Project Description: Toward a Better Understanding of the Maintenance of Genetic
Diversity and the Origin of Adaptive Novelty Using Evolutionary Algorithms
Project Summary
A novel metapopulation evolutionary algorithm is developed incorporating a diploid
genetic representation with biologically realistic forms of dominance, dynamic subpopulation
sizing, extinction/recolonization events, and differential migration. Major objectives of this
project are to demonstrate the conversion of epistatic to additive genetic variance within
subpopulations and to analyze the effect of this conversion on both the probability of
adaptive peak shifts and the maintenance of genetic diversity. The dual aims of this project
are to gain a better understanding of the interaction between selection and genetic drift
within small populations and to improve the search performance of population based
evolutionary algorithms in dynamic environments.
Project Description
1. Introduction
The development of adaptive novelty and maintenance of genetic diversity has been
a topic of great importance in the study of both natural evolution and population based
optimization algorithms. Two major contending theories of adaptive evolution were
developed early in the twentieth century: Sir Ronald Fisher’s large population size theory
(LST) [26] and Sewall Wright’s shifting balance theory (SBT) [52-56].
Fisher viewed most species as consisting of a large, randomly mating population with
an extensive history of adaptation, where genetic variability is maintained through the
continuous introduction of genetic mutations. For Fisher, the central problem of evolution
was explaining the refinement of existing adaptation in a stable or slowly changing
environment [48]. His fundamental theorem states that the rate at which the mean fitness of
a population increases is proportional to the additive genetic variation for fitness in that
population [26]. Selection acts on variation and favors advantageous mutations. This in turn,
boosts the additive genetic variation within a population and increases its response to
selection. Thus, according to the LST, mass selection and mutation are sufficient to explain
the emergence of novel adaptations in a dynamic environment and the effects of epistasis
(nonlinear gene interaction) and genetic drift (random fluctuations in gene frequencies) are
considered negligible.
Wright proposed a three-phase process of adaptation with a shifting balance between
evolutionary forces [52]. In the first phase of the SBT, genetic drift causes local
subpopulations, or demes, to randomly explore their adaptive topography. This allows some
demes to enter lower-fitness adaptive valleys that would not be reached by selection alone.
In the second phase, natural selection within demes pulls them out of adaptive valleys
toward locally adaptive peaks. This occurs by individual selection favoring those individuals
with combinations of genes that confer high fitness in the context of the genetic background
arrived at in the first phase. The third phase consists of a period of interdemic selection
where demes on different adaptive peaks grow at different rates. Fast growing high fitness
demes produce more migrants, and increase their rate of emigration while receiving relatively
few immigrants. This differential migration leads to the genotypes of fitter peaks being
spread throughout a population and causing the allele frequencies of nearby demes to shift
and come under the domain of influence of the higher fitness peak. The SBT places a large
emphasis on population structure, epistasis, and the stochastic process of genetic drift in the
role of creating adaptive novelty and maintaining population diversity.
1
The maintenance of the genetic diversity necessary to refine existing adaptations
within a continuously changing, dynamic environment is a major problem for the LST and a
source of controversy (for a thorough review of the Fisher-Wright debate see [18,19,33,48]).
As natural selection tends to hone in on an optimal genotype, advantageous mutations
become less prevalent, and genetic diversity decreases. In the event of an environmental
change, a population under the LST may lack the genetic variability necessary to redirect its
search through genotype space toward the new adaptive optima. Further, Fisher’s theory is
only able to explain the refinement of existing adaptation, but cannot explain the origin of
such adaptation. In contrast, the SBT implicitly addresses the origin of adaptive novelty and
maintenance of genetic diversity as an inevitable byproduct of adaptation in a structured
epistatic system. While genetic drift causes the fixation of alleles within demes, the epistatic
effects of alleles in one deme can be radically different from the effects of the same alleles in
another deme [48]. Thus, different gene combinations are favorable in different demes and
genetic variability is maintained in the metapopulation as a whole. In the case of an extreme
environmental change, migration between demes allows for the quick adaptive response of a
population in tracking the new fitness optima. However, the complexity of this process and
the difficulty in showing that adaptive valleys have been crossed by genetic drift is a large
source of criticism of the SBT [18,19].
Understanding the processes by which genetic variability is maintained, and the
origin of adaptive novelty, is of principal importance to modern evolutionary theory as well
as evolutionary computation. Evolutionary algorithms draw inspiration from evolutionary
biology and utilize operations analogous to natural evolution such as recombination,
mutation, and selection, in order to solve complex optimization problems. Evolutionary
algorithms address some of the same questions as evolutionary theory: How can a
population avoid converging on a suboptimal genotype? How is genetic diversity
maintained? How can adaptive novelty emerge in a dynamic environment? Thus, the FisherWright debate is at the heart of evolutionary computation as well as evolutionary biology and
a better understanding of the processes by which genetic diversity is maintained would
benefit both fields.
Indeed, the convergence of a population on a suboptimal genotype is a well known
phenomenon in the field of evolutionary computation [23]. The standard genetic algorithm
conventionally employs a large panmictic population with a strong selection policy based on
scaled environmental feedback and a very small mutation rate, which quickly eliminates
genetic diversity [15]. In traditional applications, the function representing the environment
is static and the population evolves toward a single solution. In the event of an
environmental modification, the adapted population often lacks the genetic diversity
necessary to track the changing optima [6]. It is through the maintenance of genetic diversity
that adaptive novelty is allowed to materialize in the event of an environmental change.
Thus, population diversity maintenance has received a large amount of attention in the
evolutionary computing community, particularly in research pertaining to diploidy
[11,17,28,36] and metapopulation structures [12,16,22,37-40,42-44,51]. Other mechanisms
developed to maintain genetic diversity include restart/re-initialization methods [24],
restricted mating [20,25], adaptive mutation rates [4], and the introduction of random
immigrants [34].
While evolutionary computing has enjoyed great success borrowing ideas from
evolutionary biology, the relationship between the two fields lacks reciprocity. Since these
algorithms are designed to solve complex optimization problems in engineering and
computer science, they use oversimplifications of natural biotic processes and their
2
applicability to evolutionary theory is consequently limited. However, recent advances in
evolutionary computational methods providing important insights into the evolution of
complexity [35] and communication [50] have demonstrated the value and importance of
computational methods in modeling evolutionary phenomena. To increase the use of
evolutionary algorithms in modeling processes of natural evolution, a new paradigm of
algorithm design is required; one that minimizes abstractions from theoretical biological
models.
Such a paradigm is necessary, as recent theoretical [13,14] and empirical findings [710] regarding the conversion of nonadditive to additive genetic variance in small populations
changes the significance of nonadditive genetic variance in both the LST and SBT and
warrants the re-evaluation of both theories. According to [48], neither Wright nor Fisher
discussed the conversion of epistatic to additive genetic variance within demes, its
contribution to genetic diversity between demes, or its contribution to reduced hybrid fitness
between demes. Here, evolutionary algorithms have the potential not only to facilitate an
understanding of the underlying intricacies of these complex systems, but to enhance the
overall performance of population based search routines in dynamic environments through
the incorporation of biological realism.
2. Project Objectives and Significance
As an interdisciplinary research assistant in computer science and evolutionary biology,
the PI is uniquely poised to study the impacts of recent theoretical and empirical findings
regarding the inter-conversion of variance components within small populations on both the
LST and SBT. The primary objectives of this project are:
1.
2.
3.
4.
Develop an evolutionary algorithm incorporating a metapopulation structure
with dynamic population sizing and migration, extinction/recolonization events,
and a diploid genetic representation with biologically inspired dominance
mechanisms.
Demonstrate that epistatic genetic variance is converted to additive genetic
variance within the framework of this evolutionary algorithm.
Investigate whether the conversion of epistatic genetic variance to additive
genetic variance within small populations increases the probability of adaptive
peak shifts.
Demonstrate the effectiveness of this evolutionary algorithm in maintaining
genetic diversity and generating adaptive novelty through rigorous testing on
difficult multimodal and dynamic optimization problems.
This project has potential impact in both evolutionary biology and evolutionary
computing. Understanding the significance of the conversion of nonadditive to additive
genetic variance in small populations on the LST and SBT is of great importance to
evolutionary theory. The interaction of genetic drift and selection in small populations is not
well understood in evolutionary biology and has not been thoroughly investigated in the
context of structured epistatic populations in evolutionary computing. Thus, this project has
the potential to provide insight into the Fisher-Wright debate and facilitate a greater
understanding of the stochastic effects of genetic drift in generating novel adaptations in
dynamic environments. The implementation of a metapopulation structure with sufficiently
small subpopulation sizes (so as to promote genetic drift) and a diploid genetic
representation holds the potential to better maintain population diversity and thus improve
3
the search performance of evolutionary algorithms in dynamic environments. Furthermore,
the conventional dominance mechanisms in evolutionary computing [11,17,18,36] are not
biologically inspired. Biologically realistic dominance mechanisms (as in [32]) have never
been investigated in the context of an evolutionary algorithm. The analysis of such
dominance mechanisms is important as their implementation may provide improved
evolutionary algorithm performance in multimodal and dynamic environments. Thus, this
research provides the rare opportunity of using computer science to gain insight into
fundamental questions in biological evolution, while at the same time using evolutionary
theory to further advance computer science.
3. Relation to Longer-Term Goals
As a direct extension of this project, the PI plans to investigate a) the relationship
between genetic drift and the differential scaling of genes in a structured epistatic population
b) the sensitivity of the SBT to migration parameters c) the extension of the experiments
designed for objectives 2 and 3 to accommodate N loci and d) the applicability of this
evolutionary algorithm for multi-objective optimization.
The PI has a strong interest and extensive background in computational
optimization. Upon completion of his graduate studies, the PI plans to develop
interdisciplinary curricula where courses in computer science, evolutionary biology,
population genetics, and ecology are fused together into a single program. In support of this
curriculum, he plans to develop open source web-based software that demonstrates complex
evolutionary processes such as genetic drift, natural selection, and speciation with
evolutionary algorithms. This development will integrate research and education and make a
significant contribution to students in evolutionary biology by providing their professors
with a useful pedagogical tool that will help demystify difficult evolutionary theory.
Furthermore, it will help motivate the next generation of biologists to better appreciate the
increasing importance of computational methods in the biological sciences.
4. Relation to the Present State of Knowledge
4.1 Inter-conversion of variance components
The rate of adaptive evolution is governed primarily by additive genetic variance in
both the LST and SBT [48]. However, the two theories differ greatly in the emphasis placed
on the effect of epistatic genetic variance on the rate of adaptation. Recent theoretical
developments [13,29-31,47] have changed our understanding of the relationship between
nonadditive and additive genetic variance in epistatic systems. It has been demonstrated
empirically that genetic drift and natural selection are able to work complementarily to
convert epistatic to additive genetic variance within small populations [7-10]. More recently,
Goodnight [32] showed that additive genetic variance remains consistently higher in
populations with epistasis than in populations without. While the majority of evolutionary
discussions treat nonadditive and additive genetic variances as separate entities playing very
different roles in the adaptive process, recent theory has shown that the additive and
epistatic components of genetic variation cannot be discussed in isolation from one another
in the context of small populations and genetic drift [48]. To date, this conversion of
epistatic to additive genetic variance has never been explored in the context of an
evolutionary algorithm.
4
4.2 SBT in Evolutionary Computation
While the conversion of epistatic to additive genetic variance has yet to be explored
in the evolutionary computation community, the genetic variability maintained by Wright’s
SBT has not gone unnoticed. Several research groups have attempted to abstract Wright’s
ideas for use in population diversity maintenance [12,42,43,50,37-40]. In [42] a genetic
algorithm inspired by Wright’s SBT is implemented “in order to address some of the major
criticisms leveled against it.” However, the authors abstract from Wright’s theory only those
aspects they need to improve the search performance of their genetic algorithm in a dynamic
environment and specifically ignore fundamental components of the SBT such as genetic
drift. As a result, their work fails to offer any real insight into the validity of Wright’s theory
of adaptive evolution and their efforts have been completely ignored in the evolutionary
biology literature.
Another attempt to capitalize on Wright’s SBT is found in [38] where an
asynchronous parallel genetic algorithm with a spatially structured population and local
mating strategy is developed in order to promote population diversity. The algorithm proves
to be effective in a number of applications [39,40] and Muhlenbein provides thoughtful
insight into open problems in population genetics and evolutionary biology [37]. However,
the algorithm fails to capture numerous aspects of the SBT. In particular, the stochastic
effects of genetic drift are not mentioned or employed and inter-deme migration occurs
implicitly through the overlap of mating neighborhoods instead of explicitly via differential
migration. While this research has contributed significantly to the search ability of genetic
algorithms in dynamic environments, the development of an evolutionary algorithm with the
ability to provide valid insight into Wright’s SBT has yet to be developed.
4.3 Diploidy, Multiploidy, and Dominance in Evolutionary Computation
Another major aspect of the SBT missing in the previously mentioned evolutionary
algorithms is a diploid genetic representation. In traditional
ggx!" genetic algorithms, the decision
variables are represented as haploid genotypes,
. In continuous optimization
lg!"
problems, the genotypic representation is real-valued,
, where l is the number of
ppx!"
decision variables. The genotype is then translated to phenotype,
via the mapping
():gpgpxx!="#"
. However, in biotic systems, diploid and multiploid genotypes occur
more frequently than haploid genotypes. Thus, the development of an evolutionary
algorithm intended to provide insight into the processes of natural evolution must include
multiploid genetic representations with dominance mechanisms to determine phenotypic
expression. The lmg
genotype
space for a multiploid genetic representation used in continuous
!"
optimization is
, where m is the number of haplotypes. The translation from
()gpxx!=
genotype to phenotype,
, is now more complex as dominance affects phenotypic
expression.
There have been several theoretical and empirical investigations into the role of
diploidy and multiploidy in evolutionary algorithms [11,17,27,28,36,41,46] using various
forms of dominance mechanisms. For instance, [11] appends two extra bits, called modifier
genes, to both haplotypes in his diploid genetic representation and uses an exclusive-or
dominance rule to determine phenotypic expression. In [28] and [36], the dominance
mechanism is not fixed, but allowed to evolve along with the genotype.
5
These studies in diploidy and multiploidy have demonstrated improved performance
over haploid genotypic representations in dynamic environments. This is mainly due to the
shielding of recessive genetic material from extinction until it becomes useful in the event of
an environmental change. While diploidy and multiploidy have certainly proven useful, the
application of biologically realistic dominance mechanisms such as those presented in [32]
has never been investigated in the evolutionary computing literature. Further, the application
of diploid and/or multiploid representations has never been investigated in the context of
metapopulation structures.
4.4 Genetic Drift in Evolutionary Computation
Genetic drift results in the genotypic convergence of a population due to stochastic
sampling and occurs even when there is no selection pressure. The effects of genetic drift
have long been recognized in evolutionary biology and population genetics [21]. Research
pertaining to genetic drift can also be found in the evolutionary computation literature
[2,3,28,45]. In [28], a markov chain model of genetic drift with and without mutation for a
single locus, two-allele evolutionary algorithm is devised. In [2,3] an exact formula for
calculating the mean convergence time due to genetic drift without selection and mutation
for an n-loci, two-allele genetic representation is presented. In [45] the population size at
which genetic drift fixes less salient alleles is developed in the context of a non-uniformly
scaled binary representation with tournament selection.
While a large amount of research has been performed to understand the effects of
genetic drift on the convergence of an evolutionary algorithm, no research group to date has
investigated drift in the context of a polyploidic representation. Further, no investigations
into the possible benefits of genetic drift in a metapopulation structure have ever been
performed.
5. General Plan of Work
5.1 Objective 1:
A large amount of analytical work is necessary to design this evolutionary algorithm.
First, populations must be sized to ensure that genetic drift will be able to randomly fix less
salient alleles in each subpopulation. This will require a thorough analysis across a broad
range of non-uniformly scaled genetic representations and selection policies. While [45] has
provided a detailed analysis of effective population size for exponentially scaled genetic
representations with tournament selection, a general analysis is currently absent from the
literature. Second, a novel implementation of the dominance mechanisms as presented in
[32] will have be invented.
With the aforementioned analysis completed, a metapopulation structured
evolutionary algorithm will be designed in Matlab (v.7). The imposed migration policy will be
consistent with phase three of Wright’s SBT in that more fit demes will be allowed to
produce more migrants, sending individuals with favorable genetic compositions to less fit
neighboring demes. A real-valued diploid genetic representation will be devised with the
adapted dominance mechanisms deciding the phenotypic expression of the genotype.
5.2 Objective 2:
To demonstrate that epistatic genetic variance is converted to additive genetic
variance within individual subpopulations, an experiment will be designed in which the
genotypic encoding of the control population is purely additive, while the genotypic
encoding of the experimental population is epistatic. In the experimental population, the
6
initial demes will exhibit a high degree of epistatic genetic variance. This can be measured as
the covariance between schema fitness and genotype. Schemata are the evolutionary
computing analog of the average genetical effect and are commonly used in the analysis of
evolutionary algorithms. A schema is built by simply adding a “don’t care” symbol to the
genotypic alphabet, denoted by ‘*’. A schema represents all of the strings that match it on all
positions other than ‘*’. For example, the genotypes AaBB, AaBb, and Aabb all belong to
schema Aa**. The fitness of schema Aa** is:
(#AaBB)(Fitness(AaBB)) + (#AaBb)(Fitness(AaBb)) + (#Aabb)(Fitness(Aabb)) Fitness(Aa**) = #AaBB + #AaBb + #Aa
In a system that only exhibits additive genetic variance, the covariance between schema
fitness and genotype will be unity. With epistatic genetic variation, this covariance will be less
than unity.
In this initial experiment, each subpopulation will consist of two-locus genotypes
exhibiting one of eight orthogonal forms of genetical effects [32]. The additive genetic
variation present in each subpopulation will be measured and each subpopulation will evolve
until drift fixes the alleles in each subpopulation. After the subpopulations are driven to
fixation, the additive genetic variance will again be measured. If a statistically significant
increase in additive genetic variance is found, then the conversion of epistatic to additive
genetic variance within demes will have been demonstrated.
The following example clarifies what this experiment is intended to demonstrate.
Consider the following table associating genotypes with fitness for a two-locus system with
additive-by-additive epistasis [32]:
AA
BB 1
Bb 0
bb -1
Aa
0
0
0
aa
-1
0
1
Table 1: Additive by Additive Genetical Effects
Assume the initial gene frequencies in the population are in Hardy-Weinberg equilibrium and
that the frequency of the A allele is 0.5 and the frequency of the B allele is also 0.5. Plotting
the average fitness of schema AA**, Aa**, and aa** reveals a large amount of epistatic
variance (figure 1, left: Va= 0). However, as the frequency of the B allele drifts away from
0.5, the epistatic genetic variance is converted to additive genetic variance (figure 1, right:
Va= 0.4). This example shows that the estimated average effect of a gene and its contribution
to the additive genetic variance change whenever the frequencies of its epistatic partners
change.
7
5.3 Objective 3:
To investigate whether the conversion of epistatic genetic variance to additive
genetic variance within small populations increases the probability of peak shifts, two
separate metapopulations will be generated. As in the first experiment, the genotypic
encoding of the control population is purely additive and the genotypic encoding of the
experimental population is epistatic. This initial experiment will assume two loci genotypes.
The two metapopulations will evolve in a suite of multimodal fitness landscapes as described
in table 2. Each of these multimodal landscapes consists of many local optima and only one
global optimum, with adaptive valleys between each peak. Multimodal fitness landscapes 1
and 2 are presented in figure 2.
Figure 2: Multimodal Test Landscapes, f1 and f2
The initial subpopulations will be strategically placed so they occupy different peaks
in the multimodal landscape. Both metapopulations will be allowed to evolve until a
8
termination criterion is met. Once again, the covariance between schema fitness and
genotype will be measured. This will demonstrate that epistatic genetic variance has been
converted to additive genetic variance in the experimental population. If the number of peak
shifts in the experimental population is statistically significantly larger than the number of
peak shifts in the control population, then the conversion of epistatic to additive genetic
variance will have been shown to increase the probability of peak shifts.
Test
Function
()10cos(2)10
niiifxxx!="#=$$+%&'
Domain
Maximum
()sin()niiifxxx==!"
[-5.12, 5.12]n
0
[-500, 500]n
418.9829n
211
21
()100()(1)niiiifxxxx!+="#=!!+!$%&
1222311
1()cos14000nniiiixfxxi==!"#$=%%+&'()*+,-./[-30,
2411
30]n
[-600, 600]n
0
0
Table 2: Multimodal Suite
5.4 Objective 4:
This evolutionary algorithm will be tested on a suite of dynamic fitness functions as
well as the suite of multimodal landscapes presented in table 2. Standard performance
metrics for static environments such as the rate of convergence and average absolute error
will be used for evaluation on the multimodal landscapes. Since a single time-invariant
optimum does not exist for dynamic optimization problems, a different set of performance
metrics will be used to evaluate this evolutionary algorithm in dynamic environments.
Letting T be the number of fitness evaluations and et the t-th evaluation, the metrics to be
used in this experiment [6], are:
1 xeT==!
1 Ttt

Online performance:

Offline performance:

Average absolute error:

Diversity:
o |MaxFitness – MinFitness|
o Allele-wise phenotypic variance
o Allele-wise genotypic variance
1 xeT==!{}*12max,,...,ttwhereeeee=
**1 Ttt
1
xeeT==!"
1 Ttoptimalt
Convergence plots of the best and average fitness in every generation will also be presented.
Three dynamic fitness landscapes will be used to test this evolutionary algorithm.
The first landscape is a moving parabola [6]. An environmental change occurs by simply
shifting the parabola in real space. The severity of the change can be controlled by the size
of the shift. While this function has the drawback of unimodality, it is arbitrarily scalable,
easy to define and analyze, and thoroughly examined in the literature [1,5]. Let s represent
9
the severity of the parabola shift, n be the number of dimensions, and t an index for the
environmental state. Thus, every time the parabola shifts, t is incremented. The function is
then defined as:
21(,)(())niiifxtxt!==+"
where
for linear translations,
{}
(0)01,2,...,()(1)iiiintts!!!="#=$+
for
translations,
{}random
(0)01,2,...,()(1)(0,1)
iiiiinttsN!!!="#=$+
and for circular translations,
2sin()(1)(,)(,)2cosiitttscitwherecitt!"##!"$%&'()'*+=,+=-%&'()'*+.
0:(0):iioddsieven!"=#$
!
!
with equal to the cycle length. That is, corresponds to the number of environmental
changes that occur before the cycle repeats itself.
The second dynamic landscape to be investigated is the moving peaks function [6].
This function consists of1,...,m(,)max{(),max(,(),(),())}
peaks in n-dimensional
space and is written formally as:
iiiimFxtBxPxhtwtpt==rrrr
()Bxr
where
is a time-invariant basis function, and P is the shape defining function where
each of the (0,1)N
m peaks
!" has its own time-varying parameters height (h), width (w), and location
pr
(()(1)_()(1)_()(1)()()((1)(1)(1)
). Letting
, these
parameters are formally defined as:
iiiiiiiiiihththeightseveritywtwtwidthseveritysptptvtvtrvtrvt!!""=#+=#+=#+=#+#+#
rrrrrrrr
!
rr
The vector consists of randomly drawn values for each dimension
! and determines how
much a peak’s change is! related to its previous move. That is, = 0 implies completely
random movement and =1 implies the peak will continually move in the same direction.
The complexity of this function is scalable with the number of dimensions and peaks.
The third dynamic landscape to be investigated is the oscillating peaks function
[Branke, 25-26]. This function is similar to the moving peaks function in that the landscape
consists of l (usually l=2) landscapes generated by the moving peaks function. The problem
oscillates between the l landscapes
according to a cosine function:
21()()(0)()(0)0.5cos20.51,...,
iiitifttftfilstepsl!""!#$%==++&='()*
where steps defines the number of intermediate steps in one cycle.
This evolutionary algorithm will be rigorously tested in the aforementioned
multimodal and dynamic fitness landscapes. Its performance will be carefully analyzed and
compared to other state-of-the-art optimization algorithms with respect to accuracy,
precision, and the maintenance of genetic diversity.
6. Broader Impacts of the Proposed Research
This research has potential impact in both evolutionary biology and evolutionary
computation. The insights gained regarding a) the conversion of epistatic to additive genetic
variance within demes, b) its contribution to the maintenance of genetic diversity between
10
demes, and c) whether this conversion increases the probability of adaptive peak shifts, will
complement existing theories of adaptive evolution. Further, these insights may be exploited
to improve the search performance of evolutionary algorithms in dynamic environments, an
emerging area of interest in computer science and applied mathematics.
6.1 Dissemination
The PI plans to disseminate his results through conferences and journals in
evolutionary biology and evolutionary computation. All code will be developed as open
source and will be made freely available on a website dedicated to this project. This website
will be updated regularly and dedicated solely to providing a detailed description of the
current state and future directions of the project.
6.2 Benefits to Society at Large
This work has potentially far-reaching benefits to society at large. If we are successful
in developing more effective tools for solving dynamic optimization problems, there are
innumerable applications that could benefit. Examples include, but are certainly not limited
to, stochastic job-shop scheduling [6], portfolio management, dynamic resource allocation,
risk analysis, and optimal control theory. Aside from the numerous potential practical
benefits, there are also the more intangible potential benefits toward understanding life that
may be gained through a better understanding of the maintenance of genetic diversity and
the origin of adaptive novelty.
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[6] Branke, Jurgen. 2002. Evolutionary Optimization in Dynamic Environments. Kluwer, MA.
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[19] ------. 2000. Is Wright’s Shifting Balance Theory Important in Evolution? Evolution 54:306-317.
[20] Craighurst, R., and W. Martin. 1995. Enhancing GA Performance through Crossover Prohibitions Based on Ancestry. Proceedings of
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