understanding the semantics of the genetic algorithm in dynamic environments abir alharbi william...
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Understanding the Semantics of the Genetic Algorithm in Dynamic Environments
Abir Alharbi William Rand Rick [email protected] [email protected] [email protected] Saud University Northwestern University University of MichiganMathematics Dept. Northwestern Institute on Center for the Study of
Complex Systems Complex Systems
A Case Study Using the Shaky Ladder Hyperplane-Defined Functions
Semantic versus Syntactic Understanding
Language• “Put the box on the table by
the window in the kitchen.”• Syntax assessment:
• Label prepositions, nouns, verbs, articles
• Syntactically Okay• But the syntactic assessment
misses the point, there are three different semantic interpretations
• With a semantic labeling we can better appreciate the informational content
Genetic Algorithms• “1100101”• Syntax assessment:
• Some measure of diversity • Fitness score
• But the syntactic assessment misses the point, there are many different semantic interpretations
• If we can label the building blocks that are present in the genome we can better appreciate the informational content
Semantic LabelingGenetic Algorithms• “1100101”
Language• “Put the box on the table by the
window in the kitchen.”
b1
b2 b
3b
4
b12
b23
b123
b1234
Building Block Setb
1 = 11****1 = 1
b2 = **00*** = 1
b3 = ****1** = 1
b4 = *****0* = 1
b12
= 1100**1 = 1
b23
= **001** = 1
b123
= 11001*1 = 1
b1234
= 1100101 = 1
Overview
• Previous Mysteries of the sl-hdfs• The Experiment• Average Schemata Analysis• Diversity of Schemata Analysis• Conclusion and Future Work
Previous Mysteries of the sl-hdfs
• In all variants (Cliffs, Smooth, Weight) the GA performs at least as well as, and in most cases does better, in dynamic versions of the sl-hdfs than it does in static versions• Shouldn’t the GA perform better in static environments since
the environment is not changing?
• In all cases (Static, Dynamic) the GA performs better in the Cliffs variant than the other variants• The Cliffs variant features rough transitions shouldn’t this
prevent the GA from performing optimally?
• Hypothesis: In both static environments and smoothly transitioning environments the GA prematurely converges on local optima.
The Experiment
Parameter Cliffs Variant Smooth Variant Weight Variant
Population SizeMutation RateCrossover RateGenerationsString LengthSelection TypeNumber of Elem. SchemataElementary Schemata OrderElementary Schemata Length 50Mean, Var. of Int. Schem. Wt. 3, 1Int. Constr. Method Unrestr., Random Restr., Random Restr., Neighbortdelta
wdelta 1Number of Runs
500Tournament, size 3
508
10000.0010.7
1800
Not Specified 3, 0
100
300
Average Schemata Analysis
• Four different levels of schemata• Potholes• Elementary• Intermediate• Highest Level
• Count the number of schemata of each level that are present in an individual and divide by the total number of schemata possible at that level
• Average that fraction across all individuals in the population• Average that average across all runs for each generation
Cliffs Results
• As hypothesized the shakes in the ladder prevent the GA operating in the Cliffs variant from locking on to a particular set of intermediate schemata
• Intermediate schemata decrease immediately after every shake since those schemata that were rewarded are not any more
• In some runs highest level schema found as early as just before generation 800
Smooth Variant Results
• Decrease due to shakes not as great, since intermediate schemata do not change as much
• Still within the same basin of attraction• No highest level schema until generation 1500 or so
Weight Variant Results
• Shakes appear to have no effect on the accumulation of any level of schemata
• The dynamics of the weight variant are not apparent to the GA
• Despite rapid performance increases early on the GA operating in the Weight variant environment underperforms the other two variants
Comparison of Results
• Confirms our hypothesis• In dynamic environments the GA is perturbed off local optima
and begins to accumulate different intermediate schemata• In smooth environments the GA behaves as if it were operating
in a static environment and prematurely converges
Diversity of Schemata
• Remap every string sj in the population into a new string s’j that contains a 1 at location i if sj contains schema i and a 0 if it does not
• Compute the average pairwise hamming distance between s’j and every other s’ in the population, normalizing by string length
• Average this value across all individuals in the population• Average this average across all runs for every generation
Diversity Results
• Cliffs Variant• Two phases: Exploration then Convergence• Exploration causes sharp changes in the diversity of schemata
because the individuals that are currently being rewarded have different schemata than those that were previously rewarded
• Smooth Variant exhibits a similar but weaker effect• Weight Variant
• Never affected by changes in the landscape• Lower diversity in schemata space overall indicating the GA
populations never contain within them many different schemata at the same time
Overall Conclusions
• We have provided additional confirmation for our hypothesis that dynamic environments and abrupt changes stop the GA from prematurely converging
• We can define local optima as places where it is difficult for the GA to acquire new schemata, given this definition semantic examinations like what we have done are some of the best observations for understanding the behavior of the GA
Future Work
• New Mysteries• Why does the Cliffs variant feature non-monotonic acquisition
of the potholes and the other variants do not?• Why do the spikes in the diversity graph have the shape they
do? Why do they increase in size until the optimal is found?
• “Tracing” of schemata ala radioactive tagging of genes (Paper in progress)
• New variants of the sl-hdfs that combine short building blocks with rough transitions (GECCO 2007)
Acknowledgements
• U of M’s Center for the Study of Complex Systems and Carl Simon for financial support for Rick Riolo and computational resources
• Northwestern Institute on Complex Systems for support of William Rand
Any Questions?
UnrestrictedConstruction
ElementarySchema
ElementarySchema
PotholePothole
ElementarySchema
ElementarySchema
IntermediateSchema
Highest LevelSchema
IntermediateSchema
IntermediateSchema
IntermediateSchema
Pothole
Pothole
Restricted Construction
Pothole Pothole Pothole Pothole Pothole
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
IntermediateSchema
Highest LevelSchema
ElementarySchema
ElementarySchema
RandomConstruction
ElementarySchema10******
ElementarySchema**00****
ElementarySchema****11**
ElementarySchema******10
IntermediateSchema10**11**
IntermediateSchema**00**10
Neighbor Construction
ElementarySchema10******
ElementarySchema**00****
ElementarySchema****11**
ElementarySchema******10
IntermediateSchema1000****
IntermediateSchema****1110
Shaking byForm
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema(w = 3)
IntermediateSchema(w = 3)
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema(w = 3)
IntermediateSchema(w = 3)
Shaking byWeight
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
(w = 3.12)
IntermediateSchema
(w = 2.77)
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
(w = 2.12)
IntermediateSchema(w = 2.5)
Three Variants
Variant Construction MethodElementary
Schemata LengthShaking Method
Cliffs Unrestricted, Random Undefined Form
Smooth Restricted, Random Undefined Form
Weight Restricted, Neighbor 50 Weight
Shaking The LadderCliffs VariantUndefined Length
ElementarySchema
PotholePothole
Pothole Pothole
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
Highest LevelSchema Delete
IntermediateSchemata
Generate NewIntermediateSchemata
IntermediateSchema
IntermediateSchema
IntermediateSchema
Shaking The Ladder
Pothole Pothole Pothole Pothole Pothole
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
IntermediateSchema
Highest LevelSchema Delete
IntermediateSchemata
Generate NewIntermediateSchemata
Smooth VariantUndefined Length
Shaking The Ladder
Pothole Pothole Pothole Pothole Pothole
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
ElementarySchema
IntermediateSchema
IntermediateSchema
Highest LevelSchema Delete
IntermediateWeights
Generate NewIntermediate Weights
Weight VariantShort Length
Cliffs Variant Performance Results
Smooth Variant Performance Results
Weight Variant Performance Results