semantic building blocks in genetic programming
DESCRIPTION
These are the slides from the talk at EuroGP (Int\'l Conference on Genetic Programming) 2008 in Naples, Italy, by Nic McPhee and Tyler Hutchison. This paper (based on part on this presentation) was voted best paper by the conference attendees. The paper\'s abstract: \"In this paper we present a new mechanism for studying the impact of subtree crossover in terms of semantic building blocks. This approach allows us to completely and compactly describe the semantic action of crossover, and provide insight into what does (or doesn’t) make crossover effective. Our results make it clear that a very high proportion of crossover events (typically over 75% in our experiments) are guaranteed to perform no immediately useful search in the semantic space. Our findings also indicate a strong correlation between lack of progress and high proportions of fixed contexts. These results then suggest several new, theoretically grounded, research areas.\"TRANSCRIPT
Semantic building blocks in genetic programming
Nic McPhee and Tyler Hutchison
Work done with Brian Ohs
Division of Science and MathematicsUniversity of Minnesota, Morris
Morris, Minnesota, USA
Nic is Currently on sabbatical,University of Essex, UK
26 March 2008EuroGP, Naples
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 1 / 25
Overview The big picture
The big picture
Subtree XO is old and widely usedBut why does it work?!?We present new semantic analysis of XOSemantic building blocks
Over 75% of XO events guaranteed to be useless!Ideas for new operators and representations
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 2 / 25
Overview Outline
Outline
1 The semantics of crossover
2 Empirical results
3 Extensions and applications
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 3 / 25
Semantics of XO
Outline
1 The semantics of crossoverCrossover, subtrees, and contextsSubtree semanticsContext semanticsSem of XO = (Sem of subtrees) + (Sem of contexts)
2 Empirical results
3 Extensions and applications
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 4 / 25
Semantics of XO XO, subtrees, & contexts
Crossover, subtrees, and contexts
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 5 / 25
Semantics of XO XO, subtrees, & contexts
Crossover, subtrees, and contexts
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 5 / 25
Semantics of XO XO, subtrees, & contexts
Crossover, subtrees, and contexts
Syntactically, subtree crossover joins a context and a subtreeSemantics of crossover
= (Semantics of subtree) + (Semantics of context)
We present tools for compact, complete description of semanticsfor boolean problems
Allows us to completely describeThe semantic building blocks available in the populationThe semantic possibilities available via crossover
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 6 / 25
Semantics of XO Subtree semantics
Subtree semantics
Idea for this from [Poli and Page, 2000].
X Y0011 0101
NOR
AND
1000
X
Represent semantics of (sub)treesby listing values on all of its inputs.
X Y nor(X, Y)0 0 10 1 01 0 01 1 0
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 7 / 25
Semantics of XO Context semantics
Context semantics: Fixed and flexible
Context semantics are more complex:
Some contexts are fixed:and(0, X) = 0or(1, X) = 1
0
AND 0
#
Other contexts are flexible:and(1, X) = Xnor(0, X) = ¬ X
0
NOR _
#
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 8 / 25
Semantics of XO Context semantics
Context semantics: Dependencies
gArg
semantics
Parentsemantics
#x
Context semantics depend on:The operator gThe subtree semantics ofother argument(s)The context semantics ofparent node
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 9 / 25
Semantics of XO Context semantics
Context semantics: A simple example
X
Y
0011
0101
NOR
AND
00++
#
00-0
Semantics of this context is 00-0.
No matter what we insert for ‘#’,value of the entire tree will be falsefor 3 of the 4 possible inputs.
Value of whole tree will be negatedvalue of subtree when X is true andY is false.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 10 / 25
Semantics of XO Context semantics
Sem of XO = (Sem of subtrees) + (Sem of contexts)
Semantics of a subtree XO event is “sum” of semantics of subtree andsemantics of context.
Context semantics 00-0Subtree semantics 1001XO semantics 0010
All but the third position are fixed by the contextThird position is negation of subtree value in third position
True for any context and subtree with those semantics.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 11 / 25
Semantics of XO Context semantics
All semantics: An ugly (but realistic) example
X Y0011 0101
0111
X Y0011 0101
1000
+000
000 000
0+++
+000 +000
AND
OR NOR
Can enumerate all subtreeand context semantics:
Across entirepopulationFor every generation
Allows us to analyze what’ssemantically possible viasubtree crossover.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 12 / 25
Semantics of XO Sem of XO = (Sem of subtrees) + (Sem of contexts)
Summary so far
Semantics of crossover=
(Semantics of subtrees) + (Semantics of contexts)
If we can enumerate semantics of components, then we know what’spossible (or impossible) with crossover.
Questions? (This semantics stuff is crucial - please ask!)
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 13 / 25
Empirical results
Outline
1 The semantics of crossover
2 Empirical resultsCollecting semantic dataProblems, parameters, and success ratesProportion of compatible contextsProportion of fixed contexts
3 Extensions and applications
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 14 / 25
Empirical results Collecting semantic data
We can collect new kinds of data
Proportion of fixed contextsWhat proportion of XO events are guaranteed to have nouseful effect?
Proportion of compatible contextsHow many contexts could be part of construction thesolution if mated with the right subtree?
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 15 / 25
Empirical results Problems, parameters, and success rates
Problems and parameters
Function set: Binary AND, OR, NAND, and NOR
Problem Success rate2-bit even parity 100%3-bit even parity 100%4-bit even parity 47%6-bit even parity 0%6-bit multiplexer 100%
3 easy problems, one very hard, and one in between.We weren’t trying to solve problems, so no tuning, etc.We only use crossover (no mutation), and there’s no bias awayfrom leaves.Other details in the paper.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 16 / 25
Empirical results Proportion of compatible contexts
0 9 18 27 36 45 54 63 72 81 90 99 111 123 135 147 159 171 183 195 207 219 231 243
1e−
051e
−03
1e−
01Proportion of compatible contexts
Generation
Pro
port
ion
of c
ompt
able
con
text
s
0 9 18 27 36 45 54 63 72 81 90 99 111 123 135 147 159 171 183 195 207 219 231 243
1e−
051e
−03
1e−
01
0 9 18 27 36 45 54 63 72 81 90 99 111 123 135 147 159 171 183 195 207 219 231 243
1e−
051e
−03
1e−
01
0 9 18 27 36 45 54 63 72 81 90 99 111 123 135 147 159 171 183 195 207 219 231 243
1e−
051e
−03
1e−
01
0 9 18 27 36 45 54 63 72 81 90 99 111 123 135 147 159 171 183 195 207 219 231 243
1e−
051e
−03
1e−
01
2−EP
3−EP
6−MUX
4−EP
6−EP
2−EP
3−EP
6−MUX
4−EP
6−EP
2−EP
3−EP
6−MUX
4−EP
6−EP
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 17 / 25
Empirical results Proportion of fixed contexts
0 100 200 300 400 500
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% fixed contexts over time
Generation
% fi
xed
cont
exts
2−EP3−EP6−MUX4−Flat4−EP6−EP
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 18 / 25
Extensions and applications
Outline
1 The semantics of crossover
2 Empirical results
3 Extensions and applicationsNon-boolean domainsOther representations and operatorsDesigning new approaches
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 19 / 25
Extensions and applications Non-boolean domains
Non-boolean domains
As presented, this is limited to boolean domains.It also scales badly with # of variables.Proportion of fixed contexts can be approximated, however.E.g., insert 2 (or more) constant values in ‘#’ and see if value oftree changes.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 20 / 25
Extensions and applications Other representations and operators
Other representations and operators
What’s special or different about things like Automatically DefinedFunctions (ADFs) and Grammatical Evolution (GE)?
They certainly have different crossover semantics.
Can this approach help us better understand those differences?
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 21 / 25
Extensions and applications Designing new approaches
Designing new approaches
Bummer having so many fixed contexts. Could consider this asco-evolutionary system between population of contexts and populationof subtrees. The problem then is disengagement: The (fixed) contextsalways “beat” the subtrees [de Jong and Pollack, 2004].
Can we design new operators that combat this? We tried preventingXO at fixed contexts. Great at reducing bloat, but not good at solving.
Maybe design a co-evolutionary Estimation of Distribution Algorithm(EDA) based on these semantics?
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 22 / 25
Conclusions
Conclusions
Semantics of crossover= (Semantics of subtrees) + (Semantics of contexts)
We can enumerate subtree and context semantics to betterunderstand action of subtree XOLots of fixed contexts (roughly 75%)So most XO operations are “no-ops”Can perhaps use this to understand other systems and designnew ones
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 23 / 25
Conclusions
Thanks!
Thanks for your time and attention!
Contact:[email protected]://www.morris.umn.edu/~mcphee/
[email protected]://tylersaurus.com/
Questions?
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 24 / 25
References
References
R. Poli and J. Page.Solving high-order boolean parity problems with smooth uniformcrossover, sub- machine code GP and demesGPEM, 1(1/2):37-56, 2000.
E.D. de Jong and J.B. Pollack.Ideal evaluation from coevolution.Evolutionary Computation, 12(2):159-192, 2004.
McPhee and Hutchison (U of Minn, Morris) Semantic BBs in GP 26 Mar 2008, EuroGP, Naples 25 / 25