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:
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, 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.
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.
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 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://ftp.ebi.ac.uk/pub/software/unix/saga.tar.Z
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
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)
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.
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.
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 120represents 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
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
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).
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", ftp://cs.ucl.ac.uk/genetic/papers/grid_aisb-95.ps
"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)
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://ftp.gwdg.de/pub/msdos/reports/wi/earef.eps
Boulding, K.E. (1991) "What is evolutionary economics?", Journal of Evolutionary Economics, 1, 9-17.
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.
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.
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.
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Hitch Hiker's Guide to Evolutionary Computation, Issue 9.1, released 12 April 2001
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