Controlled Observations of the Genetic Algorithm in a Changing Environment

1
Controlled Observations of the Genetic Algorithm
in a Changing Environment
Case Studies Using the Shaky Ladder Hyperplane
Defined Functions

• William Rand
• Computer Science and Engineering
• Center for the Study of Complex Systems
• wrand_at_umich.edu

2
Overview

• Introduction
• Motivation, GA, Dynamic Environments, Framework,
  Measurements
• Shaky Ladder Hyperplane-Defined Functions
• Description and Analysis
• Varying the Time between Changes
• Performance, Satisficing and Diversity Results
• The Effect of Crossover
• Experiments with Self-Adaptation
• Future Work and Conclusions

3
Motivation

• Despite years of great research examining the
  GA, more work still needs to be done, especially
  within the realm of dynamic environments
• Approach
• Applications GA works in many different
  environments, particular results
• Theory Places many limitations on results
• Middle Ground Examine a realistic GA on a set of
  constructed test functions, Systematic Controlled
  Observation
• Benefits
• Make recommendations to application practitioners
• Provide guidance for theoretical work

4
What is a GA?
Evaluative Mechanism
Population of Solutions
Inheritance with Variation
John Holland, Adaptation in Natural and
Artificial Systems, 1975
5
Dynamic Environments

• GAs are a restricted model of evolution
• Evolution is an inherently dynamic system, yet
  researchers traditionally apply GAs to static
  problems
• If building blocks exist within a problem
  framework, the GA can recombine those solutions
  to solve problems that change in time
• Application examples include Job scheduling,
  dynamic routing, and autonomous agent control
• What if we want to understand how the GA works in
  these environments?
• Applications are too complicated to comprehend
  all of the interactions, we need a test suite for
  systematic, controlled observation

6
Measures of Interest

• Robustness
• How indicative future performance is the current
  performance?
• Best Robustness Fitness of current best divided
  by fitness of previous generations best
  individual
• Average Robustness Current population fitness
  avg. divided by the avg. for the previous
  generation
• Diversity
• Measure of the variation of the genomes in the
  population
• Best Diversity Avg. Hamming distance between
  genomes of best individuals across runs
• Average Diversity Avg. across runs of avg.
  Hamming distance of whole population

• Performance
• How well the system solves an objective function
• Best Performance - Avg. across runs of the
  fitness of the best ind.
• Avg. Performance Avg. across runs of the
  fitness of the avg. ind.
• Satisficability
• Ability of the system to achieve a predetermined
  criteria
• Best Satisficability - Fraction of runs where the
  best solution exceeds a threshold
• Average Satisficability Avg. across runs of
  fraction of population to exceed threshold

7
Hyperplane Defined Functions

• HDFs were designed by John Holland, to model
  the way the individuals in a GA search
• In HDFs building blocks are described formally by
  schemata
• If search space is binary strings then schemata
  are trinary strings (0, 1, wildcard)
• Building blocks are schemata with a positive
  fitness contribution
• Combine building blocks to create higher level
  building blocks and reward the individual more
  for finding them
• Potholes are schemata with a negative fitness
  contribution

John Holland, Cohort Genetic Algorithms,
Building Blocks, and Hyperplane-Defined
Functions, 2000
8
Shaky Ladder HDFs

• Shaky ladder HDFs place 3 restrictions on HDFs

• Elementary schemata do not conflict with each
  other
• Potholes have limited costs
• Final schema is union of elementary schemata
• Gaurantees any string which matches the final
  schema is an optimally valued string
• Shaking the ladder involves changing intermediate
  schemata

9
Three Variants

• Cliffs Variant - All three groups of the fixed
  schemata are used to create the intermediate
  schemata
• Smooth Variant - Only elementary schemata are
  used to create intermediate schemata
• Weight Variant - The weights of the ladder are
  shaken instead of the form

10
Analysis of the Sl-hdfs

• The Sl-hdfs were devised to resemble an
  environment where there are regularities and a
  fixed optima
• There are two ways to show that they have these
  properties
• Match the micro-level componentry
• Carry out macro-analysis
• Standard technique is the autocorrelation of a
  random walk

11
Mutation Landscape
12
Crossover Landscape
13
Time Between Shakes Experiment

• Vary t? which is the time between shakes
• See what effect this has on the performance of
  the best individual in the current generation

Population Size 1000
Crossover Rate 0.7
Mutation Rate 0.001
Generations 1800
Selection Type Tournament, Size 3
of Elementary Schemata 50
String Length 500
of Runs 30
14
Cliffs Variant
15
Smooth Variant
16
Weight Variant
17
Results of Experiment

• t? 1801, 900 Improves performance,?Premature
  Convergence prevents finding optimal strings
• t? 1 Outperforms static environment,
  intermediate schemata provide little guidance, 19
  runs find an optimal string
• t? 25, 100 Best performance, tracks and
  adapts to changes in environment, intermediate
  schemata provide guidance but not a dead end, 30
  runs find optimal strings
• Smoother variants perform better early on, but
  then the lack of selection pressure prevents them
  from finding the global optimum

18
Comparison of Threshold Satisficability
19
Cliffs Variant Diversity Results
20
Smooth Variant Diversity Results
21
Weight Variant Diversity Results
22
Discussion of Diversity Results

• Initially thought diversity would decrease as
  time went on and the system converged, and that
  shakes would increase diversity as the GA
  explored the new solution space
• Neutral mutations allow founders to diverge
• A ladder shake decreases diversity because it
  eliminates competitors to the new best
  subpopulations
• In the Smooth and Weight variants Diversity
  increases even more due to lack of selection
  pressure
• In the Weight variant you can see Diversity
  leveling off as the population stabilizes around
  fit, but not optimal individuals

23
Crossover Experiment

• The Sl-hdf are supposed to explore the use of the
  GA in dynamic environments
• The GAs most important operator is crossover
• Therefore, if we turn crossover off the GA should
  not be able to work as well in the sl-hdf
  environments
• That is exactly what happens
• Moreover crossover has a greater effect on the GA
  operating in the Weight variant due to the short
  schemata

24
Cliffs Variant Crossover Results
25
Smooth Variant Crossover Results
26
Weight Variant Crossover Results
27
Self-Adaptation

• By controlling mutation we can control the
  balance between exploration and exploitation
  which is especially useful in a dynamic
  environment
• Many techniques have been suggested
  hypermutation, variable local search, and random
  immigrants
• Bäck proposed the use of self-adaptation in
  evolutionary strategies and later in GAs (92)
• Self-adaptation encodes a mutation rate within
  the genome
• The mutation rate becomes an additional search
  problem for the GA to solve

28
The Experiments
Experiment Type nBits Min Max Seeded? Cross?
1 Fixed 0.001 No Yes
2 Fixed 0.0005 No Yes
3 Fixed 0.0001 No Yes
4 Self, 10 0.0, 1.0 No Yes
5 Self, 15 0.0001, 0.1 No Yes
6 Self, 15 0.0001, 0.1 Yes Yes
7 Self, 15 0.0001, 0.1 Yes No
29
Performance Results (1/2)Generation 1800 Best
Individual Over 30 Runs
  1   25   100
Experiment Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev.
Fixed 0.001 .9538 .0680 1.00 0.00 1.00 0.00
Fixed 0.0005 .6320 .1534 .7473 .1155 .7892 .1230
Fixed 0.0001 .2340 .0373 .2242 .0439 .2548 .0573
Self 0-1 .1618 .0426 .1696 .0445 .1670 .0524
Self 0.0001-0.01 .3515 .0729 .3921 .1282 .3993 .0964
Seeded .3412 .0506 .3690 .1018 .3974 .0949
No Crossover .2791 .0596 .5648 .1506 .4242 .1526
30
Performance Results (2/2)Generation 1800 Best
Individual Over 30 Runs
  900   1801
Experiment Avg. Std. Dev Avg. Std. Dev
Fixed 0.001 .7424 .1144 .8428 .0745
Fixed 0.0005 .5796 .1023 .6852 .1041
Fixed 0.0001 .2435 .0530 .2710 .0571
Self 0-1 .1675 .0542 .1693 .0585
Self 0.0001-0.01 .3710 .0828 .4375 .0969
Seeded .3551 .1045 .4159 .1105
No Crossover .3242 .1037 .3782 .1011
31
Mutation Rates
32
Discussion of Self-Adaptation Results

• Self-adaptation fails to improve the balance
  between exploration and exploitation
• Tragedy of the Commons - it is to the benefit
  of each individual to have a low mutation rate,
  even though a higher average mutation rate is
  beneficial to the whole population
• Seeding with known good material does not
  always increase performance
• Some level of mutation is always good

33
Future Work

• Further Exploration of sl-hdf parameter space
• Schema Analysis
• Analysis of local optima
• What levels are attained when?
• Analysis of the sl-hdf landscape
• Population based landscape analysis
• Other dynamic analysis
• Examination of
• Other mechanisms to augment the GA
• Meta-GAs, hypermutation, multiploidy
• Co-evolution of sl-hdf's with solutions
• Combining GAs with ABMs to model ecosystems

34
Applications

• Other Areas of Evolutionary Computation
• Coevolution
• Other Evolutionary Algorithms
• Computational Economics
• Market Behavior and Failures
• Generalists vs. Specialists
• Autonomous Agents
• Software agents, Robotics
• Evolutionary Biology
• Phenotypic Plasticity, Baldwinian Learning

35
Conclusions

• Systematic, Controlled Observation allows us to
  gather regularities about an artificial system
  that is useful to both practitioners and
  theoreticians
• The sl-hdf's provide and the three variants
  presented are a useful platform for exploring the
  GA in dynamic environments
• Standard autocorrelation fails to completely
  describe some landscapes and some dynamism
• Intermediate rates of change provide a better
  environment at times by preventing premature
  convergence
• Self-adaptation is not always successful,
  sometimes it is better to explicitly control GA
  parameters

36
Acknowledgements

• Jason Atkins
• Dmitri Dolgov
• Anna Osepayshvili
• Jeff Cox
• Dave Orton
• Bil Lusa
• Dan Reeves
• Jane Coggshall
• Brian Magerko
• Bryan Pardo
• Stefan Nikles
• Eric Schlegel
• TJ Harpster
• Kristin Chiboucas
• Cibele Newman
• Julia Clay
• Bill Merrill
• Eric Larson

• John Holland
• Rick Riolo
• Scott Page, John Laird, and Martha Pollack
• Jürgen Branke
• CSCS
• Carl Simon
• Howard Oishi
• Mita Gibson
• Cosma Shalizi
• Mike Charter the admins
• Lori Coleman
• Sluce Research Group
• Dan Brown, Moira Zellner, Derek Robinson
• My Parents and Family

• RR-Group
• Robert Lindsay
• Ted Belding
• Chien-Feng Huang
• Lee Ann Fu
• Boris Mitavskiy
• Tom Bersano
• Lee Newman
• SFI, CSSS, GWE
• Floortje Alkemade
• Lazlo Guylas
• Andreas Pape
• Kirsten Copren
• Nic Geard
• Igor Nikolic
• Ed Venit
• Santiago Jaramillo
• Toby Elmhirst
• Amy Perfors

Friends Brooke Haueisen Kat Riddle Tami
Ursem Kevin Fan Jay Blome Chad Brick Ben
Larson Mike Curtis Beckie Curtis Mike Geiger
Brenda Geiger William Murphy Katy Luchini Dirk
Colbry

• CWI
• Han La Poutré
• Tomas Klos
• EECS
• William Birmingham
• Greg Wakefield
• CSEG

And Many, Many More
37
Any Questions?
38
My Contributions

• Shaky Ladder Hyperplane Defined Functions
• Three Variants
• Description of Parameter Space to be explored
• Work on describing Systematic, Controlled
  Observation Framework
• Initial experiments on sl-hdf
• Crossover Results on variants of the hdf
• Autocorrelation analysis of the hdf and sl-hdf
• Exploration of Self-Adaptation in GAs when it
  fails
• Suite of Metrics to better understand GAs in
  Dynamic Environments
• Proposals of how to extend the results to
  Coevolution

39
Motivation

• Despite decades of great research, there is more
  work that needs to be done in understanding the
  GA
• Performance metrics are not enough to explain the
  behavior of the GA, but that is what is reported
  in most experiments
• What other measures could be used to describe the
  run of a GA in order to gain a fuller
  understanding of how the GA behaves?
• The goal is not to understand the landscape or to
  classify the performance of particular variations
  of the GA
• Rather the goal is to develop a suite of measures
  that help to understand the GA via systematic,
  controlled observations

40
Exploration vs. Exploitation

• A classic problem in optimization is how to
  maintain the balance
  between exploration
  and exploitation
• k-armed bandit problem
• If we are allowed a limited number of trials at a
  k-armed bandit what is the best way to allocate
  those trials in order to maximize our overall
  utility?
• Given finite computing resources what is the best
  way to allocate our computational power to
  maximize our results?
• Classical solution Allocate exponential trials
  to the best observed distribution based on
  historic outcomes

Dubins, L.E. and Savage, L.J. (1965). How to
gamble if you must. McGraw Hill, New York.
Re-published as Inequalities for stochastic
processes. Dover, New York (1976).
41
The Genetic Algorithm

1. Generate a population of solutions to the search
   problem at random
2. Evaluate this population
3. Sort the population based on performance
4. Select a part of the population to make a new
   population
5. Perform mutation and recombination to fill out
   the new population
6. Go to step 2 until time runs out or performance
   criteria is met

42
The Environments

• Static Environment Hyperplane-defined function
  (hdf)
• Dynamic Environment New hdf's are selected from
  an equivalence set at regular intervals
• Coevolving Environment A separate problem-GA
  controls which hdf's the solution-GA faces every
  generation

43
Dynamics and the Bandit(Like Smoky and the
Bandit only without Jackie Gleason)

• Now what if the distributions underlying the
  various arms changes in time?
• The balance between exploration and exploitation
  would also have to change in time
• This presentation will attempt to examine one way
  to do that and why the mechanism presented fails

44
Qualities of Test Suites

• Whitley (96)
• Generated from elementary Building Blocks
• Resistant to hillclimbing
• Scalable in difficulty
• Canonical in form
• Holland (00)
• Generated at random, but not reverse-engineerable
• Landscape-like features
• Include all finite functions in the limit

45
Building Blocks and GAs

• GAs combine building blocks to find the solution
  to a problem
• Different individuals in a GA have different
  building blocks, through crossover they merge
• This can be used to define any possible function

Car
Wheel
Engine
46
HDF Example
Building Block Set b1 111 1 b2 00
1 b3 1 1 b4 0 1 b12
11001 1 b23 001 1 b123 110011
1 b1234 1100101 1
Sample Evaluations f(100111) b3 1 f(1111111)
b1b3-p13 1.5 f(1000100) b2 b3 b23
3 f(1100111) b1 b2 b3 b12 b23 b123 -
p12 p13 p2312 4.5
Potholes p121101 -0.5 p13 1111
-0.5 p2312 1 0011 -0.5
47
Hyperplane-defined Functions

• Defined over the set of all binary strings
• Create an elementary level building block set
  defined over the set of strings of the alphabet
  0, 1,
• Create higher level building blocks by combining
  elementary building blocks
• Assign positive weights to all building blocks
• Create a set of potholes that incorporate parts
  of multiple elementary building blocks
• Assign the potholes negative weights
• A solution string matches a building block or a
  pothole if it matches the character of the
  alphabet or if the building block has a '' at
  that location

48
Problems with the HDFs

• Problems with HDFs for systematic study in
  dynamic environments
• No way to determine optimum value of a random HDF
• No way to create new HDFs based on old ones
• Because of this there is no way to specify a
  non-random dynamic HDF

49
Creating an sl-hdf

1. Generate a set of e non-conflicting elementary
   schemata of order o (8), and of string length l
   (500), set fitness contribution u(s) (2)
2. Combine all elementary schemata to create
   highest-level schemata, and set fitness
   contribution (3)
3. Create a pothole for each elementary schemata,
   by copying all defining bits, plus some from
   another elementary schemata probabilistically (p
   0.5), and set fitness contribution (-1)
4. Generate intermediate schemata by combining
   random pairs of elementary schemata to create e /
   2 second level schemata
5. Repeat (4) for each level until the number of
   schemata to be generated for the next level is lt
   1
6. To generate a new sl-hdf from the same
   equivalence set delete the previous intermediate
   schemata and repeat steps (4) and (5)

50
Mutation Blowup
51
Crossover Blowup
52
Measures of Interest

• Average Fitness average performance of the
  system over time
• Robustness ability of the system to maintain
  steady state performance
• Satisficability ability of the system to
  maintain performance above a certain level
• Diversity difference between solutions that the
  system is currently examining

53
Cliffs Variant Performance Results
54
Smooth Variant Performance Results
55
Weight Variant Performance Results
56
Cliffs Variant Robustness Results
57
Smooth Variant Robustness Results
58
Weight Variant Robustness Results
59
Cliffs Variant Satisficability Results
60
Smooth Variant Satisficability Results
61
Weight Variant Satisficability Results
62
Crossover Results Cliffs Variant
63
Crossover Results Smooth Variant
64
Crossover Results Weight Variant
65
Why Bäcks Mechanism?

• Does not require external knowledge
• Allows the GA to choose any mutation rate
• Allows control between exploration and
  exploitation does not force one or the other
• First order approximation of self-adaptive
  mutation mechanisms in haploid organisms
• Bäck showed self-adaptation to be successful

66
SA Results Smooth Variant (1/2)Generation 1800
Best Individual Over 30 Runs
  1   25   100
Experiment Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev.
Fixed 0.001 .9183 .0673 .9162 .0686 .9162 .0644
Fixed 0.0005 .6663 .0782 .6785 .0577 .6520 .0891
Fixed 0.0001 .3073 .0521 .3038 .0548 .2965 .0633
Self 0-1 .1836 .0495 .1932 .0558 .1785 .0509
Self 0.0001-0.01 .3932 .0686 .4293 .0574 .4461 .0807
Seeded .4194 .0758 .4339 .0566 .4309 .0762
No Crossover .4030 .0611 .3974 .0686 .3990 .0822
67
SA Results Smooth Variant (2/2)Generation 1800
Best Individual Over 30 Runs
  900   1801
Experiment Avg. Std. Dev Avg. Std. Dev
Fixed 0.001 .7597 .1029 .7681 .0621
Fixed 0.0005 .6098 .1011 .6517 .0577
Fixed 0.0001 .3086 .0442 .3164 .0506
Self 0-1 .1794 .0550 .1998 .0476
Self 0.0001-0.01 .4080 .0517 .4243 .0662
Seeded .3738 .0734 .4185 .0673
No Crossover .3588 .1002 .3775 .1017
68
Mutation Rates - Smooth Variant
69
SA Results Weight Variant (1/2)Generation 1800
Best Individual Over 30 Runs
  1   25   100
Experiment Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev.
Fixed 0.001 .8390 .0348 .8315 .0637 .8433 .0518
Fixed 0.0005 .7418 .0632 .7496 .0694 .7515 .0665
Fixed 0.0001 .4480 .0689 .4425 .0706 .4503 .0734
Self 0-1 .3348 .0685 .3522 .0802 .3502 .0990
Self 0.0001-0.01 .5997 .0987 .5830 .0758 .6046 .0727
Seeded .5420 .0819 .5705 .0655 .5528 .0821
No Crossover .4886 .1013 .5046 .0946 .5255 .0893
70
SA Results Weight Variant (2/2)Generation 1800
Best Individual Over 30 Runs
  900   1801
Experiment Avg. Std. Dev Avg. Std. Dev
Fixed 0.001 .8350 .0601 .8188 .0584
Fixed 0.0005 .7597 .0814 .7513 .0773
Fixed 0.0001 .4585 .0699 .4446 .0755
Self 0-1 .3545 .1053 .3556 .0992
Self 0.0001-0.01 .6010 .0788 .6024 .0728
Seeded .5515 .0731 .5368 .0623
No Crossover .5368 .0940 .5308 .0918
71
Mutation Rates - Weight Variant
72
Discussion of Results

• Local optima drive mutation rates down
• Hard to recover from low mutation rates
• Why was self-adaptation successful in Bäcks
  experiments?
• Most of his experiments were unimodal
• Strong selection pressure
• Bäcks problems are amenable to hill-climbing

73
Additional ExperimentsMechanisms for increasing
GA performance in dynamic environments

• Adapted Evolution an external function based on
  fitness or diversity controls evolutionary
  parameters
• Meta-GAs one GA controls the evolutionary
  parameters for another GA
• Multiploidy the use of dominant and recessive
  genes to maintain a memory of previous solutions
• Niching increasing diversity by decreasing the
  fitness of simliar solutions

74
Evolutionary Biology

• Coevolution and multiple species evolution
• Exploration versus Exploitation
• Generalists versus Specialists
• Phenotypic Plasticity
• Baldwinian Learning
• Evolution of Evolvability

75
Autonomous Agent Control

• How do you create an autonomous agent which can
  adapt to changes in its environment?
• What if other agents are coevolving and
  interfacing with your agent?
• Is it possible to automatically determine when to
  switch strategies?
• Examples robot control, trading agents,
  personal assistant agents

76
Computational Economics

• Many of the same questions as Evolutionary
  Biology
• Exploration vs. Exploitation
• Generalists vs. Specialists
• Many of the same questions as Autonomous Agent
  Control
• Coevolution of agents
• When to switch strategies
• Market behavior and failures

77
Future and Other Work in Dynamic Environments

• Test suite development and the behavior of a
  simple GA in a dynamic environment (EvoStoc-2005)
• Diversity of solutions in dynamic environments
  (EvoDop-2005)
• Explore other ways to balance exploration and
  exploitation
• Hypermutation, Multiploidy, and Meta-GAs
• Schematic Analysis
• Analysis of the sl-hdf landscape
• Co-evolution of sl-hdf's with solutions
• Combining GAs with a ABMs to model ecosystems

78
Standard Explorations

• Vary td which is the time between shakes
• See what effect this has on the performance of
  the best individuals
• In the past we explored a simple GA
• Fixed mutation of one bit out of a thousand
  (0.001)
• One-point crossover creates 70 of the new
  population
• Cloning creates the other 30
• Population size of 1000
• Selection using a tournament of size 3

79
The Environments

• Static Environment Hyperplane-defined function
  (hdf)
• Dynamic Environment New hdf's are selected from
  an equivalence set at regular intervals
• Coevolving Environment A separate problem-GA
  controls which hdf's the solution-GA faces every
  generation

80
Exploration and Exploitation in Dynamic
Environments

• Ideal system might not have the same behavior as
  a static system
• Increase exploration during times of change
• Increase exploitation during times of quiescence
• The mutation rate is one control of this behavior
• Thus a dynamic mutation rate might allow the
  system to better adapt to changes
• Many techniques hypermutation, variable local
  search, and random immigrants

81
Additional ExperimentsMechanisms for increasing
GA performance in dynamic environments

• Individual Self-Adaptation individuals can
  adjust their own mutation rates
• Adapted Evolution an external function based on
  fitness or diversity controls evolutionary
  parameters
• Meta-GAs one GA controls the evolutionary
  parameters for another GA
• Multiploidy the use of dominant and recessive
  genes to maintain a memory of previous solutions
• Niching increasing diversity by decreasing the
  fitness of simliar solutions

82
Evolutionary Biology

• Coevolution and multiple species evolution
• Exploration versus Exploitation
• Generalists versus Specialists
• Phenotypic Plasticity
• Baldwinian Learning
• Evolution of Evolvability

83
Autonomous Agent Control

• How do you create an autonomous agent which can
  adapt to changes in its environment?
• What if other agents are coevolving and
  interfacing with your agent?
• Is it possible to automatically determine when to
  switch strategies?
• Examples robot control, trading agents,
  personal assistant agents

84
Computational Economics

• Many of the same questions as Evolutionary
  Biology
• Exploration vs. Exploitation
• Generalists vs. Specialists
• Many of the same questions as Autonomous Agent
  Control
• Coevolution of agents
• When to switch strategies
• Market behavior and failures

85
Different Ways To Examine Behavior

• Extreme vs. Wholistic behavior the best /
  worst a system can do vs. the behavior of the
  whole population
• Within vs. Across Runs Are we more interested
  in how well the system will do within a
  particular run or across many runs?
• Fitness vs. Composition related Fitness is an
  indication of how well an individual is doing in
  the population, but one could also measure
  characteristics of the population that are not
  related to fitness

86
Discussion of Performance Results

• A GA operating on a regular changing landscape
  will initially underperform but will eventually
  outperform a GA operating on a static landscape
• Working Hypothesis The static landscape results
  in premature convergence, whereas shaking the
  landscape forces the GA to explore multiple
  solution sub-spaces
• The average performance falls farther after a
  shake than the best performance, this is because
  the best performance loss is mitigated by
  individuals that perform well in the new
  environment

Rand, W. and R. Riolo, Shaky Ladders,
Hyperplane-Defined Functions and Genetic
Algorithms Systematic Controlled Observation in
Dynamic Environments, EvoStoc-2005
87
Discussion of Satisficability Results

• Both the static environment and the regularly
  changing environment appear to operate in a
  similar fashion despite the better overall
  performance of the changing environment
• Working Hypothesis Most basic building blocks
  are found at roughly the same rate, the dynamic
  environment is better at finding intermediate
  building blocks
• Average Satisficability closely mirrors Best,
  despite the fact that Average is within instead
  of across runs

88
Discussion of Robustness Results

• Static environment constantly maintains
  robusteness, except for a few deleterious
  mutations
• The robustness measure presented here indicates
  that fitness changes are a good indication of
  change
• Greatest change in scores in the middle
  generations, because the GA is concentrating on
  exploring intermediate schemata

89
Conclusions

• These measures help to provide a better
  understanding of how the GA works in dynamic
  environments
• By using these measurements in combination with
  each other a great understanding can be gained
  than by exploring any one of them individually
• This paper is one step toward understanding the
  behavior of GAs through systematic, controlled
  experiments

90
Future Work

• Further explorations of the parameter space of
  the sl-hdfs ( of elementary schemata, string
  length)
• Investigations into the difficulty level of the
  sl-hdf's
• Examining diversity of schemata present in the
  populations in each run