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- From: David.Beasley@cs.cf.ac.uk (David Beasley)
- Newsgroups: comp.ai.genetic,comp.answers,news.answers
- Subject: FAQ: comp.ai.genetic part 3/6 (A Guide to Frequently Asked Questions)
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- Date: 11 Apr 2001 20:23:23 GMT
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- Summary: This is part 3 of a <trilogy> entitled "The Hitch-Hiker's Guide
- to Evolutionary Computation". A periodically published list of Frequently
- Asked Questions (and their answers) about Evolutionary Algorithms,
- Life and Everything. It should be read by anyone who whishes to post
- to the comp.ai.genetic newsgroup, preferably *before* posting.
- Originator: scmdb@thrall.cs.cf.ac.uk
- Xref: senator-bedfellow.mit.edu comp.ai.genetic:21405 comp.answers:44994 news.answers:205230
-
- Archive-name: ai-faq/genetic/part3
- Last-Modified: 4/12/01
- Issue: 9.1
-
- Important note: Do NOT send email to the cs.cf.ac.uk address above: it will
- be ignored. Corrections and other correspondence should be sent to
- david.beasley@iee.org
-
- TABLE OF CONTENTS OF PART 3
- Q2: What applications of EAs are there?
-
- Q3: Who is concerned with EAs?
-
- Q4: How many EAs exist? Which?
- Q4.1: What about Alife systems, like Tierra and VENUS?
-
- Q5: What about all this Optimization stuff?
-
- ----------------------------------------------------------------------
-
- Subject: Q2: What applications of EAs are there?
-
- In principle, EAs can compute any computable function, i.e.
- everything a normal digital computer can do.
-
- But EAs are especially badly suited for problems where efficient ways
- of solving them are already known, (unless these problems are
- intended to serve as benchmarks). Special purpose algorithms, i.e.
- algorithms that have a certain amount of problem domain knowledge
- hard coded into them, will usually outperform EAs, so there is no
- black magic in EC. EAs should be used when there is no other known
- problem solving strategy, and the problem domain is NP-complete.
- That's where EAs come into play: heuristically finding solutions
- where all else fails.
-
- Following is an incomplete (sic!) list of successful EA
- applications:
-
- ARTIFICIAL LIFE
- ARTIFICIAL LIFE (ALIFE) systems attempt to simulate the kind of
- behaviour exhibited by real, living creatures. Not all Artificial
- Life systems employ EVOLUTIONARY ALGORITHMs (see Q4.1).
-
- Framsticks
-
- Framsticks is a three-dimensional life SIMULATION project. Both the
- physical structure of creatures and their control systems are
- evolved. Evolutionary algorithms are used with SELECTION, CROSSOVER
- and MUTATION. Finite element methods are used for simulation. Both
- spontaneous and directed EVOLUTIONs are possible.
-
- This system uses the standard EA framework to evolve 3D agents
- equipped with neural networks. It has proved to be an attractive tool
- for people who want to learn about the way evolutionary OPTIMIZATION
- techniques work.
-
- This is shareware, but all the evolutionary features are available
- free. The project is open, and developers can take part in it, and
- also conduct their own experiments (i.e. using their own GENETIC
- OPERATORs). There are links to the scientific papers on the web
- page, as well as the detailed program documentation. The software is
- quite general and can be used to study a range of problems, including
- coevolution of body and brain.
-
- For more details, see: http://www.frams.poznan.pl/
-
- BIOCOMPUTING
- Biocomputing, or Bioinformatics, is the field of biology dedicated to
- the automatic analysis of experimental data (mostly sequencing data).
- Several approaches to specific biocomputing problems have been
- described that involve the use of GA, GP and simulated annealing.
- General information about biocomputing (software, databases, misc.)
- can be found on the server of the European Bioinformatics Institute:
- http://www.ebi.ac.uk/ebi_home.html ENCORE has a good selection of
- pointers related to this subject. VSCN provides a detailed online
- course on bioinformatics: http://www.techfak.uni-
- bielefeld.de/bcd/Curric/welcome.html
-
- There are three main domains to which GA have been applied in
- Bioinformatics: protein folding, RNA folding, sequence alignment.
-
- Protein Folding
-
- Proteins are one of the essential components of any form of life.
- They are made of twenty different types of amino acid. These amino
- acids are chained together in order to form the protein that can
- contain from a few to several thousands residues. In most of the
- cases, the properties and the function of a protein are a result of
- its three dimensional structure. It seems that in many cases this
- structure is a direct consequence of the sequence. Unfortunately, it
- is still very difficult/impossible to deduce the three dimensional
- structure, knowing only the sequence. A part of the VSCN on-line
- bioinformatics course is dedicated to the use of GAs in Protein
- Folding Prediction. It contains an extensive bibliography and a
- detailed presentation of the subject with LOTS of explanations and
- on-line papers. The URL is: http://www.techfak.uni-
- bielefeld.de/bcd/Curric/ProtEn/contents.html
-
- Koza [KOZA92] gives one example of GP applied to Protein Folding.
- Davis [DAVIS91] gives an example of DNA conformation prediction (a
- closely related problem) in his Handbook of GAs.
-
- RNA Folding
-
- Describing the tertiary structure of an RNA molecule, is about as
- hard as for a protein, but describing the intermediate structure
- (secondary structure) is somehow easier because RNA molecules are
- using the same pairing rules as DNA, (Watson and Crick base pairing).
- There exist deterministic algorithms that given a set of constraints
- (rules), compute the more stable structure, but: (a) their time and
- memory requirement increase quadratically or more with the length of
- the sequences, and (b) they require simplified rules. Lots of effort
- has recently been put into applying GAs to this problem, and several
- papers can be found (on-line if your institute subscribes to these
- journals):
-
- A genetic Algorithm Based Molecular Modelling Technique For RNA Stem-
- loop Structures H. Ogata, Y. Akiyama and M Kanehisa, Nucleic Acid
- Research, 1995, vol 23,3 419-426
-
- An Annealing Mutation Operator in the GA for RNA folding B.A Shapiro
- and J. C. Wu, CABIOS, 1996, vol 12, 3, 171-180
-
- The computer Simulation of RNA Folding Pathway Using a Genetic
- Algorithm A.P. Gultyaev, F.D.H van Batenburg and C. W. A. Pleij in
- Journal of Molecular Biology, 1995, vol 250 37-51
-
- Simulated Annealing has also been applied successfully to this
- problem:
-
- Description of RNA folding by SA M. Schmitz and G. Steger in Journal
- of Molecular Biology, 1995, 255, 245-266
- Sequence Alignments
-
- Sequence Alignment is another important problem of Bioinformatics.
- The aim is to align together several related sequences (from two to
- hundreds) given a cost function. For the most widely used cost
- functions, the problem has been shown to be NP-complete. Several
- attempts have been made using SA:
- Multiple Sequence Alignment Using SA J. Kim, Sakti Pramanik and M.J.
- Chung, CABIOS, 1994, vol 10, 4, 419-426
-
- Multiple Sequence Alignment by Parallel SA M. Isshikawa, T. Koya and
- al, CABIOS, 1993,vol 9, 3, 267-273
-
- SAM, software which uses Hidden Markov Models for Multiple Sequence
- Alignment, can use SA to train the model. Several papers have been
- published on SAM. The software, documentation and an extensive
- bibliography can be found in:
- http://www.cse.ucsc.edu/research/compbio/sam.html
-
- More recently, various software using different methods like Gibbs
- sampling or GAs has been developed:
-
- A Gibbs Sampling Strategy for Multiple Alignment C.E. Lawrence, S. F.
- Altschull and al, Science, October 1993, vol 262, 208-214
-
- SAGA: Sequence Alignment by Genetic Algorithm C. Notredame and D.G.
- Higgins, Nucleic Acid Research, 1995, vol 24, 8,
- 1515-1524
-
- A beta release of SAGA (along with the paper) is available on the
- European Bioinformatics Institute anonymous FTP server:
- ftp.ebi.ac.uk/pub/software/unix/saga.tar.Z
-
- CELLULAR PROGRAMMING: Evolution of Parallel Cellular Machines
- Nature abounds in systems involving the actions of simple, locally-
- interacting components, that give rise to coordinated global
- behavior. These collective systems have evolved by means of natural
- SELECTION to exhibit striking problem-solving capacities, while
- functioning within a complex, dynamic ENVIRONMENT. Employing simple
- yet versatile parallel cellular models, coupled with EVOLUTIONARY
- COMPUTATION techniques, cellular programming is an approach for
- constructing man-made systems that exhibit characteristics such as
- those manifest by their natural counterparts.
-
- Parallel cellular machines hold potential both scientifically, as
- vehicles for studying phenomena of interest in areas such as complex
- adaptive systems and ARTIFICIAL LIFE, as well as practically,
- enabling the construction of novel systems, endowed with
- evolutionary, reproductive, regenerative, and learning capabilities.
-
- Web site: http://lslwww.epfl.ch/~moshes/cp.html
-
- References:
-
- Sipper, M. (1997) "Evolution of Parallel Cellular Machines: The
- Cellular Programming Approach", Springer-Verlag, Heidelberg.
-
- Sipper, M. (1996) "Co-evolving Non-Uniform Cellular Automata to
- Perform Computations", Physica D, 92, 193-208.
-
- Sipper, M. and Ruppin, E. (1997) "Co-evolving architectures for
- cellular machines", Physica D, 99, 428-441.
-
- Sipper, M. and Tomassini, M. (1996) "Generating Parallel Random
- Number Generators By Cellular Programming", International Journal of
- Modern Physics C, 7(2), 181-190.
- Sipper, M. (1997) "Evolving Uniform and Non-uniform Cellular Automata
- Networks", in Annual Reviews of Computational Physics, D. Stauffer
- (ed)
-
- Evolvable Hardware
- The idea of evolving machines, whose origins can be traced to the
- cybernetics movement of the 1940s and the 1950s, has recently
- resurged in the form of the nascent field of bio-inspired systems and
- evolvable hardware. The field draws on ideas from the EVOLUTIONARY
- COMPUTATION domain as well as on novel hardware innovations.
- Recently, the term evolware has been used to describe such evolving
- ware, with current implementations centering on hardware, while
- raising the possibility of using other forms in the future, such as
- bioware. The inaugural workshop, Towards Evolvable Hardware, took
- place in Lausanne, in October 1995, followed by the First
- International Conference on Evolvable Systems: From Biology to
- Hardware (ICES96) held in Japan, in October 1996. Another major event
- in the field, ICES98, was held in Lausanne, Switzerland, in September
- 1998.
-
- References:
-
- Sipper, M. et al (1997) "A Phylogenetic, Ontogenetic, and Epigenetic
- View of Bio-Inspired Hardware Systems", IEEE Transactions on
- Evolutionary Computation, 1(1).
-
- Sanchez, E. and Tomassini, M. (eds) (1996) "Towards Evolvable
- Hardware", Springer-Verlag, Lecture Notes in Computer Science, 1062.
-
- Higuchi, T. et al (1997) "Proceedings of First International
- Conference on Evolvable Systems: From Biology to Hardware (ICES96)",
- Springer-Verlag, Lecture Notes in Computer Science.
-
- GAME PLAYING
- GAs can be used to evolve behaviors for playing games. Work in
- evolutionary GAME THEORY typically surrounds the EVOLUTION of a
- POPULATION of players who meet randomly to play a game in which they
- each must adopt one of a limited number of moves. (Maynard-Smith
- 1982). Let's suppose it is just two moves, X and Y. The players
- receive a reward, analogous to Darwinian FITNESS, depending on which
- combination of moves occurs and which move they adopted. In more
- complicated models there may be several players and several moves.
-
- The players iterate such a game a series of times, and then move on
- to a new partner. At the end of all such moves, the players will have
- a cumulative payoff, their fitness. This fitness can then be used to
- generate a new population.
-
- The real key in using a GA is to come up with an encoding to
- represent player's strategies, one that is amenable to CROSSOVER and
- to MUTATION. Possibilities are to suppose at each iteration a player
- adopts X with some probability (and Y with one minus such). A player
- can thus be represented as a real number, or a bit-string suitably
- interpreted as a probability
-
- An alternative characterisation is to model the players as Finite
- State Machines, or Finite Automata (FA). These can be though of as a
- simple flow chart governing behaviour in the "next" play of the game
- depending upon previous plays. For example:
-
- 100 Play X
- 110 If opponent plays X go to 100
- 120 Play Y
- 130 If opponent plays X go to 100 else go to 120
- represents a strategy that does whatever its opponent did last, and
- begins by playing X, known as "Tit-For-Tat." (Axelrod 1982). Such
- machines can readily be encoded as bit-strings. Consider the encoding
- "1 0 1 0 0 1" to represent TFT. The first three bits, "1 0 1" are
- state 0. The first bit, "1" is interpreted as "Play X." The second
- bit, "0" is interpreted as "if opponent plays X go to state 1," the
- third bit, "1", is interpreted as "if the opponent plays Y, go to
- state 1." State 1 has a similar interpretation. Crossing over such
- bit-strings always yields valid strategies.
- SIMULATIONs in the Prisoner's dilemma have been undertaken (Axelrod
- 1987, Fogel 1993, Miller 1989) of these machines.
-
- Alternative representations of game players include CLASSIFIER
- SYSTEMs (Marimon, McGrattan and Sargent 1990, [GOLD89]), and Neural-
- networks (Fogel and Harrald 1994), though not necessarily with a GA.
- (Fogel 1993), and Fogel and Harrald 1994 use an Evolutionary
- Program). Chellapilla and Fogel (1999) have evolved a neural network
- which can play checkers (draughts) at near expert level.
-
- Other methods of evolving a population can be found in Lindgren 1991,
- Glance and Huberman 1993 and elsewhere.
-
- A GA for playing the game "Mastermind" has been produced. See
- http://kal-el.ugr.es/mastermind
-
- References.
-
- Axelrod, R. (1987) ``The Evolution of Strategies in the Repeated
- Prisoner's Dilemma,'' in [DAVIS91]
-
- Axelrod, R (?) ``The Complexity of Cooperation'' (See the web site,
- which includes code to implement tournaments:
- http://pscs.physics.lsa.umich.edu/Software/ComplexCoop.html )
-
- Chellapilla, K. and Fogel, D.B. (1999) ``Evolution, neural networks,
- games, and intelligence'' , Proc. IEEE, Sept., pp. 1471-1496.
-
- Miller, J.H. (1989) ``The Coevolution of Automata in the Repeated
- Prisoner's Dilemma'' Santa Fe Institute Working Paper 89-003.
-
- Marimon, Ramon, Ellen McGrattan and Thomas J. Sargent (1990) ``Money
- as a Medium of Exchange in an Economy with Artificially Intelligent
- Agents'' Journal of Economic Dynamics and Control 14, pp. 329--373.
-
- Maynard-Smith, (1982) Evolution and the Theory of Games, CUP.
-
- Lindgren, K. (1991) ``Evolutionary Phenomena in Simple Dynamics,'' in
- [ALIFEI].
-
- Holland, J.H and John Miller (1990) ``Artificially Adaptive Agents in
- Economic Theory,'' American Economic Review: Papers and Proceedings
- of the 103rd Annual Meeting of the American Economics Association:
- 365--370.
-
- Huberman, Bernado, and Natalie S. Glance (1993) "Diversity and
- Collective Action" in H. Haken and A. Mikhailov (eds.)
- Interdisciplinary Approaches to Nonlinear Systems, Springer.
-
- Fogel (1993) "Evolving Behavior in the Iterated Prisoner's Dilemma"
- Evolutionary Computation 1:1, 77-97
-
- Fogel, D.B. and Harrald, P. (1994) ``Evolving Complex Behaviour in
- the Iterated Prisoner's Dilemma,'' Proceedings of the Fourth Annual
- Meetings of the Evolutionary Programming Society, L.J. Fogel and A.W.
- Sebald eds., World Science Press.
-
- Lindgren, K. and Nordahl, M.G. "Cooperation and Community Structure
- in Artificial Ecosystems", Artificial Life, vol 1:1&2, 15-38
- Stanley, E.A., Ashlock, D. and Tesfatsion, L. (1994) "Iterated
- Prisoners Dilemma with Choice and Refusal of Partners in [ALIFEIII]
- 131-178
-
- JOB-SHOP SCHEDULING
- The Job-Shop Scheduling Problem (JSSP) is a very difficult NP-
- complete problem which, so far, seems best addressed by sophisticated
- branch and bound search techniques. GA researchers, however, are
- continuing to make progress on it. (Davis 85) started off GA
- research on the JSSP, (Whitley 89) reports on using the edge
- RECOMBINATION operator (designed initially for the TSP) on JSSPs too.
- More recent work includes (Nakano 91),(Yamada & Nakano 92), (Fang et
- al. 93). The latter three report increasingly better results on
- using GAs on fairly large benchmark JSSPs (from Muth & Thompson 63);
- neither consistently outperform branch & bound search yet, but seem
- well on the way. A crucial aspect of such work (as with any GA
- application) is the method used to encode schedules. An important
- aspect of some of the recent work on this is that better results have
- been obtained by rejecting the conventional wisdom of using binary
- representations (as in (Nakano 91)) in favor of more direct
- encodings. In (Yamada & Nakano 92), for example, a GENOME directly
- encodes operation completion times, while in (Fang et al. 93) genomes
- represent implicit instructions for building a schedule. The success
- of these latter techniques, especially since their applications are
- very important in industry, should eventually spawn advances in GA
- theory.
-
- Concerning the point of using GAs at all on hard job-shop scheduling
- problems, the same goes here as suggested above for `Timetabling':
- The GA approach enables relatively arbitrary constraints and
- objectives to be incorporated painlessly into a single OPTIMIZATION
- method. It is unlikely that GAs will outperform specialized
- knowledge-based and/or conventional OR-based approaches to such
- problems in terms of raw solution quality, however GAs offer much
- greater simplicity and flexibility, and so, for example, may be the
- best method for quick high-quality solutions, rather than finding the
- best possible solution at any cost. Also, of course, hybrid methods
- will have a lot to offer, and GAs are far easier to parallelize than
- typical knowledge-based/OR methods.
-
- Similar to the JSSP is the Open Shop Scheduling Problem (OSSP).
- (Fang et al. 93) reports an initial attempt at using GAs for this.
- Ongoing results from the same source shows reliable achievement of
- results within less than 0.23% of optimal on moderately large OSSPs
- (so far, up to 20x20), including an improvement on the previously
- best known solution for a benchmark 10x10 OSSP. A simpler form of job
- shop problem is the Flow-Shop Sequencing problem; recent successful
- work on applying GAs to this includes (Reeves 93)."
-
- Other scheduling problems
-
- In contrast to job shop scheduling some maintenance scheduling
- problems consider which activities to schedule within a planned
- maintenance period, rather than seeking to minimise the total time
- taken by the activities. The constraints on which parts may be taken
- out of service for maintenance at particular times may be very
- complex, particularly as they will in general interact. Some initial
- work is given in (Langdon, 1995).
-
- References
-
- Davis, L. (1985) "Job-Shop Scheduling with Genetic Algorithms",
- [ICGA85], 136-140.
-
- Muth, J.F. & Thompson, G.L. (1963) "Industrial Scheduling". Prentice
- Hall, Englewood Cliffs, NJ, 1963.
- Nakano, R. (1991) "Conventional Genetic Algorithms for Job-Shop
- Problems", [ICGA91], 474-479.
-
- Reeves, C.R. (1993) "A Genetic Algorithm for Flowshop Sequencing",
- Coventry Polytechnic Working Paper, Coventry, UK.
-
- Whitley, D., Starkweather, T. & D'Ann Fuquay (1989) "Scheduling
- Problems and Traveling Salesmen: The Genetic Edge Recombination
- Operator", [ICGA89], 133-140.
-
- Fang, H.-L., Ross, P., & Corne D. (1993) "A Promising Genetic
- Algorithm Approach to Job-Shop Scheduling, Rescheduling & Open-Shop
- Scheduling Problems", [ICGA93], 375-382.
-
- Yamada, T. & Nakano, R. (1992) "A Genetic Algorithm Applicable to
- Large-Scale Job-Shop Problems", [PPSN92], 281-290.
-
- Langdon, W.B. (1995) "Scheduling Planned Maintenance of the (UK)
- National Grid", cs.ucl.ac.uk/genetic/papers/grid_aisb-95.ps
-
- MANAGEMENT SCIENCES
- "Applications of EA in management science and closely related fields
- like organizational ecology is a domain that has been covered by some
- EA researchers - with considerable bias towards scheduling problems.
- Since I believe that EA have considerable potential for applications
- outside the rather narrow domain of scheduling and related
- combinatorial problems, I started collecting references about the
- status quo of EA-applications in management science. This report
- intends to make available my findings to other researchers in the
- field. It is a short overview and lists some 230 references to
- current as well as finished research projects. [..]
-
- "At the end of the paper, a questionnaire has been incorporated that
- may be used for this purpose. Other comments are also appreciated."
-
- --- from the Introduction of (Nissen 93)
-
- References
-
- Nissen, V. (1993) "Evolutionary Algorithms in Management Science: An
- Overview and List of References", Papers on Economics and Evolution,
- edited by the European Study Group for Evolutionary Economics. This
- report is also avail. via anon. FTP from
- ftp.gwdg.de/pub/msdos/reports/wi/earef.eps
-
- Boulding, K.E. (1991) "What is evolutionary economics?", Journal of
- Evolutionary Economics, 1, 9-17.
-
- NON-LINEAR FILTERING
- New connections between GENETIC ALGORITHMs and Non Linear Filtering
- Theory have been established. GAs have already been successfully
- applied to a large class of non-linear filtering problems such as
- RADAR / SONAR/ GPS signal processing. This relatively new branch of
- GA application has also lead to new results on the convergence of
- GAs: large deviations, fluctuations...
-
- Some preprints and references on this topic are available in the web
- page: http://www-sv.cict.fr/lsp/Delmoral/index.html
-
- The new results also points out some natural connections between:
- genetic type algorithms, information theory, non-linear filtering
- theory, interacting and branching particle systems.
-
- TIMETABLING
- This has been addressed quite successfully with GAs. A very common
- manifestation of this kind of problem is the timetabling of exams or
- classes in Universities, etc.
-
- The first application of GAs to the timetabling problem was to build
- the schedule of the teachers in an Italian high school. The
- research, conducted at the Department of Electronics and Information
- of Politecnico di Milano, Italy, showed that a GA was as good as Tabu
- Search, and better than simulated annealing, at finding teacher
- schedules satisfying a number of hard and soft constraints. The
- software package developed is now in current use in some high schools
- in Milano. (Colorni et al 1990)
-
- At the Department of Artificial Intelligence, University of
- Edinburgh, timetabling the MSc exams is now done using a GA (Corne et
- al. 93, Fang 92). An example of the use of GAs for timetabling
- classes is (Abramson & Abela 1991).
-
- In the exam timetabling case, the FITNESS function for a GENOME
- representing a timetable involves computing degrees of punishment for
- various problems with the timetable, such as clashes, instances of
- students having to take consecutive exams, instances of students
- having (eg) three or more exams in one day, the degree to which
- heavily-subscribed exams occur late in the timetable (which makes
- marking harder), overall length of timetable, etc. The modular nature
- of the fitness function has the key to the main potential strength of
- using GAs for this sort of thing as opposed to using conventional
- search and/or constraint programming methods. The power of the GA
- approach is the ease with which it can handle arbitrary kinds of
- constraints and objectives; all such things can be handled as
- weighted components of the fitness function, making it easy to adapt
- the GA to the particular requirements of a very wide range of
- possible overall objectives . Very few other timetabling methods, for
- example, deal with such objectives at all, which shows how difficult
- it is (without GAs) to graft the capacity to handle arbitrary
- objectives onto the basic "find shortest- length timetable with no
- clashes" requirement. The proper way to weight/handle different
- objectives in the fitness function in relation to the general GA
- dynamics remains, however, an important research problem!
-
- GAs thus offer a combination of simplicity, flexibility & speed which
- competes very favorably with other approaches, but are unlikely to
- outperform knowledge-based (etc) methods if the best possible
- solution is required at any cost. Even then, however, hybridisation
- may yield the best of both worlds; also, the ease (if the hardware is
- available!) of implementing GAs in parallel enhances the possibility
- of using them for good, fast solutions to very hard timetabling and
- similar problems.
-
- References
-
- Abramson & Abela (1991) "A Parallel Genetic Algorithm for Solving the
- School Timetabling Problem", Technical Report, Division of I.T.,
- C.S.I.R.O, April 1991. (Division of Information Technology,
- C.S.I.R.O., c/o Dept. of Communication & Electronic Engineering,
- Royal Melbourne Institute of Technology, PO BOX 2476V, Melbourne
- 3001, Australia)
-
- Colorni A., M. Dorigo & V. Maniezzo (1990). Genetic Algorithms And
- Highly Constrained Problems: The Time-Table Case. Proceedings of the
- First International Workshop on Parallel Problem Solving from Nature,
- Dortmund, Germany, Lecture Notes in Computer Science 496, Springer-
- Verlag, 55-59.
- http://iridia.ulb.ac.be/dorigo/dorigo/conferences/IC.01-PPSN1.ps.gz
-
- Colorni A., M. Dorigo & V. Maniezzo (1990). Genetic Algorithms: A
- New Approach to the Time-Table Problem. NATO ASI Series, Vol.F 82,
- COMBINATORIAL OPTIMIZATION, (Ed. M.Akguel and others), Springer-
- Verlag, 235-239.
- http://iridia.ulb.ac.be/dorigo/dorigo/conferences/IC.02-NATOASI90.ps.gz
-
- Colorni A., M. Dorigo & V. Maniezzo (1990). A Genetic Algorithm to
- Solve the Timetable Problem. Technical Report No. 90-060,
- Politecnico di Milano, Italy.
- http://iridia.ulb.ac.be/dorigo/dorigo/tec.reps/TR.01-TTP.ps.gz
- Corne, D. Fang, H.-L. & Mellish, C. (1993) "Solving the Modular Exam
- Scheduling Problem with Genetic Algorithms". Proc. of 6th Int'l
- Conf. on Industrial and Engineering Applications of Artificial
- Intelligence & Expert Systems, ISAI.
-
- Fang, H.-L. (1992) "Investigating GAs for scheduling", MSc
- Dissertation, University of Edinburgh Dept. of Artificial
- Intelligence, Edinburgh, UK.
-
- ------------------------------
-
- Subject: Q3: Who is concerned with EAs?
-
- EVOLUTIONARY COMPUTATION attracts researchers and people of quite
- dissimilar disciplines, i.e. EC is a interdisciplinary research
- field:
-
- Computer scientists
- Want to find out about the properties of sub-symbolic information
- processing with EAs and about learning, i.e. adaptive systems in
- general.
-
- They also build the hardware necessary to enable future EAs
- (precursors are already beginning to emerge) to huge real world
- problems, i.e. the term "massively parallel computation" [HILLIS92],
- springs to mind.
-
- Engineers
- Of many kinds want to exploit the capabilities of EAs on many areas
- to solve their application, esp. OPTIMIZATION problems.
-
- Roboticists
- Want to build MOBOTs (MOBile ROBOTs, i.e. R2D2's and #5's cousins)
- that navigate through uncertain ENVIRONMENTs, without using built-in
- "maps". The MOBOTS thus have to adapt to their surroundings, and
- learn what they can do "move-through-door" and what they can't "move-
- through-wall" on their own by "trial-and-error".
-
- Cognitive scientists
- Might view CFS as a possible apparatus to describe models of thinking
- and cognitive systems.
-
- Physicists
- Use EC hardware, e.g. Hillis' (Thinking Machine Corp.'s) Connection
- Machine to model real world problems which include thousands of
- variables, that run "naturally" in parallel, and thus can be modelled
- more easily and esp. "faster" on a parallel machine, than on a
- serial "PC" one.
-
- Biologists
- Are finding EAs useful when it comes to protein folding and other
- such bio-computational problems (see Q2).
-
- EAs can also be used to model the behaviour of real POPULATIONs of
- organisms. Some biologists are hostile to modeling, but an entire
- community of Population Biologists arose with the 'evolutionary
- synthesis' of the 1930's created by the polymaths R.A. Fisher, J.B.S.
- Haldane, and S. Wright. Wright's SELECTION in small populations,
- thereby avoiding local optima) is of current interest to both
- biologists and ECers -- populations are naturally parallel.
-
- A good exposition of current population Biology modeling is J.
- Maynard Smith's text Evolutionary Genetics. Richard Dawkin's Selfish
- Gene and Extended Phenotype are unparalleled (sic!) prose expositions
- of evolutionary processes. Rob Collins' papers are excellent
- parallel GA models of evolutionary processes (available in [ICGA91]
- and by FTP from ftp.cognet.ucla.edu/pub/alife/papers/ ).
-
- As fundamental motivation, consider Fisher's comment: "No practical
- biologist interested in (e.g.) sexual REPRODUCTION would be led to
- work out the detailed consequences experienced by organisms having
- three or more sexes; yet what else should [s/]he do if [s/]he wishes
- to understand why the sexes are, in fact, always
- two?" (Three sexes would make for even weirder grammar, [s/]he
- said...)
-
- Chemists
- And in particular biochemists and molecular chemists, are interested
- in problems such as the conformational analysis of molecular clusters
- and related problems in molecular sciences. The application of GAs
- to molecular systems has opened an interesting area of research and
- the number of chemists involved in it increases day-by-day.
-
- Some typical research topics include:
-
- o protein folding; o conformational analysis and energy
- minimization; o docking algorithms for drug-design; o solvent site
- prediction in macromolecules;
- Several papers have been published in journals such as Journal of
- Computational Chemistry and Journal of Computer-Aided Design.
-
- Some interesting WWW sites related to the applications of GAs to
- chemistry (or molecular science in general) include:
-
- o http://garage.cps.msu.edu/projects/biochem/biochem.html about GAs
- in biochemistry (water site prediction, drug-design and protein
- folding); o
- http://www.tc.cornell.edu/Edu/SPUR/SPUR94/Main/John.html about the
- application of GAs to the search of conformational energy minima;
- o http://cmp.ameslab.gov/cmp/CMP_Theory/gsa/gen2.html By using a
- GA in combiation with a Tight-binding model, David Deaven and Kai-
- Ming Ho founded fullerene cages (including C60) starting from
- random coordinates.
- See also Q2 for applications in biocomputing.
-
- Philosophers
- and some other really curious people may also be interested in EC for
- various reasons.
-
- ------------------------------
-
- Subject: Q4: How many EAs exist? Which?
-
- The All Stars
- There are currently 3 main paradigms in EA research: GENETIC
- ALGORITHMs, EVOLUTIONARY PROGRAMMING, and EVOLUTION STRATEGIEs.
- CLASSIFIER SYSTEMs and GENETIC PROGRAMMING are OFFSPRING of the GA
- community. Besides this leading crop, there are numerous other
- different approaches, alongside hybrid experiments, i.e. there exist
- pieces of software residing in some researchers computers, that have
- been described in papers in conference proceedings, and may someday
- prove useful on certain tasks. To stay in EA slang, we should think
- of these evolving strands as BUILDING BLOCKs, that when recombined
- someday, will produce new offspring and give birth to new EA
- paradigm(s).
-
- One such interesting offspring is the Memetic Algorithm. This is a
- hybrid evolutionary algorithm, which makes use of local search
- operators. For details, see
- http://www.densis.fee.unicamp.br/~moscato/memetic_home.html
-
- Promising Rookies
- As far as "solving complex function and COMBINATORIAL OPTIMIZATION
- tasks" is concerned, Davis' work on real-valued representations and
- adaptive operators should be mentioned (Davis 89). Moreover Whitley's
- Genitor system incorporating ranking and "steady state" mechanism
- (Whitley 89), Goldberg's "messy GAs", involves adaptive
- representations (Goldberg 91), and Eshelman's CHC algorithm (Eshelman
- 91). For real FUNCTION OPTIMIZATION, Differential EVOLUTION seems
- hard to beat in terms of convergence speed as well as simplicity:
- With just three control variables, tuning is particularly easy to do.
-
- For "the design of robust learning systems", i.e. the field
- characterized by CFS, Holland's (1986) CLASSIFIER SYSTEM, with its
- state-of-the-art implementation CFS-C (Riolo 88), we should note
- developments in SAMUEL (Grefenstette 89), GABIL (De Jong & Spears
- 91), and GIL (Janikow 91).
-
- References
-
- Davis, L. (1989) "Adapting operator probabilities in genetic
- algorithms", [ICGA89], 60-69.
-
- De Jong K.A. & Spears W. (1991) "Learning concept classification
- rules using genetic algorithms". Proc. 12th IJCAI, 651-656, Sydney,
- Australia: Morgan Kaufmann.
-
- Dorigo M. & E. Sirtori (1991)."ALECSYS: A Parallel Laboratory for
- Learning Classifier Systems". Proceedings of the Fourth International
- Conference on Genetic Algorithms, San Diego, California, R.K.Belew
- and L.B.Booker (Eds.), Morgan Kaufmann, 296-302.
-
- Dorigo M. (1995). "ALECSYS and the AutonoMouse: Learning to Control a
- Real Robot by Distributed Classifier Systems". Machine Learning, 19,
- 3, 209-240.
-
- Eshelman, L.J. et al. (1991) "Preventing premature convergence in
- genetic algorithms by preventing incest", [ICGA91], 115-122.
-
- Goldberg, D. et al. (1991) "Don't worry, be messy", [ICGA91], 24-30.
-
- Grefenstette, J.J. (1989) "A system for learning control strategies
- with genetic algorithms", [ICGA89], 183-190.
-
- Holland, J.H. (1986) "Escaping brittleness: The possibilities of
- general-purpose learning algorithms applied to parallel rule-based
- systems". In R. Michalski, J. Carbonell, T. Mitchell (eds), Machine
- Learning: An Artificial Intelligence Approach. Los Altos: Morgan
- Kaufmann.
-
- Janikow C. (1991) "Inductive learning of decision rules from
- attribute-based examples: A knowledge-intensive Genetic Algorithm
- approach". TR91-030, The University of North Carolina at Chapel Hill,
- Dept. of Computer Science, Chapel Hill, NC.
-
- Riolo, R.L. (1988) "CFS-C: A package of domain independent
- subroutines for implementing classifier systems in arbitrary, user-
- defined environments". Logic of computers group, Division of
- computer science and engineering, University of Michigan.
-
- Whitley, D. et al. (1989) "The GENITOR algorithm and selection
- pressure: why rank-based allocation of reproductive trials is best",
- [ICGA89], 116-121.
-
- ------------------------------
-
- Subject: Q4.1: What about Alife systems, like Tierra and VENUS?
-
- None of these are EVOLUTIONARY ALGORITHMs, but all of them use the
- evolutionary metaphor as their "playing field".
-
- Tierra
- Synthetic organisms have been created based on a computer metaphor of
- organic life in which CPU time is the ``energy'' resource and memory
- is the ``material'' resource. Memory is organized into informational
- patterns that exploit CPU time for self-replication. MUTATION
- generates new forms, and EVOLUTION proceeds by natural SELECTION as
- different GENOTYPEs compete for CPU time and memory space.
-
- Observation of nature shows that evolution by natural selection is
- capable of both OPTIMIZATION and creativity. Artificial models of
- evolution have demonstrated the optimizing ability of evolution, as
- exemplified by the field of GENETIC ALGORITHMs. The creative aspects
- of evolution have been more elusive to model. The difficulty derives
- in part from a tendency of models to specify the meaning of the
- ``genome'' of the evolving entities, precluding new meanings from
- emerging. I will present a natural model of evolution demonstrating
- both optimization and creativity, in which the GENOME consists of
- sequences of executable machine code.
-
- From a single rudimentary ancestral ``creature'', very quickly there
- evolve parasites, which are not able to replicate in isolation
- because they lack a large portion of the genome. However, these
- parasites search for the missing information, and if they locate it
- in a nearby creature, parasitize the information from the neighboring
- genome, thereby effecting their own replication.
-
- In some runs, hosts evolve immunity to attack by parasites. When
- immune hosts appear, they often increase in frequency, devastating
- the parasite POPULATIONs. In some runs where the community comes to
- be dominated by immune hosts, parasites evolve that are resistant to
- immunity.
-
- Hosts sometimes evolve a response to parasites that goes beyond
- immunity, to actual (facultative) hyper-parasitism. The hyper-
- parasite deceives the parasite causing the parasite to devote its
- energetic resources to replication of the hyper-parastie genome.
- This drives the parasites to extinction. Evolving in the absence of
- parasites, hyper-parasites completely dominate the community,
- resulting in a relatively uniform community characterized by a high
- degree of relationship between INDIVIDUALs. Under these
- circumstances, sociality evolves, in the form of creatures which can
- only replicate in aggregations.
-
- The cooperative behavior of the social hyper-parasites makes them
- vulnerable to a new class of parasites. These cheaters, hyper-hyper-
- parasites, insert themselves between cooperating social individuals,
- deceiving the social creatures, causing them to replicate the genomes
- of the cheaters.
-
- The only genetic change imposed on the simulator is random bit flips
- in the machine code of the creatures. However, it turns out that
- parasites are very sloppy replicators. They cause significant
- RECOMBINATION and rearrangement of the genomes. This spontaneous
- sexuality is a powerful force for evolutionary change in the system.
-
- One of the most interesting aspects of this instance of life is that
- the bulk of the evolution is based on adaptation to the biotic
- ENVIRONMENT rather than the physical environment. It is co-evolution
- that drives the system.
-
- --- "Tierra announcement" by Tom Ray (1991)
- How to get Tierra?
- Tierra is available (source and executables, for Unix and NT) from
- alife.santafe.edu/pub/SOFTWARE/Tierra
- .
-
- Related work
-
- David Bennett <dmb@pfxcorp.com> reported in March 2000: Much new work
- has been done in Tierra since 1993. Thomas Ray
- <tray@mail.nhn.ou.edu> is now working in Japan. I have been using
- another similar system called Avida. It has some advantages, and a
- significant body of research results. The contact for Avida is
- <avida@krl.caltech.edu>.
-
- References
-
- Ray, T. S. (1991) "Is it alive, or is it GA?" in [ICGA91], 527--534.
-
- Ray, T. S. (1991) "An approach to the synthesis of life." in
- [ALIFEII], 371--408.
-
- Ray, T. S. (1991) "Population dynamics of digital organisms." in
- [ALIFEII].
-
- Ray, T. S. (1991) "Evolution and optimization of digital
- organisms." Scientific Excellence in Supercomputing: The IBM 1990
- Contest Prize Papers, Eds. Keith R. Billingsley, Ed Derohanes, Hilton
- Brown, III. Athens, GA, 30602, The Baldwin Press, The University of
- Georgia.
-
- Ray, T. S. (1992) "Evolution, ecology and optimization of digital
- organisms." Santa Fe Institute working paper 92-08-042.
-
- Ray, T. S. "Evolution, complexity, entropy, and artificial reality."
- submitted Physica D.
-
- Ray, T. S. (1993) "An evolutionary approach to synthetic biology,
- Zen and the art of creating life. Artificial Life 1(1).
-
- VENUS
- Steen Rasmussen's (et al.) VENUS I+II "coreworlds" as described in
- [ALIFEII] and [LEVY92], are inspired by A.K. Dewdney's well-known
- article (Dewdney 1984). Dewdney proposed a game called "Core Wars",
- in which hackers create computer programs that battle for control of
- a computer's "core" memory (Strack 93). Since computer programs are
- just patterns of information, a successful program in core wars is
- one that replicates its pattern within the memory, so that eventually
- most of the memory contains its pattern rather than that of the
- competing program.
-
- VENUS is a modification of Core Wars in which the Computer programs
- can mutate, thus the pseudo assembler code creatures of VENUS evolve
- steadily. Furthermore each memory location is endowed with
- "resources" which, like sunshine are added at a steady state. A
- program must have sufficient resources in the regions of memory it
- occupies in order to execute. The input of resources determines
- whether the VENUS ecosystem is a "jungle" or a "desert." In jungle
- ENVIRONMENTs, Rasmussen et al. observe the spontaneous emergence of
- primitive "copy/split" organisms starting from (structured) random
- initial conditions.
-
- --- [ALIFEII], p.821
-
- Dewdney, A.K. (1984) "Computer Recreations: In the Game called Core
- War Hostile Programs Engage in a Battle of Bits", Sci. Amer. 250(5),
- 14-22.
- Farmer & Belin (1992) "Artificial Life: The Coming Evolution",
- [ALIFEII], 815-840.
-
- Rasmussen, et al. (1990) "The Coreworld: Emergence and Evolution of
- Cooperative Structures in a Computational Chemistry", [FORREST90],
- 111-134.
-
- Rasmussen, et al. (1992) "Dynamics of Programmable Matter",
- [ALIFEII], 211-254.
-
- Strack (1993) "Core War Frequently Asked Questions (
- rec.games.corewar FAQ)" Avail. by anon. FTP from
- rtfm.mit.edu/pub/usenet/news.answers/games/corewar-faq.Z
-
- PolyWorld
- Larry Yaeger's PolyWorld as described in [ALIFEIII] and [LEVY92] is
- available via anonymous FTP from
- alife.santafe.edu/pub/SOFTWARE/Polyworld/
-
- "The subdirectories in this "polyworld" area contain the source code
- for the PolyWorld ecological simulator, designed and written by Larry
- Yaeger, and Copyright 1990, 1991, 1992 by Apple Computer.
-
- PostScript versions of my ARTIFICIAL LIFE III technical paper have
- now been added to the directory. These should be directly printable
- from most machines. Because some unix systems' "lpr" commands cannot
- handle very large files (ours at least), I have split the paper into
- Yaeger.ALife3.1.ps and Yaeger.ALife3.2.ps. These files can be ftp-ed
- in "ascii" mode. For unix users I have also included compressed
- versions of both these files (indicated by the .Z suffix), but have
- left the uncompressed versions around for people connecting from non-
- unix systems. I have not generated PostScript versions of the
- images, because they are color and the resulting files are much too
- large to store, retrieve, or print. Accordingly, though I have
- removed a Word-formatted version of the textual body of the paper
- that used to be here, I have left a Word-formatted version of the
- color images. If you wish to acquire it, you will need to use the
- binary transfer mode to move it to first your unix host and then to a
- Macintosh (unless Word on a PC can read it - I don't know), and you
- may need to do something nasty like use ResEdit to set the file type
- and creator to match those of a standard Word document (Type = WDBN,
- Creator = MSWD). [..]"
-
- --- from the README by Larry Yaeger <larryy@apple.com>
-
- General Alife repositories?
- Also, all of the following FTP sites carry ALIFE related info:
-
- ftp.cognet.ucla.edu/pub/alife/ ,
- life.anu.edu.au/pub/complex_systems/alife/ ,
- ftp.cogs.susx.ac.uk/pub/reports/csrp/ , xyz.lanl.gov/nlin-sys/ ,
- alife.santafe.edu/pub/ .
-
- ------------------------------
-
- Subject: Q5: What about all this Optimization stuff?
-
- Just think of an OPTIMIZATION problem as a black box. A large black
- box. As large as, for example, a Coca-Cola vending machine. Now, we
- don't know anything about the inner workings of this box, but see,
- that there are some regulators to play with, and of course we know,
- that we want to have a bottle of the real thing...
-
- Putting this everyday problem into a mathematical model, we proceed
- as follows:
-
- (1) we label all the regulators with x and a number starting from 1;
- the result is a vector x, i.e. (x_1,...,x_n), where n is the
- number of visible regulators.
-
- (2) we must find an objective function, in this case it's obvious, we
- want to get k bottles of the real thing, where k is equal to 1.
- [some might want a "greater or equal" here, but we restricted
- ourselves to the visible regulators (we all know that sometimes a
- "kick in the right place" gets use more than 1, but I have no
- idea how to put this mathematically...)]
-
- (3) thus, in the language some mathematicians prefer to speak in:
- f(x) = k = 1. So, what we have here is a maximization problem
- presented in a form we know from some boring calculus lessons,
- and we also know that there at least a dozen utterly
- uninteresting techniques to solve problems presented this way...
-
- What can we do in order to solve this problem?
- We can either try to gain more knowledge or exploit what we already
- know about the interior of the black box. If the objective function
- turns out to be smooth and differentiable, analytical methods will
- produce the exact solution.
-
- If this turns out to be impossible, we might resort to the brute
- force method of enumerating the entire SEARCH SPACE. But with the
- number of possibilities growing exponentially in n, the number of
- dimensions (inputs), this method becomes infeasible even for low-
- dimensional spaces.
-
- Consequently, mathematicians have developed theories for certain
- kinds of problems leading to specialized OPTIMIZATION procedures.
- These algorithms perform well if the black box fulfils their
- respective prerequisites. For example, Dantzig's simplex algorithm
- (Dantzig 66) probably represents the best known multidimensional
- method capable of efficiently finding the global optimum of a linear,
- hence convex, objective function in a search space limited by linear
- constraints. (A USENET FAQ on linear programming is maintained by
- Professor Robert Fourer <4er@iems.nwu.edu> (and "nonlinear-
- programming-faq") that is posted monthly to sci.op-research and is
- mostly interesting to read. It is also available from http://www-
- unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html )
-
- Gradient strategies are no longer tied to these linear worlds, but
- they smooth their world by exploiting the objective function's first
- partial derivatives one has to supply in advance. Therefore, these
- algorithms rely on a locally linear internal model of the black box.
-
- Newton strategies additionally require the second partial
- derivatives, thus building a quadratic internal model. Quasi-Newton,
- conjugate gradient and variable metric strategies approximate this
- information during the search.
-
- The deterministic strategies mentioned so far cannot cope with
- deteriorations, so the search will stop if anticipated improvements
- no longer occur. In a multimodal ENVIRONMENT these algorithms move
- "uphill" from their respective starting points. Hence, they can only
- converge to the next local optimum.
-
- Newton-Raphson-methods might even diverge if a discrepancy between
- their internal assumptions and reality occurs. But of course, these
- methods turn out to be superior if a given task matches their
- requirements. Not relying on derivatives, polyeder strategy, pattern
- search and rotating coordinate search should also be mentioned here
- because they represent robust non-linear optimization algorithms
- (Schwefel 81).
-
- Dealing with technical optimization problems, one will rarely be able
- to write down the objective function in a closed form. We often need
- a SIMULATION model in order to grasp reality. In general, one cannot
- even expect these models to behave smoothly. Consequently,
- derivatives do not exist. That is why optimization algorithms that
- can successfully deal with black box-type situations have been
- developed. The increasing applicability is of course paid for by a
- loss of "convergence velocity," compared to algorithms specially
- designed for the given problem. Furthermore, the guarantee to find
- the global optimum no longer exists!
-
- But why turn to nature when looking for more powerful algorithms?
- In the attempt to create tools for various purposes, mankind has
- copied, more often instinctively than geniously, solutions invented
- by nature. Nowadays, one can prove in some cases that certain forms
- or structures are not only well adapted to their ENVIRONMENT but have
- even reached the optimum (Rosen 67). This is due to the fact that the
- laws of nature have remained stable during the last 3.5 billion
- years. For instance, at branching points the measured ratio of the
- diameters in a system of blood-vessels comes close to the theoretical
- optimum provided by the laws of fluid dynamics (2^-1/3). This, of
- course, only represents a limited, engineering point of view on
- nature. In general, nature performs adaptation, not optimization.
-
- The idea to imitate basic principles of natural processes for optimum
- seeking procedures emerged more than three decades ago (cf Q10.3).
- Although these algorithms have proven to be robust and direct
- OPTIMIZATION tools, it is only in the last five years that they have
- caught the researchers' attention. This is due to the fact that many
- people still look at organic EVOLUTION as a giantsized game of dice,
- thus ignoring the fact that this model of evolution cannot have
- worked: a human germ-cell comprises approximately 50,000 GENEs, each
- of which consists of about 300 triplets of nucleic bases. Although
- the four existing bases only encode 20 different amino acids,
- 20^15,000,000, ie circa 10^19,500,000 different GENOTYPEs had to be
- tested in only circa 10^17 seconds, the age of our planet. So, simply
- rolling the dice could not have produced the diversity of today's
- complex living systems.
-
- Accordingly, taking random samples from the high-dimensional
- parameter space of an objective function in order to hit the global
- optimum must fail (Monte-Carlo search). But by looking at organic
- evolution as a cumulative, highly parallel sieving process, the
- results of which pass on slightly modified into the next sieve, the
- amazing diversity and efficiency on earth no longer appears
- miraculous. When building a model, the point is to isolate the main
- mechanisms which have led to today's world and which have been
- subjected to evolution themselves. Inevitably, nature has come up
- with a mechanism allowing INDIVIDUALs of one SPECIES to exchange
- parts of their genetic information (RECOMBINATION or CROSSOVER), thus
- being able to meet changing environmental conditions in a better way.
-
- Dantzig, G.B. (1966) "Lineare Programmierung und Erweiterungen",
- Berlin: Springer. (Linear programming and extensions)
-
- Kursawe, F. (1994) " Evolution strategies: Simple models of natural
- processes?", Revue Internationale de Systemique, France (to appear).
-
- Rosen, R. (1967) "Optimality Principles in Biologie", London:
- Butterworth.
-
- Schwefel, H.-P. (1981) "Numerical Optimization of Computer Models",
- Chichester: Wiley.
-
- ------------------------------
-
- Copyright (c) 1993-2000 by J. Heitkoetter and D. Beasley, all rights
- reserved.
-
- This FAQ may be posted to any USENET newsgroup, on-line service, or
- BBS as long as it is posted in its entirety and includes this
- copyright statement. This FAQ may not be distributed for financial
- gain. This FAQ may not be included in commercial collections or
- compilations without express permission from the author.
-
- End of ai-faq/genetic/part3
- ***************************
-
- --
-
-