reationists occasionally charge that
evolution is useless as a scientific theory because it
produces no practical benefits and has no relevance to
daily life. However, the evidence of biology alone shows
that this claim is untrue. There are numerous natural
phenomena for which evolution gives us a sound theoretical
underpinning. To name just one, the observed development of
resistance - to insecticides in crop pests, to antibiotics
in bacteria, to chemotherapy in cancer cells, and to
anti-retroviral drugs in viruses such as HIV - is a
straightforward consequence of the laws of mutation and
selection, and understanding these principles has helped us
to craft strategies for dealing with these harmful
organisms. The evolutionary postulate of common descent has
aided the development of new medical drugs and techniques
by giving researchers a good idea of which organisms they
should experiment on to obtain results that are most likely
to be relevant to humans. Finally, the principle of
selective breeding has been used to great effect by humans
to create customized organisms unlike anything found in
nature for their own benefit. The canonical example, of
course, is the many varieties of domesticated dogs (breeds
as diverse as bulldogs, chihuahuas and dachshunds have been
produced from wolves in only a few thousand years), but
less well-known examples include cultivated maize (very
different from its wild relatives, none of which have the
familiar "ears" of human-grown corn), goldfish (like dogs,
we have bred varieties that look dramatically different
from the wild type), and dairy cows (with immense udders
far larger than would be required just for nourishing
offspring).
Critics might charge that creationists can explain these
things without recourse to evolution. For example,
creationists often explain the development of resistance to
antibiotic agents in bacteria, or the changes wrought in
domesticated animals by artificial selection, by presuming
that God decided to create organisms in fixed groups,
called "kinds" or baramin. Though natural
microevolution or human-guided artificial selection can
bring about different varieties within the originally
created "dog-kind," or "cow-kind," or "bacteria-kind" (!),
no amount of time or genetic change can transform one
"kind" into another. However, exactly how the creationists
determine what a "kind" is, or what mechanism prevents
living things from evolving beyond its boundaries, is
invariably never explained.
But in the last few decades, the continuing advance of
modern technology has brought about something new.
Evolution is now producing practical benefits in a very
different field, and this time, the creationists cannot
claim that their explanation fits the facts just as well.
This field is computer science, and the benefits come from
a programming strategy called genetic algorithms.
This essay will explain what genetic algorithms are and
will show how they are relevant to the
evolution/creationism debate.
What is a genetic algorithm?
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Concisely stated, a genetic algorithm (or GA for short)
is a programming technique that mimics biological evolution
as a problem-solving strategy. Given a specific problem to
solve, the input to the GA is a set of potential solutions
to that problem, encoded in some fashion, and a metric
called a fitness function that allows each candidate
to be quantitatively evaluated. These candidates may be
solutions already known to work, with the aim of the GA
being to improve them, but more often they are generated at
random.
The GA then evaluates each candidate according to the
fitness function. In a pool of randomly generated
candidates, of course, most will not work at all, and these
will be deleted. However, purely by chance, a few may hold
promise - they may show activity, even if only weak and
imperfect activity, toward solving the problem.
These promising candidates are kept and allowed to
reproduce. Multiple copies are made of them, but the copies
are not perfect; random changes are introduced during the
copying process. These digital offspring then go on to the
next generation, forming a new pool of candidate solutions,
and are subjected to a second round of fitness evaluation.
Those candidate solutions which were worsened, or made no
better, by the changes to their code are again deleted; but
again, purely by chance, the random variations introduced
into the population may have improved some individuals,
making them into better, more complete or more efficient
solutions to the problem at hand. Again these winning
individuals are selected and copied over into the next
generation with random changes, and the process repeats.
The expectation is that the average fitness of the
population will increase each round, and so by repeating
this process for hundreds or thousands of rounds, very good
solutions to the problem can be discovered.
As astonishing and counterintuitive as it may seem to
some, genetic algorithms have proven to be an enormously
powerful and successful problem-solving strategy,
dramatically demonstrating the power of evolutionary
principles. Genetic algorithms have been used in a wide
variety of fields to evolve solutions to problems as
difficult as or more difficult than those faced by human
designers. Moreover, the solutions they come up with are
often more efficient, more elegant, or more complex than
anything comparable a human engineer would produce. In some
cases, genetic algorithms have come up with solutions that
baffle the programmers who wrote the algorithms in the
first place!
Methods of representation
Before a genetic algorithm can be put to work on any
problem, a method is needed to encode potential solutions
to that problem in a form that a computer can process. One
common approach is to encode solutions as binary strings:
sequences of 1's and 0's, where the digit at each position
represents the value of some aspect of the solution.
Another, similar approach is to encode solutions as arrays
of integers or decimal numbers, with each position again
representing some particular aspect of the solution. This
approach allows for greater precision and complexity than
the comparatively restricted method of using binary numbers
only and often "is intuitively closer to the problem space"
(Fleming and Purshouse 2002, p.
1228).
This technique was used, for example, in the work of
Steffen Schulze-Kremer, who wrote a genetic algorithm to
predict the three-dimensional structure of a protein based
on the sequence of amino acids that go into it (Mitchell 1996, p. 62).
Schulze-Kremer's GA used real-valued numbers to represent
the so-called "torsion angles" between the peptide bonds
that connect amino acids. (A protein is made up of a
sequence of basic building blocks called amino acids, which
are joined together like the links in a chain. Once all the
amino acids are linked, the protein folds up into a complex
three-dimensional shape based on which amino acids attract
each other and which ones repel each other. The shape of a
protein determines its function.) Genetic algorithms for
training neural networks
often use this method of encoding also.
A third approach is to represent individuals in a GA as
strings of letters, where each letter again stands for a
specific aspect of the solution. One example of this
technique is Hiroaki Kitano's "grammatical encoding"
approach, where a GA was put to the task of evolving a
simple set of rules called a context-free grammar that was
in turn used to generate neural networks for a variety of
problems (Mitchell 1996, p.
74).
The virtue of all three of these methods is that they
make it easy to define operators that cause the random
changes in the selected candidates: flip a 0 to a 1 or vice
versa, add or subtract from the value of a number by a
randomly chosen amount, or change one letter to another.
(See the section on Methods of
change for more detail about the genetic operators.)
Another strategy, developed principally by John Koza of
Stanford University and called genetic programming,
represents programs as branching data structures called
trees (Koza et al. 2003, p. 35). In
this approach, random changes can be brought about by
changing the operator or altering the value at a given node
in the tree, or replacing one subtree with another.
Figure 1: Three simple program
trees of the kind normally used in genetic programming. The
mathematical expression that each one represents is given
underneath.
It is important to note that evolutionary algorithms do
not need to represent candidate solutions as data strings
of fixed length. Some do represent them in this way, but
others do not; for example, Kitano's grammatical encoding
discussed above can be efficiently scaled to create large
and complex neural networks, and Koza's genetic programming
trees can grow arbitrarily large as necessary to solve
whatever problem they are applied to.
Methods of selection
There are many different techniques which a genetic
algorithm can use to select the individuals to be copied
over into the next generation, but listed below are some of
the most common methods. Some of these methods are mutually
exclusive, but others can be and often are used in
combination.
Elitist selection: The most fit members of each
generation are guaranteed to be selected. (Most GAs do not
use pure elitism, but instead use a modified form where the
single best, or a few of the best, individuals from each
generation are copied into the next generation just in case
nothing better turns up.)
Fitness-proportionate selection: More fit
individuals are more likely, but not certain, to be
selected.
Roulette-wheel selection: A form of
fitness-proportionate selection in which the chance of an
individual's being selected is proportional to the amount
by which its fitness is greater or less than its
competitors' fitness. (Conceptually, this can be
represented as a game of roulette - each individual gets a
slice of the wheel, but more fit ones get larger slices
than less fit ones. The wheel is then spun, and whichever
individual "owns" the section on which it lands each time
is chosen.)
Scaling selection: As the average fitness of the
population increases, the strength of the selective
pressure also increases and the fitness function becomes
more discriminating. This method can be helpful in making
the best selection later on when all individuals have
relatively high fitness and only small differences in
fitness distinguish one from another.
Tournament selection: Subgroups of individuals
are chosen from the larger population, and members of each
subgroup compete against each other. Only one individual
from each subgroup is chosen to reproduce.
Rank selection: Each individual in the population
is assigned a numerical rank based on fitness, and
selection is based on this ranking rather than absolute
differences in fitness. The advantage of this method is
that it can prevent very fit individuals from gaining
dominance early at the expense of less fit ones, which
would reduce the population's genetic diversity and might
hinder attempts to find an acceptable solution.
Generational selection: The offspring of the
individuals selected from each generation become the entire
next generation. No individuals are retained between
generations.
Steady-state selection: The offspring of the
individuals selected from each generation go back into the
pre-existing gene pool, replacing some of the less fit
members of the previous generation. Some individuals are
retained between generations.
Hierarchical selection: Individuals go through
multiple rounds of selection each generation. Lower-level
evaluations are faster and less discriminating, while those
that survive to higher levels are evaluated more
rigorously. The advantage of this method is that it reduces
overall computation time by using faster, less selective
evaluation to weed out the majority of individuals that
show little or no promise, and only subjecting those who
survive this initial test to more rigorous and more
computationally expensive fitness evaluation.
Methods of change
Once selection has chosen fit individuals, they must be
randomly altered in hopes of improving their fitness for
the next generation. There are two basic strategies to
accomplish this. The first and simplest is called
mutation. Just as mutation in living things changes
one gene to another, so mutation in a genetic algorithm
causes small alterations at single points in an
individual's code.
The second method is called crossover, and
entails choosing two individuals to swap segments of their
code, producing artificial "offspring" that are
combinations of their parents. This process is intended to
simulate the analogous process of recombination that occurs
to chromosomes during sexual reproduction. Common forms of
crossover include single-point crossover, in which a
point of exchange is set at a random location in the two
individuals' genomes, and one individual contributes all
its code from before that point and the other contributes
all its code from after that point to produce an offspring,
and uniform crossover, in which the value at any
given location in the offspring's genome is either the
value of one parent's genome at that location or the value
of the other parent's genome at that location, chosen with
50/50 probability.
Figure 2: Crossover and mutation.
The above diagrams illustrate the effect of each of these
genetic operators on individuals in a population of 8-bit
strings. The upper diagram shows two individuals undergoing
single-point crossover; the point of exchange is set
between the fifth and sixth positions in the genome,
producing a new individual that is a hybrid of its
progenitors. The second diagram shows an individual
undergoing mutation at position 4, changing the 0 at that
position in its genome to a 1.
Other problem-solving techniques
With the rise of artificial life computing and the
development of heuristic methods, other computerized
problem-solving techniques have emerged that are in some
ways similar to genetic algorithms. This section explains
some of these techniques, in what ways they resemble GAs
and in what ways they differ.
- Neural networks
A neural network, or neural net for short, is a
problem-solving method based on a computer model of how
neurons are connected in the brain. A neural network
consists of layers of processing units called nodes joined
by directional links: one input layer, one output layer,
and zero or more hidden layers in between. An initial
pattern of input is presented to the input layer of the
neural network, and nodes that are stimulated then transmit
a signal to the nodes of the next layer to which they are
connected. If the sum of all the inputs entering one of
these virtual neurons is higher than that neuron's
so-called activation threshold, that neuron itself
activates, and passes on its own signal to neurons in the
next layer. The pattern of activation therefore spreads
forward until it reaches the output layer and is there
returned as a solution to the presented input. Just as in
the nervous system of biological organisms, neural networks
learn and fine-tune their performance over time via
repeated rounds of adjusting their thresholds until the
actual output matches the desired output for any given
input. This process can be supervised by a human
experimenter or may run automatically using a learning
algorithm (Mitchell 1996, p.
52). Genetic algorithms have been used both to build and to
train neural networks.
Figure 3: A simple feedforward neural network, with
one input layer consisting of four neurons, one hidden
layer consisting of three neurons, and one output layer
consisting of four neurons. The number on each neuron
represents its activation threshold: it will only fire if
it receives at least that many inputs. The diagram shows
the neural network being presented with an input string and
shows how activation spreads forward through the network to
produce an output.
- Hill-climbing
Similar to genetic algorithms, though more systematic and
less random, a hill-climbing algorithm begins with one
initial solution to the problem at hand, usually chosen at
random. The string is then mutated, and if the mutation
results in higher fitness for the new solution than for the
previous one, the new solution is kept; otherwise, the
current solution is retained. The algorithm is then
repeated until no mutation can be found that causes an
increase in the current solution's fitness, and this
solution is returned as the result (Koza et al. 2003, p. 59). (To
understand where the name of this technique comes from,
imagine that the space of all possible solutions to a given
problem is represented as a three-dimensional contour
landscape. A given set of coordinates on that landscape
represents one particular solution. Those solutions that
are better are higher in altitude, forming hills and peaks;
those that are worse are lower in altitude, forming
valleys. A "hill-climber" is then an algorithm that starts
out at a given point on the landscape and moves inexorably
uphill.) Hill-climbing is what is known as a greedy
algorithm, meaning it always makes the best choice
available at each step in the hope that the overall best
result can be achieved this way. By contrast, methods such
as genetic algorithms and simulated annealing, discussed
below, are not greedy; these methods sometimes make
suboptimal choices in the hopes that they will lead
to better solutions later on.
- Simulated annealing
Another optimization technique similar to evolutionary
algorithms is known as simulated annealing. The idea
borrows its name from the industrial process of
annealing in which a material is heated to above a
critical point to soften it, then gradually cooled in order to erase
defects in its crystalline structure, producing a more
stable and regular lattice arrangement of atoms (Haupt and Haupt 1998, p. 16). In
simulated annealing, as in genetic algorithms, there is a
fitness function that defines a fitness landscape; however,
rather than a population of candidates as in GAs, there is
only one candidate solution. Simulated annealing also adds
the concept of "temperature", a global numerical quantity
which gradually decreases over time. At each step of the
algorithm, the solution mutates (which is equivalent to
moving to an adjacent point of the fitness landscape). The
fitness of the new solution is then compared to the fitness
of the previous solution; if it is higher, the new solution
is kept. Otherwise, the algorithm makes a decision whether
to keep or discard it based on temperature. If the
temperature is high, as it is initially, even changes that
cause significant decreases in fitness may be kept and used
as the basis for the next round of the algorithm, but as
temperature decreases, the algorithm becomes more and more
inclined to only accept fitness-increasing changes.
Finally, the temperature reaches zero and the system
"freezes"; whatever configuration it is in at that point
becomes the solution. Simulated annealing is often used for
engineering design applications such as determining the
physical layout of components on a computer chip (Kirkpatrick, Gelatt and Vecchi
1983).
The earliest instances of what might today be called
genetic algorithms appeared in the late 1950s and early
1960s, programmed on computers by evolutionary biologists
who were explicitly seeking to model aspects of natural
evolution. It did not occur to any of them that this
strategy might be more generally applicable to artificial
problems, but that recognition was not long in coming:
"Evolutionary computation was definitely in the air in the
formative days of the electronic computer" (Mitchell 1996, p.2). By 1962,
researchers such as G.E.P. Box, G.J. Friedman, W.W. Bledsoe
and H.J. Bremermann had all independently developed
evolution-inspired algorithms for function optimization and
machine learning, but their work attracted little followup.
A more successful development in this area came in 1965,
when Ingo Rechenberg, then of the Technical University of
Berlin, introduced a technique he called evolution
strategy, though it was more similar to hill-climbers
than to genetic algorithms. In this technique, there was no
population or crossover; one parent was mutated to produce
one offspring, and the better of the two was kept and
became the parent for the next round of mutation (Haupt and Haupt 1998, p.146). Later
versions introduced the idea of a population. Evolution
strategies are still employed today by engineers and
scientists, especially in Germany.
The next important development in the field came in
1966, when L.J. Fogel, A.J. Owens and M.J. Walsh introduced
in America a technique they called evolutionary
programming. In this method, candidate solutions to
problems were represented as simple finite-state machines;
like Rechenberg's evolution strategy, their algorithm
worked by randomly mutating one of these simulated machines
and keeping the better of the two (Mitchell 1996, p.2; Goldberg 1989, p.105). Also like
evolution strategies, a broader formulation of the
evolutionary programming technique is still an area of
ongoing research today. However, what was still lacking in
both these methodologies was recognition of the importance
of crossover.
As early as 1962, John Holland's work on adaptive
systems laid the foundation for later developments; most
notably, Holland was also the first to explicitly propose
crossover and other recombination operators. However, the
seminal work in the field of genetic algorithms came in
1975, with the publication of the book Adaptation in
Natural and Artificial Systems. Building on earlier
research and papers both by Holland himself and by
colleagues at the University of Michigan, this book was the
first to systematically and rigorously present the concept
of adaptive digital systems using mutation, selection and
crossover, simulating processes of biological evolution, as
a problem-solving strategy. The book also attempted to put
genetic algorithms on a firm theoretical footing by
introducing the notion of schemata (Mitchell 1996, p.3; Haupt and Haupt 1998, p.147). That
same year, Kenneth De Jong's important dissertation
established the potential of GAs by showing that they could
perform well on a wide variety of test functions, including
noisy, discontinuous, and multimodal search landscapes (Goldberg 1989, p.107).
These foundational works established more widespread
interest in evolutionary computation. By the early to
mid-1980s, genetic algorithms were being applied to a broad
range of subjects, from abstract mathematical problems like
bin-packing and graph coloring to tangible engineering
issues such as pipeline flow control, pattern recognition
and classification, and structural optimization (Goldberg 1989, p. 128).
At first, these applications were mainly theoretical.
However, as research continued to proliferate, genetic
algorithms migrated into the commercial sector, their rise
fueled by the exponential growth of computing power and the
development of the Internet. Today, evolutionary
computation is a thriving field, and genetic algorithms are
"solving problems of everyday interest" (Haupt and Haupt 1998, p.147) in areas
of study as diverse as stock market prediction and
portfolio planning, aerospace engineering, microchip
design, biochemistry and molecular biology, and scheduling
at airports and assembly lines. The power of evolution has
touched virtually any field one cares to name, shaping the
world around us invisibly in countless ways, and new uses
continue to be discovered as research is ongoing. And at
the heart of it all lies nothing more than Charles Darwin's
simple, powerful insight: that the random chance of
variation, coupled with the law of selection, is a
problem-solving technique of immense power and nearly
unlimited application.
What are the strengths of GAs?
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- The first and most important
point is that genetic algorithms are intrinsically
parallel. Most other algorithms are serial and can only
explore the solution space to a problem in one direction at
a time, and if the solution they discover turns out to be
suboptimal, there is nothing to do but abandon all work
previously completed and start over. However, since GAs
have multiple offspring, they can explore the solution
space in multiple directions at once. If one path turns out
to be a dead end, they can easily eliminate it and continue
work on more promising avenues, giving them a greater
chance each run of finding the optimal solution.
However, the advantage of parallelism goes beyond this.
Consider the following: All the 8-digit binary strings
(strings of 0's and 1's) form a search space, which can be
represented as ******** (where the * stands for "either 0
or 1"). The string 01101010 is one member of this space.
However, it is also a member of the space 0*******,
the space 01******, the space 0******0, the space 0*1*1*1*,
the space 01*01**0, and so on. By evaluating the fitness of
this one particular string, a genetic algorithm would be
sampling each of these many spaces to which it belongs.
Over many such evaluations, it would build up an
increasingly accurate value for the average fitness
of each of these spaces, each of which has many members.
Therefore, a GA that explicitly evaluates a small number of
individuals is implicitly evaluating a much larger group of
individuals - just as a pollster who asks questions of a
certain member of an ethnic, religious or social group
hopes to learn something about the opinions of all members
of that group, and therefore can reliably predict national
opinion while sampling only a small percentage of the
population. In the same way, the GA can "home in" on the
space with the highest-fitness individuals and find the
overall best one from that group. In the context of
evolutionary algorithms, this is known as the Schema
Theorem, and is the "central advantage" of a GA over other
problem-solving methods (Holland
1992, p. 68; Mitchell 1996,
p.28-29; Goldberg 1989,
p.20).
- Due to the parallelism that
allows them to implicitly evaluate many schema at once,
genetic algorithms are particularly well-suited to solving
problems where the space of all potential solutions is
truly huge - too vast to search exhaustively in any
reasonable amount of time. Most problems that fall into
this category are known as "nonlinear". In a linear
problem, the fitness of each component is independent, so
any improvement to any one part will result in an
improvement of the system as a whole. Needless to say, few
real-world problems are like this. Nonlinearity is the
norm, where changing one component may have ripple effects
on the entire system, and where multiple changes that
individually are detrimental may lead to much greater
improvements in fitness when combined. Nonlinearity results
in a combinatorial explosion: the space of 1,000-digit
binary strings can be exhaustively searched by evaluating
only 2,000 possibilities if the problem is linear, whereas
if it is nonlinear, an exhaustive search requires
evaluating 21000 possibilities -
a number that would take over 300 digits to write out in
full.
Fortunately, the implicit parallelism of a GA allows it to
surmount even this enormous number of possibilities,
successfully finding optimal or very good results in a
short period of time after directly sampling only small
regions of the vast fitness landscape (Forrest 1993, p. 877). For example,
a genetic algorithm developed jointly by engineers from
General Electric and Rensselaer Polytechnic Institute
produced a high-performance jet engine turbine design that
was three times better than a human-designed configuration
and 50% better than a configuration designed by an expert
system by successfully navigating a solution space
containing more than 10387
possibilities. Conventional methods for designing such
turbines are a central part of engineering projects that
can take up to five years and cost over $2 billion; the
genetic algorithm discovered this solution after two days
on a typical engineering desktop workstation (Holland 1992, p.72).
- Another notable strength of
genetic algorithms is that they perform well in problems
for which the fitness landscape is complex - ones where the
fitness function is discontinuous, noisy, changes over
time, or has many local optima. Most practical problems
have a vast solution space, impossible to search
exhaustively; the challenge then becomes how to avoid the
local optima - solutions that are better than all the
others that are similar to them, but that are not as good
as different ones elsewhere in the solution space. Many
search algorithms can become trapped by local optima: if
they reach the top of a hill on the fitness landscape, they
will discover that no better solutions exist nearby and
conclude that they have reached the best one, even though
higher peaks exist elsewhere on the map.
Evolutionary algorithms, on the other hand, have proven to
be effective at escaping local optima and discovering the
global optimum in even a very rugged and complex fitness
landscape. (It should be noted that, in reality, there is
usually no way to tell whether a given solution to a
problem is the one global optimum or just a very high local
optimum. However, even if a GA does not always deliver a
provably perfect solution to a problem, it can almost
always deliver at least a very good solution.) All four of
a GA's major components - parallelism, selection, mutation,
and crossover - work together to accomplish this. In the
beginning, the GA generates a diverse initial population,
casting a "net" over the fitness landscape. (Koza (2003, p. 506) compares this to an army
of parachutists dropping onto the landscape of a problem's
search space, with each one being given orders to find the
highest peak.) Small mutations enable each individual to
explore its immediate neighborhood, while selection focuses
progress, guiding the algorithm's offspring uphill to more
promising parts of the solution space (Holland 1992, p. 68).
However, crossover is the key element that distinguishes
genetic algorithms from other methods such as hill-climbers
and simulated annealing. Without crossover, each individual
solution is on its own, exploring the search space in its
immediate vicinity without reference to what other
individuals may have discovered. However, with crossover in
place, there is a transfer of information between
successful candidates - individuals can benefit from what
others have learned, and schemata can be mixed and
combined, with the potential to produce an offspring that
has the strengths of both its parents and the weaknesses of
neither. This point is illustrated in Koza et al. 1999, p.486, where the
authors discuss a problem of synthesizing a lowpass filter
using genetic programming. In one generation, two parent
circuits were selected to undergo crossover; one parent had
good topology (components such as inductors and capacitors
in the right places) but bad sizing (values of inductance
and capacitance for its components that were far too low).
The other parent had bad topology, but good sizing. The
result of mating the two through crossover was an offspring
with the good topology of one parent and the good sizing of
the other, resulting in a substantial improvement in
fitness over both its parents.
The problem of finding the global optimum in a space with
many local optima is also known as the dilemma of
exploration vs. exploitation, "a classic problem for all
systems that can adapt and learn" (Holland 1992, p. 69). Once an
algorithm (or a human designer) has found a problem-solving
strategy that seems to work satisfactorily, should it
concentrate on making the best use of that strategy, or
should it search for others? Abandoning a proven strategy
to look for new ones is almost guaranteed to involve losses
and degradation of performance, at least in the short term.
But if one sticks with a particular strategy to the
exclusion of all others, one runs the risk of not
discovering better strategies that exist but have not yet
been found. Again, genetic algorithms have shown themselves
to be very good at striking this balance and discovering
good solutions with a reasonable amount of time and
computational effort.
- Another area in which
genetic algorithms excel is their ability to manipulate
many parameters simultaneously (Forrest 1993, p. 874). Many
real-world problems cannot be stated in terms of a single
value to be minimized or maximized, but must be expressed
in terms of multiple objectives, usually with tradeoffs
involved: one can only be improved at the expense of
another. GAs are very good at solving such problems: in
particular, their use of parallelism enables them to
produce multiple equally good solutions to the same
problem, possibly with one candidate solution optimizing
one parameter and another candidate optimizing a different
one (Haupt and Haupt 1998, p.17),
and a human overseer can then select one of these
candidates to use. If a particular solution to a
multiobjective problem optimizes one parameter to a degree
such that that parameter cannot be further improved without
causing a corresponding decrease in the quality of some
other parameter, that solution is called Pareto
optimal or non-dominated (Coello 2000, p. 112).
- Finally, one of the
qualities of genetic algorithms which might at first appear
to be a liability turns out to be one of their strengths:
namely, GAs know nothing about the problems they are
deployed to solve. Instead of using previously known
domain-specific information to guide each step and making
changes with a specific eye towards improvement, as human
designers do, they are "blind watchmakers" (Dawkins 1996); they make
random changes to their candidate solutions and then
use the fitness function to determine whether those changes
produce an improvement.
The virtue of this technique is that it allows genetic
algorithms to start out with an open mind, so to speak.
Since its decisions are based on randomness, all
possible search pathways are theoretically open to a GA; by
contrast, any problem-solving strategy that relies on prior
knowledge must inevitably begin by ruling out many pathways
a priori, therefore missing any novel solutions that
may exist there (Koza et al. 1999,
p. 547). Lacking preconceptions based on established
beliefs of "how things should be done" or what "couldn't
possibly work", GAs do not have this problem. Similarly,
any technique that relies on prior knowledge will break
down when such knowledge is not available, but again, GAs
are not adversely affected by ignorance (Goldberg 1989, p. 23). Through
their components of parallelism, crossover and mutation,
they can range widely over the fitness landscape, exploring
regions which intelligently produced algorithms might have
overlooked, and potentially uncovering solutions of
startling and unexpected creativity that might never have
occurred to human designers. One vivid illustration of this
is the rediscovery, by genetic programming, of the concept
of negative feedback - a principle crucial to many
important electronic components today, but one that, when
it was first discovered, was denied a patent for nine years
because the concept was so contrary to established beliefs
(Koza et al. 2003, p. 413).
Evolutionary algorithms, of course, are neither aware nor
concerned whether a solution runs counter to established
beliefs - only whether it works.
What are the limitations of GAs?
|
|
Although genetic algorithms have proven to be an
efficient and powerful problem-solving strategy, they are
not a panacea. GAs do have certain limitations; however, it
will be shown that all of these can be overcome and none of
them bear on the validity of biological evolution.
- The first, and most
important, consideration in creating a genetic algorithm is
defining a representation for the problem. The language
used to specify candidate solutions must be robust; i.e.,
it must be able to tolerate random changes such that fatal
errors or nonsense do not consistently result.
There are two main ways of achieving this. The first, which
is used by most genetic algorithms, is to define
individuals as lists of numbers - binary-valued,
integer-valued, or real-valued - where each number
represents some aspect of a candidate solution. If the
individuals are binary strings, 0 or 1 could stand for the
absence or presence of a given feature. If they are lists
of numbers, these numbers could represent many different
things: the weights of the links in a neural network, the
order of the cities visited in a given tour, the spatial
placement of electronic components, the values fed into a
controller, the torsion angles of peptide bonds in a
protein, and so on. Mutation then entails changing these
numbers, flipping bits or adding or subtracting random
values. In this case, the actual program code does not
change; the code is what manages the simulation and keeps
track of the individuals, evaluating their fitness and
perhaps ensuring that only values realistic and possible
for the given problem result.
In another method, genetic programming, the actual program
code does change. As discussed in the section Methods of representation,
GP represents individuals as executable trees of code that
can be mutated by changing or swapping subtrees. Both of
these methods produce representations that are robust
against mutation and can represent many different kinds of
problems, and as discussed in the section Some specific examples, both have had
considerable success.
This issue of representing candidate solutions in a robust
way does not arise in nature, because the method of
representation used by evolution, namely the genetic code,
is inherently robust: with only a very few exceptions, such
as a string of stop codons, there is no such thing as a
sequence of DNA bases that cannot be translated into a
protein. Therefore, virtually any change to an individual's
genes will still produce an intelligible result, and so
mutations in evolution have a higher chance of producing an
improvement. This is in contrast to human-created languages
such as English, where the number of meaningful words is
small compared to the total number of ways one can combine
letters of the alphabet, and therefore random changes to an
English sentence are likely to produce nonsense.
- The problem of how to write
the fitness function must be carefully considered so that
higher fitness is attainable and actually does equate to a
better solution for the given problem. If the fitness
function is chosen poorly or defined imprecisely, the
genetic algorithm may be unable to find a solution to the
problem, or may end up solving the wrong problem. (This
latter situation is sometimes described as the tendency of
a GA to "cheat", although in reality all that is happening
is that the GA is doing what it was told to do, not what
its creators intended it to do.) An example of this can be
found in Graham-Rowe 2002, in
which researchers used an evolutionary algorithm in
conjunction with a reprogrammable hardware array, setting
up the fitness function to reward the evolving circuit for
outputting an oscillating signal. At the end of the
experiment, an oscillating signal was indeed being produced
- but instead of the circuit itself acting as an
oscillator, as the researchers had intended, they
discovered that it had become a radio receiver that was
picking up and relaying an oscillating signal from a nearby
piece of electronic equipment!
This is not a problem in nature, however. In the laboratory
of biological evolution there is only one fitness function,
which is the same for all living things - the drive to
survive and reproduce, no matter what adaptations make this
possible. Those organisms which reproduce more abundantly
compared to their competitors are more fit; those which
fail to reproduce are unfit.
- In addition to making a
good choice of fitness function, the other parameters of a
GA - the size of the population, the rate of mutation and
crossover, the type and strength of selection - must be
also chosen with care. If the population size is too small,
the genetic algorithm may not explore enough of the
solution space to consistently find good solutions. If the
rate of genetic change is too high or the selection scheme
is chosen poorly, beneficial schema may be disrupted and
the population may enter error catastrophe, changing too
fast for selection to ever bring about convergence.
Living things do face similar difficulties, and
evolution has dealt with them. It is true that if a
population size falls too low, mutation rates are too high,
or the selection pressure is too strong (such a situation
might be caused by drastic environmental change), then the
species may go extinct. The solution has been "the
evolution of evolvability" - adaptations that alter a
species' ability to adapt. For example, most living things
have evolved elaborate molecular machinery that checks for
and corrects errors during the process of DNA replication,
keeping their mutation rate down to acceptably low levels;
conversely, in times of severe environmental stress, some
bacterial species enter a state of hypermutation
where the rate of DNA replication errors rises sharply,
increasing the chance that a compensating mutation will be
discovered. Of course, not all catastrophes can be evaded,
but the enormous diversity and highly complex adaptations
of living things today show that, in general, evolution is
a successful strategy. Likewise, the diverse applications
of and impressive results produced by genetic algorithms
show them to be a powerful and worthwhile field of
study.
- One type of problem that
genetic algorithms have difficulty dealing with are
problems with "deceptive" fitness functions (Mitchell 1996, p.125), those where
the locations of improved points give misleading
information about where the global optimum is likely to be
found. For example, imagine a problem where the search
space consisted of all eight-character binary strings, and
the fitness of an individual was directly proportional to
the number of 1s in it - i.e., 00000001 would be less fit
than 00000011, which would be less fit than 00000111, and
so on - with two exceptions: the string 11111111 turned out
to have very low fitness, and the string 00000000 turned
out to have very high fitness. In such a problem, a GA (as
well as most other algorithms) would be no more likely to
find the global optimum than random search.
The resolution to this problem is the same for both genetic
algorithms and biological evolution: evolution is not a
process that has to find the single global optimum every
time. It can do almost as well by reaching the top of a
high local optimum, and for most situations, this will
suffice, even if the global optimum cannot easily be
reached from that point. Evolution is very much a
"satisficer" - an algorithm that delivers a "good enough"
solution, though not necessarily the best possible
solution, given a reasonable amount of time and effort
invested in the search. The Evidence for Jury-Rigged
Design in Nature FAQ gives examples of this very
outcome appearing in nature. (It is also worth noting that
few, if any, real-world problems are as fully deceptive as
the somewhat contrived example given above. Usually, the
location of local improvements gives at least some
information about the location of the global
optimum.)
- One well-known problem
that can occur with a GA is known as premature
convergence. If an individual that is more fit than
most of its competitors emerges early on in the course of
the run, it may reproduce so abundantly that it drives down
the population's diversity too soon, leading the algorithm
to converge on the local optimum that that individual
represents rather than searching the fitness landscape
thoroughly enough to find the global optimum (Forrest 1993, p. 876; Mitchell 1996, p. 167). This is an
especially common problem in small populations, where even
chance variations in reproduction rate may cause one
genotype to become dominant over others.
The most common methods implemented by GA researchers to
deal with this problem all involve controlling the strength
of selection, so as not to give excessively fit individuals
too great of an advantage. Rank,
scaling and tournament selection, discussed earlier,
are three major means for accomplishing this; some methods
of scaling selection include sigma scaling, in which
reproduction is based on a statistical comparison to the
population's average fitness, and Boltzmann selection, in
which the strength of selection increases over the course
of a run in a manner similar to the "temperature" variable
in simulated annealing (Mitchell
1996, p. 168).
Premature convergence does occur in nature (where it
is called genetic
drift by biologists). This should not be surprising; as
discussed above, evolution as a problem-solving strategy is
under no obligation to find the single best solution,
merely one that is good enough. However, premature
convergence in nature is less common since most beneficial
mutations in living things produce only small, incremental
fitness improvements; mutations that produce such a large
fitness gain as to give their possessors dramatic
reproductive advantage are rare.
- Finally, several
researchers (Holland 1992, p.72;
Forrest 1993, p.875; Haupt and Haupt 1998, p.18) advise
against using genetic algorithms on analytically solvable
problems. It is not that genetic algorithms cannot find
good solutions to such problems; it is merely that
traditional analytic methods take much less time and
computational effort than GAs and, unlike GAs, are usually
mathematically guaranteed to deliver the one exact
solution. Of course, since there is no such thing as a
mathematically perfect solution to any problem of
biological adaptation, this issue does not arise in
nature.
Some specific examples of GAs
|
|
As the power of evolution gains increasingly widespread
recognition, genetic algorithms have been used to tackle a
broad variety of problems in an extremely diverse array of
fields, clearly showing their power and their potential.
This section will discuss some of the more noteworthy uses
to which they have been put.
- Acoustics
Sato et al. 2002 used genetic
algorithms to design a concert hall with optimal acoustic
properties, maximizing the sound quality for the audience,
for the conductor, and for the musicians on stage. This
task involves the simultaneous optimization of multiple
variables. Beginning with a shoebox-shaped hall, the
authors' GA produced two non-dominated solutions, both of
which were described as "leaf-shaped" (p.526). The authors
state that these solutions have proportions similar to
Vienna's Grosser Musikvereinsaal, which is widely agreed to
be one of the best - if not the best - concert hall in the
world in terms of acoustic properties.
Porto, Fogel and Fogel 1995 used
evolutionary programming to train neural networks to
distinguish between sonar reflections from different types
of objects: man-made metal spheres, sea mounts, fish and
plant life, and random background noise. After 500
generations, the best evolved neural network had a
probability of correct classification ranging between 94%
and 98% and a probability of misclassification between 7.4%
and 1.5%, which are "reasonable probabilities of detection
and false alarm" (p.21). The evolved network matched the
performance of another network developed by simulated
annealing and consistently outperformed networks trained by
back propagation, which "repeatedly stalled at suboptimal
weight sets that did not yield satisfactory results"
(p.21). By contrast, both stochastic methods showed
themselves able to overcome these local optima and produce
smaller, effective and more robust networks; but the
authors suggest that the evolutionary algorithm, unlike
simulated annealing, operates on a population and so takes
advantage of global information about the search space,
potentially leading to better performance in the long
run.
Tang et al. 1996 survey the uses of
genetic algorithms within the field of acoustics and signal
processing. One area of particular interest involves the
use of GAs to design Active Noise Control (ANC) systems,
which cancel out undesired sound by producing sound waves
that destructively interfere with the unwanted noise. This
is a multiple-objective problem requiring the precise
placement and control of multiple loudspeakers; GAs have
been used both to design the controllers and find the
optimal placement of the loudspeakers for such systems,
resulting in the "effective attenuation of noise" (p.33) in
experimental tests.
- Aerospace
engineering
Obayashi et al. 2000 used a
multiple-objective genetic algorithm to design the wing
shape for a supersonic aircraft. Three major considerations
govern the wing's configuration - minimizing aerodynamic
drag at supersonic cruising speeds, minimizing drag at
subsonic speeds, and minimizing aerodynamic load (the
bending force on the wing). These objectives are mutually
exclusive, and optimizing them all simultaneously requires
tradeoffs to be made.
The chromosome in this problem is a string of 66
real-valued numbers, each of which corresponds to a
specific aspect of the wing: its shape, its thickness, its
twist, and so on. Evolution with elitist rank selection was
simulated for 70 generations, with a population size of 64
individuals. At the termination of this process, there were
several Pareto-optimal individuals, each one representing a
single non-dominated solution to the problem. The paper
notes that these best-of-run individuals have "physically
reasonable" characteristics, indicating the validity of the
optimization technique (p.186). To further evaluate the
quality of the solutions, six of the best were compared to
a supersonic wing design produced by the SST Design Team of
Japan's National Aerospace Laboratory. All six were
competitive, having drag and load values approximately
equal to or less than the human-designed wing; one of the
evolved solutions in particular outperformed the NAL's
design in all three objectives. The authors note that the
GA's solutions are similar to a design called the "arrow
wing" which was first suggested in the late 1950s, but
ultimately abandoned in favor of the more conventional
delta-wing design.
In a follow-up paper (Sasaki et al.
2001), the authors repeat their experiment while adding
a fourth objective, namely minimizing the twisting
moment of the wing (a known potential problem for
arrow-wing SST designs). Additional control points for
thickness are also added to the array of design variables.
After 75 generations of evolution, two of the best
Pareto-optimal solutions were again compared to the
Japanese National Aerospace Laboratory's wing design for
the NEXST-1 experimental supersonic airplane. It was found
that both of these designs (as well as one optimal design
from the previous simulation, discussed above) were
physically reasonable and superior to the NAL's design in
all four objectives.
Williams, Crossley and Lang
2001 applied genetic algorithms to the task of spacing
satellite orbits to minimize coverage blackouts. As
telecommunications technology continues to improve, humans
are increasingly dependent on Earth-orbiting satellites to
perform many vital functions, and one of the problems
engineers face is designing their orbital trajectories.
Satellites in high Earth orbit, around 22,000 miles up, can
see large sections of the planet at once and be in constant
contact with ground stations, but these are far more
expensive to launch and more vulnerable to cosmic
radiation. It is more economical to put satellites in low
orbits, as low as a few hundred miles in some cases, but
because of the curvature of the Earth it is inevitable that
these satellites will at times lose line-of-sight access to
surface receivers and thus be useless. Even constellations
of several satellites experience unavoidable blackouts and
losses of coverage for this reason. The challenge is to
arrange the satellites' orbits to minimize this downtime.
This is a multi-objective problem, involving the
minimization of both the average blackout time for all
locations and the maximum blackout time for any one
location; in practice, these goals turn out to be mutually
exclusive.
When the GA was applied to this problem, the evolved
results for three, four and five-satellite constellations
were unusual, highly asymmetric orbit configurations, with
the satellites spaced by alternating large and small gaps
rather than equal-sized gaps as conventional techniques
would produce. However, this solution significantly reduced
both average and maximum revisit times, in some cases by up
to 90 minutes. In a news article about the results, Dr.
William Crossley noted that "engineers with years of
aerospace experience were surprised by the higher
performance offered by the unconventional design".
| Keane and Brown 1996 used a GA
to evolve a new design for a load-bearing truss or boom
that could be assembled in orbit and used for satellites,
space stations and other aerospace construction projects.
The result, a twisted, organic-looking structure that has
been compared to a human leg bone, uses no more material
than the standard truss design but is lightweight, strong
and far superior at damping out damaging vibrations, as was
confirmed by real-world tests of the final product. And yet
"No intelligence made the designs. They just evolved" (Petit 1998). The authors of the paper
further note that their GA only ran for 10 generations due
to the computationally intensive nature of the simulation,
and the population had not become stagnant. Continuing the
run for more generations would undoubtedly have produced
further improvements in performance. |
Figure 4: A genetically optimized three-dimensional
truss with improved frequency response. (Adapted from [1].) |
Finally, as reported in Gibbs
1996, Lockheed Martin has used a genetic algorithm to
evolve a series of maneuvers to shift a spacecraft from one
orientation to another within 2% of the theoretical minimum
time for such maneuvers. The evolved solution was 10%
faster than a solution hand-crafted by an expert for the
same problem.
- Astronomy and
astrophysics
Charbonneau 1995 suggests
the usefulness of GAs for problems in astrophysics by
applying them to three example problems: fitting the
rotation curve of a galaxy based on observed rotational
velocities of its components, determining the pulsation
period of a variable star based on time-series data, and
solving for the critical parameters in a
magnetohydrodynamic model of the solar wind. All three of
these are hard multi-dimensional nonlinear problems.
Charbonneau's genetic algorithm, PIKAIA, uses generational,
fitness-proportionate ranking selection coupled with
elitism, ensuring that the single best individual is copied
over once into the next generation without modification.
PIKAIA has a crossover rate of 0.65 and a variable mutation
rate that is set to 0.003 initially and gradually increases
later on, as the population approaches convergence, to
maintain variability in the gene pool.
In the galactic rotation-curve problem, the GA produced two
curves, both of which were very good fits to the data (a
common result in this type of problem, in which there is
little contrast between neighboring hilltops); further
observations can then distinguish which one is to be
preferred. In the time-series problem, the GA was
impressively successful in autonomously generating a
high-quality fit for the data, but harder problems were not
fitted as well (although, Charbonneau points out, these
problems are equally difficult to solve with conventional
techniques). The paper suggests that a hybrid GA employing
both artificial evolution and standard analytic techniques
might perform better. Finally, in solving for the six
critical parameters of the solar wind, the GA successfully
determined the value of three of them to an accuracy of
within 0.1% and the remaining three to accuracies of within
1 to 10%. (Though lower experimental error for these three
would always be preferable, Charbonneau notes that there
are no other robust, efficient methods for experimentally
solving a six-dimensional nonlinear problem of this type; a
conjugate gradient method works "as long as a very
good starting guess can be provided" (p.323). By contrast,
GAs do not require such finely tuned domain-specific
knowledge.)
Based on the results obtained so far, Charbonneau suggests
that GAs can and should find use in other difficult
problems in astrophysics, in particular inverse problems
such as Doppler imaging and helioseismic inversions. In
closing, Charbonneau argues that GAs are a "strong and
promising contender" (p.324) in this field, one that can be
expected to complement rather than replace traditional
optimization techniques, and concludes that "the bottom
line, if there is to be one, is that genetic algorithms
work, and often frightfully well" (p.325).
- Chemistry
High-powered, ultrashort pulses of laser energy can split
apart complex molecules into simpler molecules, a process
with important applications to organic chemistry and
microelectronics. The specific end products of such a
reaction can be controlled by modulating the phase of the
laser pulse. However, for large molecules, solving for the
desired pulse shape analytically is too difficult: the
calculations are too complex and the relevant
characteristics (the potential energy surfaces of the
molecules) are not known precisely enough.
Assion et al. 1998 solved this
problem by using an evolutionary algorithm to design the
pulse shape. Instead of inputting complex, problem-specific
knowledge about the quantum characteristics of the input
molecules to design the pulse to specifications, the EA
fires a pulse, measures the proportions of the resulting
product molecules, randomly mutates the beam
characteristics with the hope of getting these proportions
closer to the desired output, and the process repeats.
(Rather than fine-tune any characteristics of the laser
beam directly, the authors' GA represents individuals as a
set of 128 numbers, each of which is a voltage value that
controls the refractive index of one of the pixels in the
laser light modulator. Again, no problem-specific knowledge
about the properties of either the laser or the reaction
products is needed.) The authors state that their
algorithm, when applied to two sample substances,
"automatically finds the best configuration... no matter
how complicated the molecular response may be" (p.920),
demonstrating "automated coherent control on products that
are chemically different from each other and from the
parent molecule" (p.921).
In the early to mid-1990s, the widespread adoption of a
novel drug design technique called combinatorial
chemistry revolutionized the pharmaceutical industry.
In this method, rather than the painstaking, precise
synthesis of a single compound at a time, biochemists
deliberately mix a wide variety of reactants to produce an
even wider variety of products - hundreds, thousands or
millions of different compounds per batch - which can then
be rapidly screened for biochemical activity. In designing
libraries of reactants for this technique, there are two
main approaches: reactant-based design, which chooses
optimized groups of reactants without considering what
products will result, and product-based design, which
selects reactants most likely to produce products with the
desired properties. Product-based design is more difficult
and complex, but has been shown to result in better and
more diverse combinatorial libraries and a greater
likelihood of getting a usable result.
In a paper funded by GlaxoSmithKline's research and
development department, Gillet
2002 discusses the use of a multiobjective genetic
algorithm for the product-based design of combinatorial
libraries. In choosing the compounds that go into a
particular library, qualities such as molecular diversity
and weight, cost of supplies, toxicity, absorption,
distribution, and metabolism must all be considered. If the
aim is to find molecules similar to an existing molecule of
known function (a common method of new drug design),
structural similarity can also be taken into account. This
paper presents a multiobjective approach where a set of
Pareto-optimal results that maximize or minimize each of
these objectives can be developed. The author concludes
that the GA was able to simultaneously satisfy the criteria
of molecular diversity and maximum synthetic efficiency,
and was able to find molecules that were drug-like as well
as "very similar to given target molecules after exploring
a very small fraction of the total search space"
(p.378).
In a related paper, Glen and Payne
1995 discuss the use of genetic algorithms to
automatically design new molecules from scratch to fit a
given set of specifications. Given an initial population
either generated randomly or using the simple molecule
ethane as a seed, the GA randomly adds, removes and alters
atoms and molecular fragments with the aim of generating
molecules that fit the given constraints. The GA can
simultaneously optimize a large number of objectives,
including molecular weight, molecular volume, number of
bonds, number of chiral centers, number of atoms, number of
rotatable bonds, polarizability, dipole moment, and more in
order to produce candidate molecules with the desired
properties. Based on experimental tests, including one
difficult optimization problem that involved generating
molecules with properties similar to ribose (a sugar
compound frequently mimicked in antiviral drugs), the
authors conclude that the GA is an "excellent idea
generator" (p.199) that offers "fast and powerful
optimisation properties" and can generate "a diverse set of
possible structures" (p.182). They go on to state, "Of
particular note is the powerful optimising ability of the
genetic algorithm, even with relatively small population
sizes" (p.200). In a sign that these results are not merely
theoretical, Lemley 2001 reports
that the Unilever corporation has used genetic algorithms
to design new antimicrobial compounds for use in cleansers,
which it has patented.
- Electrical
engineering
A field-programmable gate array, or FPGA for short, is a
special type of circuit board with an array of logic cells,
each of which can act as any type of logic gate, connected
by flexible interlinks which can connect cells. Both of
these functions are controlled by software, so merely by
loading a special program into the board, it can be altered
on the fly to perform the functions of any one of a vast
variety of hardware devices.
Dr. Adrian Thompson has exploited this device, in
conjunction with the principles of evolution, to produce a
prototype voice-recognition circuit that can distinguish
between and respond to spoken commands using only 37 logic
gates - a task that would have been considered impossible
for any human engineer. He generated random bit strings of
0s and 1s and used them as configurations for the FPGA,
selecting the fittest individuals from each generation,
reproducing and randomly mutating them, swapping sections
of their code and passing them on to another round of
selection. His goal was to evolve a device that could at
first discriminate between tones of different frequencies
(1 and 10 kilohertz), then distinguish between the spoken
words "go" and "stop".
This aim was achieved within 3000 generations, but the
success was even greater than had been anticipated. The
evolved system uses far fewer cells than anything a human
engineer could have designed, and it does not even need the
most critical component of human-built systems - a clock.
How does it work? Thompson has no idea, though he has
traced the input signal through a complex arrangement of
feedback loops within the evolved circuit. In fact, out of
the 37 logic gates the final product uses, five of them are
not even connected to the rest of the circuit in any way -
yet if their power supply is removed, the circuit stops
working. It seems that evolution has exploited some subtle
electromagnetic effect of these cells to come up with its
solution, yet the exact workings of the complex and
intricate evolved structure remain a mystery (Davidson 1997).
Altshuler and Linden 1997 used
a genetic algorithm to evolve wire antennas with
pre-specified properties. The authors note that the design
of such antennas is an imprecise process, starting with the
desired properties and then determining the antenna's shape
through "guesses.... intuition, experience, approximate
equations or empirical studies" (p.50). This technique is
time-consuming, often does not produce optimal results, and
tends to work well only for relatively simple, symmetric
designs. By contrast, in the genetic algorithm approach,
the engineer specifies the antenna's electromagnetic
properties, and the GA automatically synthesizes a matching
configuration.
Figure 5: A crooked-wire genetic antenna
(after Altshuler and Linden
1997, figure 1). |
Altshuler and Linden used their GA to
design a circularly polarized seven-segment antenna with
hemispherical coverage; the result is shown to the left.
Each individual in the GA consisted of a binary chromosome
specifying the three-dimensional coordinates of each end of
each wire. Fitness was evaluated by simulating each
candidate according to an electromagnetic wiring code, and
the best-of-run individual was then built and tested. The
authors describe the shape of this antenna, which does not
resemble traditional antennas and has no obvious symmetry,
as "unusually weird" and "counter-intuitive" (p.52), yet it
had a nearly uniform radiation pattern with high bandwidth
both in simulation and in experimental testing, excellently
matching the prior specification. The authors conclude that
a genetic algorithm-based method for antenna design shows
"remarkable promise". "...this new design procedure is
capable of finding genetic antennas able to effectively
solve difficult antenna problems, and it will be
particularly useful in situations where existing designs
are not adequate" (p.52). |
- Financial
markets
Mahfoud and Mani 1996 used a
genetic algorithm to predict the future performance of 1600
publicly traded stocks. Specifically, the GA was tasked
with forecasting the relative return of each stock, defined
as that stock's return minus the average return of all 1600
stocks over the time period in question, 12 weeks (one
calendar quarter) into the future. As input, the GA was
given historical data about each stock in the form of a
list of 15 attributes, such as price-to-earnings ratio and
growth rate, measured at various past points in time; the
GA was asked to evolve a set of if/then rules to classify
each stock and to provide, as output, both a recommendation
on what to do with regards to that stock (buy, sell, or no
prediction) and a numerical forecast of the relative
return. The GA's results were compared to those of an
established neural net-based system which the authors had
been using to forecast stock prices and manage portfolios
for three years previously. Of course, the stock market is
an extremely noisy and nonlinear system, and no predictive
mechanism can be correct 100% of the time; the challenge is
to find a predictor that is accurate more often than
not.
In the experiment, the GA and the neural net each made
forecasts at the end of the week for each one of the 1600
stocks, for twelve consecutive weeks. Twelve weeks after
each prediction, the actual performance was compared with
the predicted relative return. Overall, the GA
significantly outperformed the neural network: in one trial
run, the GA correctly predicted the direction of one stock
47.6% of the time, made no prediction 45.8% of the time,
and made an incorrect prediction only 6.6% of the time, for
an overall predictive accuracy of 87.8%. Although the
neural network made definite predictions more often, it was
also wrong in its predictions more often (in fact, the
authors speculate that the GA's greater ability to make no
prediction when the data were uncertain was a factor in its
success; the neural net always produces a prediction unless
explicitly restricted by the programmer). In the 1600-stock
experiment, the GA produced a relative return of +5.47%,
versus +4.40% for the neural net - a statistically
significant difference. In fact, the GA also significantly
outperformed three major stock market indices - the S&P
500, the S&P 400, and the Russell 2000 - over this
period; chance was excluded as the cause of this result at
the 95% confidence level. The authors attribute this
compelling success to the ability of the genetic algorithm
to learn nonlinear relationships not readily apparent to
human observers, as well as the fact that it lacks a human
expert's "a priori bias against counterintuitive or
contrarian rules" (p.562).
Similar success was achieved by Andreou, Georgopoulos and Likothanassis
2002, who used hybrid genetic algorithms to evolve
neural networks that predicted the exchange rates of
foreign currencies up to one month ahead. As opposed to the
last example, where GAs and neural nets were in
competition, here the two worked in concert, with the GA
evolving the architecture (number of input units, number of
hidden units, and the arrangement of the links between
them) of the network which was then trained by a filter
algorithm.
As historical information, the algorithm was given 1300
previous raw daily values of five currencies - the American
dollar, the German deutsche mark, the French franc, the
British pound, and the Greek drachma - and asked to predict
their future values 1, 2, 5, and 20 days ahead. The hybrid
GA's performance, in general, showed a "remarkable level of
accuracy" (p.200) in all cases tested, outperforming
several other methods including neural networks alone.
Correlations for the one-day case ranged from 92 to 99%,
and though accuracy decreased over increasingly greater
time lags, the GA continued to be "quite successful"
(p.206) and clearly outperformed the other methods. The
authors conclude that "remarkable prediction success has
been achieved in both a one-step ahead and a multistep
predicting horizon" (p.208) - in fact, they state that
their results are better by far than any related predictive
strategies attempted on this data series or other
currencies.
The uses of GAs on the financial markets have begun to
spread into real-world brokerage firms. Naik 1996 reports that LBS Capital
Management, an American firm headquartered in Florida, uses
genetic algorithms to pick stocks for a pension fund it
manages. Coale 1997 and Begley and Beals 1995 report that
First Quadrant, an investment firm in California that
manages over $2.2 billion, uses GAs to make investment
decisions for all of their financial services. Their
evolved model earns, on average, $255 for every $100
invested over six years, as opposed to $205 for other types
of modeling systems.
- Game
playing
One of the most novel and compelling demonstrations of the
power of genetic algorithms was presented by Chellapilla and Fogel 2001, who
used a GA to evolve neural networks that could play the
game of checkers. The authors state that one of the major
difficulties in these sorts of strategy-related problems is
the credit assignment problem - in other words, how
does one write a fitness function? It has been widely
believed that the mere criterion of win, lose or draw does
not provide sufficient information for an evolutionary
algorithm to figure out what constitutes good play.
In this paper, Chellapilla and Fogel overturn that
assumption. Given only the spatial positions of pieces on
the checkerboard and the total number of pieces possessed
by each side, they were able to evolve a checkers program
that plays at a level competitive with human experts,
without any intelligent input as to what constitutes good
play - indeed, the individuals in the evolutionary algorithm
were not even told what the criteria for a win were, nor were
they told the result of any one game.
In Chellapilla and Fogel's representation, the game state was represented by a numeric list of 32 elements, with each position in the list corresponding to an available position on the board. The value at each position was either 0 for an unoccupied square, -1 if that
square was occupied by an enemy checker, +1 if that square
was occupied by one of the program's checkers, and -K or +K
for a square occupied by an enemy or friendly king. (The
value of K was not pre-specified, but again was determined
by evolution over the course of the algorithm.)
Accompanying this was a neural network with multiple
processing layers and one input layer with a node for each
of the possible 4x4, 5x5, 6x6, 7x7 and 8x8 squares on the
board. The output of the neural net for any given
arrangement of pieces was a value from -1 to +1 indicating
how good it felt that position was for it. For each move,
the neural network was presented with a game tree listing
all possible moves up to four turns into the future, and a
move decision was made based on which branch of the tree
produced the best results for it.
The evolutionary algorithm began with a population of 15 neural networks with randomly generated weights and biases assigned to each node and link; each individual then reproduced once, generating an offspring with variations in the values of the network. These 30 individuals then competed for survival by playing against each other, with each individual competing against 5 randomly chosen opponents per turn. 1 point was awarded for each win and 2 points were deducted for each loss. The 15 best performers, based on total score, were selected to produce offspring for the next generation, and the process repeated. Evolution was continued for 840 generations (approximately six months of computer time).
| Class |
Rating |
| Senior Master |
2400+ |
| Master |
2200-2399 |
| Expert |
2000-2199 |
| Class A |
1800-1999 |
| Class B |
1600-1799 |
| Class C |
1400-1599 |
| Class J |
< 200 |
|
The single best individual that emerged
from this selection was entered as a competitor on the
gaming website www.zone.com. Over a period
of two months, it played against 165 human opponents
comprising a range of high skill levels, from class C to
master, according to the ranking system of the United
States Chess Federation (shown at left, some ranks omitted
for clarity). Of these games, the neural net won 94, lost
39 and drew 32; based on the rankings of the opponents in
these games, the evolved neural net was equivalent to a
player with a mean rating of 2045.85, placing it at the
expert level - a higher ranking than 99.61% of over 80,000
players registered at the website. One of the neural net's
most significant victories was when it defeated a player
ranked 98th out of all registered players, whose rating was
just 27 points below master level. |
Tests conducted with a simple piece-differential program
(which bases moves solely on the difference between the number of checkers remaining to each side) with an eight-move look-ahead showed the neural net to be significantly superior, with a
rating over 400 points higher. "A program that relies only
on the piece count and an eight-ply search will defeat a
lot of people, but it is not an expert. The best evolved
neural network is" (p.425). Even when it was searching
positions two further moves ahead than the neural net, the
piece-differential program lost decisively in eight out of
ten games. This conclusively demonstrates that the evolved
neural net is not merely counting pieces, but is somehow
processing spatial characteristics of the board to decide
its moves. The authors point out that opponents on zone.com
often commented that the neural net's moves were "strange",
but its overall level of play was described as "very tough"
or with similar complimentary terms.
To further test the evolved neural network (which the
authors named "Anaconda" since it often won by restricting
its opponents' mobility), it was played against a
commercial checkers program, Hoyle's Classic Games,
distributed by Sierra Online (Chellapilla and Fogel 2000).
This program comes with a variety of built-in characters,
each of whom plays at a different skill level. Anaconda was
tested against three characters ("Beatrice", "Natasha" and
"Leopold") designated as expert-level players, playing one
game as red and one game as white against each of them with
a six-ply look-ahead. Though the authors doubted that this
depth of look-ahead would give Anaconda the ability to play
at the expert skill level it had previously shown, it won
six straight victories out of all six games played. Based
on this outcome, the authors expressed skepticism over
whether the Hoyle software played at the skill level
advertised, though it should be noted that they reached
this conclusion based solely on the ease with which
Anaconda defeated it!
The ultimate test of Anaconda was given in Chellapilla and Fogel 2002,
where the evolved neural net was matched against the best
checkers player in the world: Chinook, a
program designed principally by Dr. Jonathan Schaeffer of
the University of Alberta. Rated at 2814 in 1996 (with its
closest human competitors rated in the 2600s), Chinook
incorporates a book of opening moves provided by human
grandmasters, a sophisticated set of middle-game
algorithms, and a complete database of all possible moves
with ten pieces on the board or less, so it never makes a
mistake in the endgame. An enormous amount of human
intelligence and expertise went into the design of this
program.
Chellapilla and Fogel pitted Anaconda against Chinook in a
10-game tournament, with Chinook playing at a 5-ply skill
level, making it roughly approximate to master level.
Chinook won this contest, four wins to two with four draws.
(Interestingly, the authors note, in two of the games that
ended as draws, Anaconda held the lead with four kings to
Chinook's three. Furthermore, one of Chinook's wins came
from a 10-ply series of movies drawn from its endgame
database, which Anaconda with an 8-ply look-ahead could not
have anticipated. If Anaconda had had access to an endgame
database of the same quality as Chinook's, the outcome of
the tournament might well have been a victory for Anaconda,
four wins to three.) These results "provide good support
for the expert-level rating that Anaconda earned on
www.zone.com" (p.76), with an overall rating of 2030-2055,
comparable to the 2045 rating it earned by playing against
humans. While Anaconda is not an invulnerable player, it is
able to play competitively at the expert level and hold its
own against a variety of extremely skilled human checkers
players. When one considers the very simple fitness
criterion under which these results were obtained, the
emergence of Anaconda provides dramatic corroboration of
the power of evolution.
- Geophysics
Sambridge and Gallagher 1993
used a genetic algorithm to locate earthquake hypocenters
based on seismological data. (The hypocenter is the point
beneath the Earth's surface at which an earthquake begins.
The epicenter is the point on the surface directly above
the hypocenter.) This is an exceedingly complex task, since
the properties of seismic waves depend on the properties of
the rock layers through which they travel. The traditional
method for locating the hypocenter relies upon what is
known as a seismic inversion algorithm, which starts with a
best guess of the location, calculates the derivatives of
wave travel time with respect to source position, and
performs a matrix operation to provide an updated location.
This process is repeated until an acceptable solution is
reached. (This Post
of the Month, from November 2003, provides more
information.) However, this method requires derivative
information and is prone to becoming trapped on local
optima.
A location algorithm that does not depend on derivative
information or velocity models can avoid these shortfalls
by calculating only the forward problem - the difference
between observed and predicted wave arrival times for
different hypocenter locations. However, an exhaustive
search based on this method would be far too
computationally expensive. This, of course, is precisely
the type of optimization problem at which genetic
algorithms excel. Like all GAs, the one proposed by the
cited paper is parallel in nature - rather than
progressively perturbing a single hypocenter closer and
closer to the solution, it begins with a cloud of potential
hypocenters which shrinks over time to converge on a single
solution. The authors state that their approach "can
rapidly locate near optimal solutions without an exhaustive
search of the parameter space" (p.1467), displays "highly
organized behavior resulting in efficient search" and is "a
compromise between the efficiency of derivative based
methods and the robustness of a fully nonlinear exhaustive
search" (p.1469). The authors conclude that their genetic
algorithm is "efficient for truly global optimization"
(p.1488) and "a powerful new tool for performing robust
hypocenter location" (p.1489).
- Materials
engineering
Giro, Cyrillo and Galvão
2002 used genetic algorithms to design electrically
conductive carbon-based polymers known as polyanilines.
These polymers, a recently invented class of synthetic
materials, have "large technological potential
applications" and may open up windows onto "new fundamental
physical phenomena" (p.170). However, due to their high
reactivity, carbon atoms can form a virtually infinite
number of structures, making a systematic search for new
molecules with interesting properties all but impossible.
In this paper, the authors apply a GA-based approach to the
task of designing new molecules with pre-specified
properties, starting with a randomly generated population
of initial candidates. They conclude that their methodology
can be a "very effective tool" (p.174) to guide
experimentalists in the search for new compounds and is
general enough to be extended to the design of novel
materials belonging to virtually any class of
molecules.
Weismann, Hammel and Bäck
1998 applied evolutionary algorithms to a "nontrivial"
(p.162) industrial problem: the design of multilayer
optical coatings used for filters that reflect, transmit or
absorb light of specified frequencies. These coatings are
used in the manufacture of sunglasses, for example, or
compact discs. Their manufacture is a precise task: the
layers must be laid down in a particular sequence and
particular thicknesses to produce the desired result, and
uncontrollable environmental variations in the
manufacturing environment such as temperature, pollution
and humidity may affect the performance of the finished
product. Many local optima are not robust against such
variations, meaning that maximum product quality must be
paid for with higher rates of undesirable deviation. The
particular problem considered in this paper also had
multiple criteria: in addition to the reflectance, the
spectral composition (color) of the reflected light was
also considered.
The EA operated by varying the number of coating layers and
the thickness of each, and produced designs that were
"substantially more robust to parameter variation" (p.166)
and had higher average performance than traditional
methods. The authors conclude that "evolutionary algorithms
can compete with or even outperform traditional methods"
(p.167) of multilayer optical coating design, without
having to incorporate domain-specific knowledge into the
search function and without having to seed the population
with good initial designs.
One more use of GAs in the field of materials engineering
merits mention: Robin et al. 2003
used GAs to design exposure patterns for an electron
lithography beam, used to etch submicrometer-scale
structures onto integrated circuits. Designing these
patterns is a highly difficult task; it is cumbersome and
wasteful to determine them experimentally, but the high
dimensionality of the search space defeats most search
algorithms. As many as 100 parameters must be optimized
simultaneously to control the electron beam and prevent
scattering and proximity effects that would otherwise ruin
the fine structures being sculpted. The forward problem -
determining the resulting structure as a function of the
electron dose - is straightforward and easy to simulate,
but the inverse problem of determining the electron
dose to produce a given structure, which is what is being
solved here, is far harder and no deterministic solution
exists.
Genetic algorithms, which are "known to be able to find
good solutions to very complex problems of high
dimensionality" (p.75) without needing to be supplied with
domain-specific information on the topology of the search
landscape, were applied successfully to this problem. The
paper's authors employed a steady-state GA with
roulette-wheel selection in a computer simulation, which
yielded "very good optimized" (p.77) exposure patterns. By
contrast, a type of hill-climber known as a
simplex-downhill algorithm was applied to the same problem,
without success; the SD method quickly became trapped in
local optima which it could not escape, yielding solutions
of poor quality. A hybrid approach of the GA and SD methods
also could not improve on the results delivered by the GA
alone.
- Mathematics and
algorithmics
Although some of the most promising applications and
compelling demonstrations of GAs' power are in the field of
engineering design, they are also relevant to "pure"
mathematical problems. Haupt and Haupt
1998 (p.140) discuss the use of GAs to solve high-order
nonlinear partial differential equations, typically by
finding the values for which the equations equal zero, and
give as an example a near-perfect GA solution for the
coefficients of the fifth-order Super Korteweg-de Vries
equation.
Sorting a list of items into order is an important task in
computer science, and a sorting network is an
efficient way to accomplish this. A sorting network is a
fixed list of comparisons performed on a set of a given
size; in each comparison, two elements are compared and
exchanged if not in order. Koza et al.
1999, p. 952 used genetic programming to evolve minimal
sorting networks for 7-item sets (16 comparisons), 8-item
sets (19 comparisons), and 9-item sets (25 comparisons). Mitchell 1996, p.21, discusses the
use of genetic algorithms by W. Daniel Hillis to find a
61-comparison sorting network for a 16-item set, only one
step more than the smallest known. This latter example is
particularly interesting for two innovations it used:
diploid chromosomes, and more notably, host-parasite
coevolution. Both the sorting networks and the test cases
evolved alongside each other; sorting networks were given
higher fitness based on how many test cases they sorted
correctly, while test cases were given higher fitness based
on how many sorting networks they could "trick" into
sorting incorrectly. The GA with coevolution performed
significantly better than the same GA without it.
One final, noteworthy example of GAs in the field of
algorithmics can be found in Koza et
al. 1999, who used genetic programming to discover a
rule for the majority classification problem in
one-dimensional cellular automata that is better than all
known rules written by humans. A one-dimensional cellular
automaton can be thought of as a finite tape with a given
number of positions (cells) on it, each of which can hold
either the state 0 or the state 1. The automaton runs for a
given number of time steps; at each step, every cell
acquires a new value based on its previous value and the
value of its nearest neighbors. (The Game
of Life is a two-dimensional cellular automaton.) The
majority classification problem entails finding a table of
rules such that, if more than half the cells on the tape
are 1 initially, all the cells go to 1; otherwise all the
cells go to 0. The challenge lies in the fact that any
individual cell can only access information about its
nearest neighbors; therefore, good rule sets must somehow
find a way to transmit information about distant regions of
the tape.
It is known that a perfect solution to this problem does
not exist - no rule set can accurately classify all
possible initial configurations - but over the past twenty
years, there has been a long succession of increasingly
better solutions. In 1978, three researchers developed the
so-called GKL rule, which correctly classifies 81.6% of the
possible initial states. In 1993, a better rule with an
accuracy of 81.8% was discovered; in 1995, another rule
with accuracy of 82.178% was found. All of these rules
required significant work by intelligent, creative humans
to develop. By contrast, the best rule discovered by a run
of genetic programming, given in Koza
et al. 1999, p.973, has an overall accuracy of 82.326%
- better than any of the human-created solutions that have
been developed over the last two decades. The authors note
that their new rules are qualitatively different from
previously published rules, employing fine-grained internal
representations of state density and intricate sets of
signals for communicating information over long
distance.
- Military and law
enforcement
Kewley and Embrechts 2002 used
genetic algorithms to evolve tactical plans for military
battles. The authors note that "[p]lanning for a tactical
military battle is a complex, high-dimensional task which
often bedevils experienced professionals" (p.163), not only
because such decisions are usually made under high-stress
conditions, but also because even simple plans require a
great number of conflicting variables and outcomes to take
into account: minimizing friendly casualties, maximizing
enemy casualties, controlling desired terrain, conserving
resources, and so on. Human planners have difficulty
dealing with the complexities of this task and often must
resort to "quick and dirty" approaches, such as doing
whatever worked last time.
To overcome these difficulties, the authors of the cited
paper developed a genetic algorithm to automate the
creation of battle plans, in conjunction with a graphical
battle simulator program. The commander enters the
preferred outcome, and the GA automatically evolves a
battle plan; in the simulation used, factors such as the
topography of the land, vegetative cover, troop movement
speed, and firing accuracy were taken into account. In this
experiment, co-evolution was also used to improve the
quality of the solutions: battle plans for the enemy forces
evolved concurrently with friendly plans, forcing the GA to
correct any weaknesses in its own plan that an enemy could
exploit. To measure the quality of solutions produced by
the GA, they were compared to battle plans for the same
scenario produced by a group of "experienced military
experts... considered to be very capable of developing
tactical courses of action for the size forces used in this
experiment" (p.166). These seasoned experts both developed
their own plan and, when the GA's solution was complete,
were given a chance to examine it and modify it as they saw
fit. Finally, all the sets of plans were run multiple times
on the simulator to determine their average quality.
The results speak for themselves: the evolved solution
outperformed both the military experts' own plan and the
plan produced by their modifications to the GA's solution.
"...[T]he plans produced by automated algorithms had a
significantly higher mean performance than those generated
by experienced military experts" (p.161). Furthermore, the
authors note that the GA's plan made good tactical sense.
(It involved a two-pronged attack on the enemy position by
mechanized infantry platoons supported by attack
helicopters and ground scouts, in conjunction with unmanned
aerial vehicles conducting reconnaissance to direct
artillery fire.) In addition, the evolved plan included
individual friendly units performing doctrinal missions -
an emergent property that appeared during the course of the
run, rather than being specified by the experimenter. In
increasingly networked modern battlefields, the attractive
potential of an evolutionary algorithm that can automate
the production of high-quality tactical plans should be
obvious.
An interesting use of GAs in law enforcement was reported
in Naik 1996, which described the
"FacePrints" software, a project to help witnesses identify
and describe criminal suspects. The cliched image of the
police sketch artist drawing a picture of the suspect's
face in response to witnesses' promptings is a difficult
and inefficient method: most people are not good at
describing individual aspects of a person's face, such as
the size of the nose or shape of the jaw, but instead are
better at recognizing whole faces. FacePrints takes
advantage of this by using a genetic algorithm that evolves
pictures of faces based on databases of hundreds of
individual features that can be combined in a vast number
of ways. The program shows randomly generated face images
to witnesses, who pick the ones that most resemble the
person they saw; the selected faces are then mutated and
bred together to generate new combinations of features, and
the process repeats until an accurate portrait of the
suspect's face emerges. In one real-life robbery case, the
final portraits created by the three witnesses were
strikingly similar, and the resulting picture was printed
in the local paper.
- Molecular biology
In living things, transmembrane proteins are
proteins that protrude through a cellular membrane.
Transmembrane proteins often perform important functions
such as sensing the presence of certain substances outside
the cell or transporting them into the cell. Understanding
the behavior of a transmembrane protein requires
identifying the segment of that protein that is actually
embedded within the membrane, which is called the
transmembrane domain. Over the last two decades,
molecular biologists have published a succession of
increasingly accurate algorithms for this purpose.
All proteins used by living things are made up of the same
20 amino acids. Some of these amino acids are
hydrophobic, meaning they are repelled by water, and
some are hydrophilic, meaning they are attracted to
water. Amino acid sequences that are part of a
transmembrane domain are more likely to be hydrophobic.
However, hydrophobicity is not a precisely defined
characteristic, and there is no one agreed-upon scale for
measuring it.
Koza et al. 1999, chapter 16, used
genetic programming to design an algorithm to identify
transmembrane domains of a protein. Genetic programming was
given a set of standard mathematical operators to work
with, as well as a set of boolean amino-acid-detecting
functions that return +1 if the amino acid at a given
position is the amino acid they detect and otherwise return
-1. (For example, the A? function takes as an argument one
number corresponding to a position within the protein, and
returns +1 if the amino acid at that position is alanine,
which is denoted by the letter A; otherwise it returns -1).
A single shared memory variable kept a running count of the
overall sum, and when the algorithm completed, the protein
segment was identified as a transmembrane domain if its
value was positive. Given only these tools, would it entail
the creation of new information for a human designer to
produce an efficient solution to this problem?
The solutions produced by genetic programming were
evaluated for fitness by testing them on 246 protein
segments whose transmembrane status was known. The
best-of-run individual was then evaluated on 250
additional, out-of-sample, test cases and compared to the
performance of the four best known human-written algorithms
for the same purpose. The result: Genetic programming
produced a transmembrane segment-identifying algorithm with
an overall error rate of 1.6% - significantly lower than
all four human-written algorithms, the best of which had an
error rate of 2.5%. The genetically designed algorithm,
which the authors dubbed the 0-2-4 rule, operates as
follows:
- Increment the running sum by 4 for each instance of
glutamic acid (an electrically charged and highly
hydrophilic) amino acid in the protein segment.
- Increment the running sum by 0 for each instance of
alanine, phenylalanine, isoleucine, leucine, methionine, or
valine (all highly hydrophobic amino acids) in the
protein segment.
- Increment the running sum by 2 for each instance of all
other amino acids.
- If [(SUM - 3.1544)/0.9357] is less than the length of
the protein segment, classify that segment as a
transmembrane domain; otherwise, classify it as a
nontransmembrane domain.
- Pattern recognition and
data mining
Competition in the telecommunications industry today is
fierce, and a new term - "churn" - has been coined to
describe the rapid rate at which subscribers switch from
one service provider to another. Churn costs telecom
carriers a large amount of money each year, and reducing
churn is an important factor in increasing profitability.
If carriers can contact customers who are likely to switch
and offer them special incentives to stay, churn rates can
be reduced; but no carrier has the resources to contact
more than a small percent of its customers. The problem is
therefore how to identify customers who are more likely to
churn. All carriers have extensive databases of customer
information that can theoretically be used for this
purpose; but what method works best for sifting through
this vast amount of data to identify the subtle patterns
and trends that signify a customer's likelihood of
churning?
Au, Chan and Yao 2003 applied genetic
algorithms to this problem to generate a set of if-then
rules that predict the churning probability of different
groups of customers. In their GA, the first generation of
rules, all of which had one condition, was generated using
a probabilistic induction technique. Subsequent generations
then refine these, combining simple, single-condition rules
into more complex, multi-condition rules. The fitness
measure used an objective "interestingness" measure of
correlation which requires no subjective input. The
evolutionary data-mining algorithm was tested on a
real-world database of 100,000 subscribers provided by a
Malaysian carrier, and its performance was compared against
two alternative methods: a multilayer neural network and a
widely used decision-tree-based algorithm, C4.5. The
authors state that their EA was able to discover hidden
regularities in the database and was "able to make accurate
churn prediction under different churn rates" (p.542),
outperforming C4.5 under all circumstances, outperforming
the neural network under low monthly churn rates and
matching the neural network under larger churn rates, and
reaching conclusions more quickly in both cases. Some
further advantages of the evolutionary approach are that it
can operate efficiently even when some data fields are
missing and that it can express its findings in easily
understood rule sets, unlike the neural net.
Among some of the more interesting rules discovered by the
EA are as follows: subscribers are more likely to churn if
they are personally subscribed to the service plan and have
not been admitted to any bonus scheme (a potential solution
is to admit all such subscribers to bonus schemes);
subscribers are more likely to churn if they live in Kuala
Lumpur, are between 36 and 44 in age, and pay their bills
with cash (presumably because it is easier for subscribers
who pay cash, rather than those whose accounts are
automatically debited, to switch providers); and
subscribers living in Penang who signed up through a
certain dealer are more likely to churn (this dealer may be
providing poor customer service and should be
investigated).
Rizki, Zmuda and Tamburino 2002
used evolutionary algorithms to evolve a complex pattern
recognition system with a wide variety of potential uses.
The authors note that the task of pattern recognition is
increasingly being performed by machine learning
algorithms, evolutionary algorithms in particular. Most
such approaches begin with a pool of predefined features,
from which an EA can select appropriate combinations for
the task at hand; by contrast, this approach began from the
ground up, first evolving individual feature detectors in
the form of expression trees, then evolving cooperative
combinations of those detectors to produce a complete
pattern recognition system. The evolutionary process
automatically selects the number of feature detectors, the
complexity of the detectors, and the specific aspects of
the data each detector responds to.
To test their system, the authors gave it the task of
classifying aircraft based on their radar reflections. The
same kind of aircraft can return quite different signals
depending on the angle and elevation at which it is viewed,
and different kinds of aircraft can return very similar
signals, so this is a non-trivial task. The evolved pattern
recognition system correctly classified 97.2% of the
targets, a higher net percentage than any of the three
other techniques - a perceptron neural network, a
nearest-neighbor classifier algorithm, and a radial basis
algorithm - against which it was tested. (The radial basis
network's accuracy was only 0.5% less than the evolved
classifier, which is not a statistically significant
difference, but the radial basis network required 256
feature detectors while the evolved recognition system used
only 17.) As the authors state, "The recognition systems
that evolve use fewer features than systems formed using
conventional techniques, yet achieve comparable or superior
recognition accuracy" (p.607). Various aspects of their
system have also been applied to problems including optical
character recognition, industrial inspection and medical
image analysis.
Hughes and Leyland 2000 also
applied multiple-objective GAs to the task of classifying
targets based on their radar reflections. High-resolution
radar cross section data requires massive amounts of disk
storage space, and it is very computationally intensive to
produce an actual model of the source from the data. By
contrast, the authors' GA-based approach proved very
successful, producing a model as good as the traditional
iterative approach while reducing the computational
overhead and storage requirements to the point where it was
feasible to generate good models on a desktop computer. By
contrast, the traditional iterative approach requires ten
times the resolution and 560,000 times as many accesses of
image data to produce models of similar quality. The
authors conclude that their results "clearly demonstrate"
(p.160) the ability of the GA to process both two- and
three-dimensional radar data of any level of resolution
with far fewer calculations than traditional methods, while
retaining acceptably high accuracy.
- Robotics
The international RoboCup tournament is a
project to promote advances in robotics, artificial
intelligence, and related fields by providing a standard
problem where new technologies can be tried out -
specifically, it is an annual soccer tournament between
teams of autonomous robots. (The stated goal is to develop
a team of humanoid robots that can win against the
world-champion human soccer team by 2050; at the present
time, most of the competing robot teams are wheeled.) The
programs that control the robotic team members must display
complex behavior, deciding when to block, when to kick, how
to move, when to pass the ball to teammates, how to
coordinate defense and offense, and so on. In the simulator
league of the 1997 competition, David Andre and Astro
Teller entered a team named Darwin United whose control
programs had been developed automatically from the ground
up by genetic programming, a challenge to the conventional
wisdom that "this problem is just too difficult for such a
technique" (Andre and Teller 1999,
p. 346).
To solve this difficult problem, Andre and Teller provided
the genetic programming algorithm with a set of primitive
control functions such as turning, moving, kicking, and so
on. (These functions were themselves subject to change and
refinement during the course of evolution.) Their fitness
function, written to reward good play in general rather
than scoring specifically, provided a list of increasingly
important objectives: getting near the ball, kicking the
ball, keeping the ball on the opponent's side of the field,
moving in the correct direction, scoring goals, and winning
the game. It should be noted that no code was provided to
teach the team specifically how to achieve these
complex objectives. The evolved programs were then
evaluated using a hierarchical selection model: first, the
candidate teams were tested on an empty field and rejected
if they did not score a goal within 30 seconds. Next, they
were evaluated against a team of stationary "kicking posts"
that kick the ball toward the opposite side of the field.
Thirdly, the team played a game against the winning team
from the RoboCup 1997 competition. Finally, teams that
scored at least one goal against this team were played off
against each other to determine which was best.
Out of 34 teams in its division, Darwin United ultimately
came in 17th, placing squarely in the middle of the field
and outranking half of the human-written entries. While a
tournament victory would undoubtedly have been more
impressive, this result is competitive and significant in
its own right, and appears even more so in the light of
history. About 25 years ago, chess-playing computer
programs were in their infancy; a computer had only
recently entered even a regional competition for the first
time, although it did not win (Sagan
1979, p.286). But "[a] machine that plays chess in the
middle range of human expertise is a very capable machine"
(ibid.), and it might be said that the same is true of
robot soccer. Just as chess-playing machines compete at
world grandmaster levels today, what types of systems will
genetic programming be producing 20 or 30 years from
now?
- Routing and
scheduling
Burke and Newall 1999 used genetic
algorithms to schedule exams among university students. The
timetable problem in general is known to be NP-complete,
meaning that no method is known to find a
guaranteed-optimal solution in a reasonable amount of time.
In such a problem, there are both hard constraints - two
exams may not be assigned to the same room at the same time
- and soft constraints - students should not be assigned to
multiple exams in succession, if possible, to minimize
fatigue. Hard constraints must be satisfied, while soft
constraints should be satisfied as far as possible. The
authors dub their hybrid approach for solving this problem
a "memetic algorithm": an evolutionary algorithm with
rank-based, fitness-proportionate selection, combined with
a local hill-climber to optimize solutions found by the EA.
The EA was applied to data sets from four real universities
(the smallest of which had an enrollment of 25,000
students), and its results were compared to results
produced by a heuristic backtracking method, a
well-established algorithm that is among the best known for
this problem and that is used at several real universities.
Compared to this method, the EA produced a result with a
quite uniform 40% reduction in penalty.
He and Mort 2000 applied genetic
algorithms to the problem of finding optimal routing paths
in telecommunications networks (such as phone networks and
the Internet) which are used to relay data from senders to
recipients. This is an NP-hard optimization problem, a type
of problem for which GAs are "extremely well suited... and
have found an enormous range of successful applications in
such areas" (p.42). It is also a multiobjective problem,
balancing conflicting objectives such as maximizing data
throughput, minimizing transmission delay and data loss,
finding low-cost paths, and distributing the load evenly
among routers or switches in the network. Any successful
real-world algorithm must also be able to re-route around
primary paths that fail or become congested.
In the authors' hybrid GA, a shortest-path-first algorithm,
which minimizes the number of "hops" a given data packet
must pass through, is used to generate the seed for the
initial population. However, this solution does not take
into account link congestion or failure, which are
inevitable conditions in real networks, and so the GA takes
over, swapping and exchanging sections of paths. When
tested on a data set derived from a real Oracle network
database, the GA was found to be able to efficiently route
around broken or congested links, balancing traffic load
and maximizing the total network throughput. The authors
state that these results demonstrate the "effectiveness and
scalability" of the GA and show that "optimal or
near-optimal solutions can be achieved" (p.49).
This technique has found real-world applications for
similar purposes, as reported in Begley and Beals 1995. The
telecommunications company U.S. West (now merged with
Qwest) was faced with the task of laying a network of
fiber-optic cable. Until recently, the problem of designing
the network to minimize the total length of cable laid was
solved by an experienced engineer; now the company uses a
genetic algorithm to perform the task automatically. The
results: "Design time for new networks has fallen from two
months to two days and saves US West $1 million to $10
million each" (p.70).
Jensen 2003 and Chryssolouris and Subramaniam
2001 applied genetic algorithms to the task of
generating schedules for job shops. This is an NP-hard
optimization problem with multiple criteria: factors such
as cost, tardiness, and throughput must all be taken into
account, and job schedules may have to be rearranged on the
fly due to machine breakdowns, employee absences, delays in
delivery of parts, and other complications, making
robustness in a schedule an important consideration. Both
papers concluded that GAs are significantly superior to
commonly used dispatching rules, producing efficient
schedules that can more easily handle delays and
breakdowns. These results are not merely theoretical, but
have been applied to real-world situations:
As reported in Naik 1996,
organizers of the 1992 Paralympic Games used a GA to
schedule events. As reported in Petzinger 1995, John Deere &
Co. has used GAs to generate schedules for a Moline,
Illinois plant that manufactures planters and other heavy
agricultural equipment. Like luxury cars, these can be
built in a wide variety of configurations with many
different parts and options, and the vast number of
possible ways to build them made efficient scheduling a
seemingly intractable problem. Productivity was hampered by
scheduling bottlenecks, worker teams were bickering, and
money was being lost. Finally, in 1993, Deere turned to
Bill Fulkerson, a staff analyst and engineer who conceived
of using a genetic algorithm to produce schedules for the
plant. Overcoming initial skepticism, the GA quickly proved
itself: monthly output has risen by 50 percent, overtime
has nearly vanished, and other Deere plants are
incorporating GAs into their own scheduling.
As reported in Rao 1998, Volvo has
used an evolutionary program called OptiFlex to schedule
its million-square-foot factory in Dublin, Virginia, a task
that requires handling hundreds of constraints and millions
of possible permutations for each vehicle. Like all genetic
algorithms, OptiFlex works by randomly combining different
scheduling possibilities and variables, determines their
fitness by ranking them according to costs, benefits and
constraints, then causes the best solutions to swap genes
and sends them back into the population for another trial.
Until recently, this daunting task was handled by a human
engineer who took up to four days to produce the schedule
for each week; now, thanks to GAs, this task can be
completed in one day with minimal human intervention.
As reported in Lemley 2001,
United Distillers and Vintners, a Scottish company that is
the largest and most profitable spirits distributor in the
world and accounts for over one-third of global grain
whiskey production, uses a genetic algorithm to manage its
inventory and supply. This is a daunting task, requiring
the efficient storage and distribution of over 7 million
barrels containing 60 distinct recipes among a vast system
of warehouses and distilleries, depending on a multitude of
factors such as age, malt number, wood type and market
conditions. Previously, coordinating this complex flow of
supply and demand required five full-time employees. Today,
a few keystrokes on a computer instruct a genetic algorithm
to generate a new schedule each week, and warehouse
efficiency has nearly doubled.
Beasley, Sonander and Havelock
2001 used a GA to schedule airport landings at London
Heathrow, the United Kingdom's busiest airport. This is a
multiobjective problem that involves, among other things,
minimizing delays and maximizing number of flights while
maintaining adequate separation distances between planes
(air vortices that form in a plane's wake can be dangerous
to another flying too closely behind). When compared to
actual schedules from a busy period at the airport, the GA
was able to reduce average wait time by 2-5%, equating to
one to three extra flights taking off and landing per hour
- a significant improvement. However, even greater
improvements have been achieved: as reported in Wired 2002, major international
airports and airlines such as Heathrow, Toronto, Sydney,
Las Vegas, San Francisco, America West Airlines,
AeroMexico, and Delta Airlines are using genetic algorithms
to schedule takeoffs, landings, maintenance and other
tasks, in the form of Ascent Technology's SmartAirport
Operations Center software (see http://www.ascent.com/faq.html).
Breeding and mutating solutions in the form of schedules
