Thierens & Goldberg, 1994)


Population size


BB supply (Goldberg
et al.
2001)


Decision making (Goldberg
et al.

1992)


Decision making + supply (Harik
et al
. 1997)


Model building (Yu
et al
. 2007)

9

Reference:

Thierens & Goldberg (1994),
Convergence models of genetic algorithm selection schemes
.

Goldberg
et al
(2001),
On the supply of building blocks
.

Goldberg
et al
(1992),
Genetic algorithms, noise, and the sizing of populations
.

Harik
et al
(1997),
The gambler's ruin problem, genetic algorithms, and the sizing of populations
.

Yu
et al
(2007),
Population Sizing for entropy
-
based model building in genetic algorithms
.

GA Design Theory


Goldberg, 1992.


Know what GA processes: Building blocks (BBs).


Ensure BB growth.


Know BB challengers.


Ensure BB supply.


Ensure BB speed.


Ensure good BB decisions.


Ensure good BB mixing (exchange).



Goldberg (2002),
Design of Innovation
.

Skepticism of the BBH


Not realistic



BB exist?


In real problem, it’s more likely existing BBs.


No overlap BB?


It ‘s more likely exist! But too hard to analysis and design at
this time.


How about real
-
value?


Too hard to develop theories on real number.

11

Skepticism of the BBH (cont’d)


Weak theoretical foundations. (Wright et al. 2003)



“The various claims about Gas that are traditionally
made under the name of the building block
hypothesis have, to date , no basis in theory, in some
cases, are simply incoherent.”

12

Reference: Wright et al. (2003),
Implicit Parallelism
.

Skepticism of the BBH (cont’d)


Experiments side. (Forrest and Mitchell, 1993)



“While the disruptive effects that we observed
(hitchhiking, premature convergence, etc.) … , there
is as yet no theorem associating them with the
building
-
block structure of a given problem.”

13

Reference: Forrest & Mitchell (1993),
Relative building
-
block fitness and building
-
block
hypothesis
.

Hitchhiking


Once an instance of a high
-
fitness schema is
discovered, the “unfit” material, especially that just
next to the fit parts, spread along with the fit
material. Slows discovery of good schemas in those
positions.



Sampling of the different regions is not independent.

14

Hitchhiking (cont’d)

15

Skepticism of the BBH (cont’d)


Strong Assumption. (Burjorjee, 2009)



Two strong assumption:


Abundant Basic Building Blocks


Heirarchical Synergism



Too strong to accept this hypothesis.

16

Reference: Burjorjee (2009),
The Fundamental Problem with the Building Block Hypothesis
.