Genetic algorithms are implemented as a computer simulation in which a population of abstract representations (called chromosomes or the genotype or the genome) of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem evolves toward better solutions. Traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified (recombined and possibly mutated) to form a new population. The new population is then used in the next iteration of the algorithm.
Genetic algorithms find application in computer science, engineering, economics,chemistry, physics, mathematics and other fields.
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GA procedure
A typical genetic algorithm requires two things to be defined:
- a genetic representation of the solution domain,
- a fitness function to evaluate the solution domain.
A standard representation of the solution is as an array of bits. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, that facilitates simple crossover operation. Variable length representations were also used, but crossover implementation is more complex in this case. Tree-like representations are explored in Genetic programming and free-form representations are explored in HBGA.
The fitness function is defined over the genetic representation and measures the quality of the represented solution. The fitness function is always problem dependent. For instance, in the knapsack problem we want to maximize the total value of objects that we can put in a knapsack of some fixed capacity. A representation of a solution might be an array of bits, where each bit represents a different object, and the value of the bit (0 or 1) represents whether or not the object is in the knapsack. Not every such representation is valid, as the size of objects may exceed the capacity of the knapsack. The fitness of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise. In some problems, it is hard or even impossible to define the fitness expression; in these cases, interactive genetic algorithms are used.
Once we have the genetic representation and the fitness function defined, GA proceeds to initialize a population of solutions randomly, then improve it through repetitive application of mutation, crossover, and selection operators.
Initialization
Initially many individual solutions are randomly generated to form an initial population. The population size depends on the nature of the problem, but typically contains several hundreds or thousands of possible solutions. Traditionally, the population is generated randomly, covering the entire range of possible solutions (the search space). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found.
Selection
During each successive epoch, a proportion of the existing population is selected to breed a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as this process may be very time-consuming.
Most functions are stochastic and designed so that a small proportion of less fit solutions are selected. This helps keep the diversity of the population large, preventing premature convergence on poor solutions. Popular and well-studied selection methods include roulette wheel selection and tournament selection.
Reproduction
The next step is to generate a second generation population of solutions from those selected through genetic operators: crossover (also called recombination), and/or mutation.
For each new solution to be produced, a pair of "parent" solutions is selected for breeding from the pool selected previously. By producing a "child" solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its "parents". New parents are selected for each child, and the process continues until a new population of solutions of appropriate size is generated.
These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally the average fitness will have increased by this procedure for the population, since only the best organisms from the first generation are selected for breeding, along with a small proportion of less fit solutions, for reasons already mentioned above.
Termination
This generational process is repeated until a termination condition has been reached. Common terminating conditions are
- A solution is found that satisfies minimum criteria
- Fixed number of generations reached
- Allocated budget (computation time/money) reached
- The highest ranking solution's fitness is reaching or has reached a plateau such that successive iterations no longer produce better results
- Manual inspection
- Combinations of the above
Pseudo-code algorithm
Choose initial population Evaluate the fitnesses of individuals in the population Repeat Select best-ranking individuals to reproduce Breed new generation through crossover and mutation (genetic operations) and give birth to offspring Evaluate the individual fitnesses of the offspring Replace worst ranked part of population with offspring Until terminating condition
Observations
There are several general observations about the generation of solutions via a genetic algorithm:
- In many problems with sufficient complexity, GAs may have a tendency to converge towards local optima rather than the global optimum of the problem. The likelihood of this occurring depends on the shape of the fitness landscape: certain problems may provide an easy ascent towards a global optimum, others may make it easier for the function to find the local optima. This problem may be alleviated by using a different fitness function, increasing the rate of mutation, or by using selection techniques that maintain a diverse population of solutions.
- Operating on dynamic data sets is difficult, as genomes begin to converge early on towards solutions which may no longer be valid for later data. Several methods have been proposed to remedy this by increasing genetic diversity somehow and preventing early convergence, either by increasing the probability of mutation when the solution quality drops (called triggered hypermutation), or by occasionally introducing entirely new, randomly generated elements into the gene pool (called random immigrants). Recent research has also shown the benefits of using biological exaptation (or preadaptation) in solving this problem.
- GAs cannot effectively solve problems in which the only fitness measure is right/wrong, as there is no way to converge on the solution. (No hill to climb). In these cases, a random search may find a solution as quickly as a GA.
- Selection is clearly an important genetic operator, but opinion is divided over the importance of crossover versus mutation. Some argue that crossover is the most important, while mutation is only necessary to ensure that potential solutions are not lost. Others argue that crossover in a largely uniform population only serves to propagate innovations originally found by mutation, and in a non-uniform population crossover is nearly always equivalent to a very large mutation (which is likely to be catastrophic).
- Often, GAs can rapidly locate good solutions, even for difficult search spaces.
- For specific optimization problems and problem instantiations, simpler optimization algorithms may find better solutions than genetic algorithms (given the same amount of computation time). Alternative and complementary algorithms include simulated annealing, hill climbing, and swarm intelligence (e.g.: ant colony optimization, particle swarm optimization).
- As with all current machine learning problems it is worth tuning the parameters such as mutation probability, recombination probability and population size to find reasonable settings for the problem class being worked on. A very small mutation rate may lead to genetic drift (which is non-ergodic in nature) or premature convergence of the genetic algorithm in a local optimum. A mutation rate that is too high may lead to loss of good solutions. There are theoretical but not yet practical upper and lower bounds for these parameters that can help guide selection.
- The implementation and evaluation of the fitness function is an important factor in the speed and efficiency of the algorithm.
Variants
The simplest algorithm represents each chromosome as a bit string. Typically, numeric parameters can be represented by integers, though it is possible to use floating point representations. The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a linked list, hashes, objects, or any other imaginable data structure. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains.
When bit strings representations of integers are used, Gray coding is often employed. In this way, small changes in the integer can be readily effected through mutations or crossovers. This has been found to help prevent premature convergence at so called Hamming walls, in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution.
Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Theoretically, the smaller the alphabet, the better the performance, but paradoxically, good results have been obtained from using real-valued chromosomes.
A slight, but very successful variant of the general process of constructing a new population is to allow some of the better organisms from the current generation to carry over to the next, unaltered. This strategy is known as elitist selection.
Parallel implementations of genetic algorithms come in two flavours. Coarse grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring individuals for selection and reproduction. Other variants, like genetic algorithms for online optimization problems, introduce time-dependence or noise in the fitness function.
Problem domains
Problems which appear to be particularly appropriate for solution by genetic algorithms include timetabling and scheduling problems, and many scheduling software packages are based on GAs. GAs have also been applied to engineering. Genetic algorithms are often applied as an approach to solve global optimization problems.
As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex fitness landscape as recombination is designed to move the population away from local optima that a traditional hill climbing algorithm might get stuck in.
History
Computer simulations of evolution started with Nils Aall Barricelli in 1954. Barricelli was simulating the evolution of automata that played a simple card game. Starting in 1957, the Australian quantitative geneticist Alex Fraser published a series of papers on simulation of artificial selection of organisms with multiple loci controlling a measurable trait. From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970) and Crosby (1973). Many early papers are reprinted by Fogel (1998).
Although Barricelli had also used evolutionary simulation as a general optimization method, genetic algorithms became a widely recognized optimization method as a result of the work of John Holland in the early 1970s, and particularly his 1975 book. His work originated with studies of cellular automata, conducted by Holland and his colleagues at the University of Michigan. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held at The University of Illinois. As academic interest grew, the dramatic increase in desktop computational power allowed for practical application of the new technique. In 1989, The New York Times writer John Markoff wrote about Evolver, the first commercially available desktop genetic algorithm. Custom computer applications began to emerge in a wide variety of fields, and these algorithms are now used by a majority of Fortune 500 companies to solve difficult scheduling, data fitting, trend spotting and budgeting problems, and virtually any other type of combinatorial optimization problem.
Related techniques
- Ant colony optimization (ACO) uses many ants (or agents) to traverse the solution space and find locally productive areas. While usually inferior to genetic algorithms and other forms of local search, it is able to produce results in problems where no global or up-to-date perspective can be obtained, and thus the other methods cannot be applied.
- Bacteriologic Algorithms (BA) inspired by evolutionary ecology and, more particularly, bacteriologic adaptation. Evolutionary ecology is the study of living organisms in the context of their environment, with the aim of discovering how they adapt. Its basic concept is that in a heterogeneous environment, you can’t find one individual that fits the whole environment. So, you need to reason at the population level. BAs have shown better results than GAs on problems such as complex positioning problems (antennas for cell phones, urban planning, and so on) or data mining (see http://www.irisa.fr/triskell/publis/2005/Baudry05d.pdf).
- Cross-entropy method The Cross-entropy (CE) method generates candidates solutions via a parameterized probability distribution. The parameters are updated via cross-entropy minimization, so as to generate better samples in the next iteration.
- Evolution strategies (ES) evolve linear individuals by means of mutation. ES algorithms are designed particulary to solve problems in the real-value domain.
- Extremal optimization (EO) Unlike GAs, which work with a population of candidate solutions, EO evolves a single solution and makes local modifications to the worst components. This requires that a suitable representation be selected which permits individual solution components to be assigned a quality measure ("fitness"). The governing principle behind this algorithm is that of emergent improvement through selectively removing low-quality components and replacing them with a randomly selected component. This is decidedly at odds with a GA that selects good solutions in an attempt to make better solutions.
- Genetic programming (GP) is a related technique popularized by John Koza in which computer programs, rather than function parameters, are optimized. Genetic programming often uses tree-based internal data structures to represent the computer programs for adaptation instead of the list structures typical of genetic algorithms.
- Interactive genetic algorithms (IGA) are genetic algorithms that use human evaluation. They are usually applied to domains where it is hard to design a computational fitness function, for example, evolving images, music, artistic designs and forms to fit users' aesthetic preference.
- Memetic algorithm (MA), also called hybrid genetic algorithm among others, is a relatively new evolutionary method where local search is applied during the evolutionary cycle. The idea of memetic algorithms comes from memes, which–unlike genes–can adapt themselves. In some problem areas they are shown to be more efficient than traditional evolutionary algorithms.
- Simulated annealing (SA) is a related global optimization technique that traverses the search space by testing random mutations on an individual solution. A mutation that increases fitness is always accepted. A mutation that lowers fitness is accepted probabilistically based on the difference in fitness and a decreasing temperature parameter. In SA parlance, one speaks of seeking the lowest energy instead of the maximum fitness. SA can also be used within a standard GA algorithm by starting with a relatively high rate of mutation and decreasing it over time along a given schedule.
- Stochastic optimization is an umbrella set of methods that includes GAs and numerous other approaches.
- Tabu search (TS) is similar to Simulated Annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest energy of those generated. In order to prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.
Building block hypothesis
[Goldberg, 1989, page 41], talking of binary bit string genetic algorithms, says:
- Short, low order, and highly fit schemata are sampled, recombined [crossed over], and resampled to form strings of potentially higher fitness. In a way, by working with these particular schemata [the building blocks], we have reduced the complexity of our problem; instead of building high-performance strings by trying every conceivable combination, we construct better and better strings from the best partial solutions of past samplings.
- Just as a child creates magnificent fortresses through the arrangement of simple blocks of wood [building blocks], so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks.
Note [Goldberg, 1989] suggests that building blocks are highly fit schemata with only a few defined bits (low order), and that these are close together (short).
Applications
- Artificial Creativity
Automated design, including research on composite material design and multi-objective design of automotive components for crashworthiness, weight savings, and other characteristics.
Automated design of mechatronic systems using bond graphs and genetic programming (NSF).
Automated design of industrial equipment using catalogs of exemplar lever patterns.
Calculation of Bound states and Local-density approximations.
Chemical kinetics (gas and solid phases)
Configuration applications, particularly physics applications of optimal molecule configurations for particular systems like C60 (buckyballs).
Container loading optimization.
Code-breaking, using the GA to search large solution spaces of ciphers for the one correct decryption.
Design of water distribution systems.
Distributed computer network topologies.
Electronic circuit design, known as Evolvable hardware.
File allocation for a distributed system.
JGAP: Java Genetic Algorithms Package, also includes support for Genetic Programming
Parallelization of GAs/GPs including use of hierarchical decomposition of problem domains and design spaces nesting of irregular shapes using feature matching and GAs.
Game Theory Equilibrium Resolution.
Learning Robot behavior using Genetic Algorithms.
Learning fuzzy rule base using genetic algorithms.
Linguistic analysis, including Grammar Induction and other aspects of Natural Language Processing (NLP) such as word sense disambiguation.
Mobile communications infrastructure optimization.
Molecular Structure Optimization (Chemistry).
Multiple population topologies and interchange methodologies.
Optimisation of data compression systems, for example using wavelets.
Protein folding and protein/ligand docking.
Plant floor layout.
Representing rational agents in economic models such as the cobweb model.
Scheduling applications, including job-shop scheduling. The objective being to schedule jobs in a sequence dependent or non-sequence dependent setup environment in order to maximize the volume of production while minimizing penalties such as tardiness.
Software engineering
Solving the machine-component grouping problem required for cellular manufacturing systems.
Tactical asset allocation and international equity strategies.
Timetabling problems, such as designing a non-conflicting class timetable for a large university.
Training artificial neural networks when pre-classified training examples are not readily obtainable (neuroevolution).
Traveling Salesman Problem.
Robot learning, obstacle avoidance.
References
- Barricelli, Nils Aall (1954), Esempi numerici di processi di evoluzione, Methodos, pp. 45-68.
- Crosby, Jack L. (1973), Computer Simulation in Genetics, John Wiley & Sons, London.
- Fentress, Sam W (2005), Exaptation as a means of evolving complex solutions, MA Thesis, University of Edinburgh. (pdf)
- Fogel, David B. (editor) (1998) Evolutionary Computation: The Fossil Record, IEEE Press, New York.
- Fraser, Alex S. (1957), Simulation of Genetic Systems by Automatic Digital Computers. I. Introduction. Australian Journal of Biological Sciences vol. 10 484-491.
- Fraser, Alex and Donald Burnell (1970), Computer Models in Genetics, McGraw-Hill, New York.
- Goldberg, David E (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Kluwer Academic Publishers, Boston, MA.
- Goldberg, David E (2002), The Design of Innovation: Lessons from and for Competent Genetic Algorithms, Addison-Wesley, Reading, MA.
- Harvey, Inman (1992), Species Adaptation Genetic Algorithms: A basis for a continuing SAGA, in 'Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life', F.J. Varela and P. Bourgine (eds.), MIT Press/Bradford Books, Cambridge, MA, pp. 346-354.
- Holland, John H (1975), Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor
- Koza, John (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press. ISBN 0-262-11170-5
- Matthews, Robert A J (1993), The use of genetic algorithms in cryptanalysis, Cryptologia vol 17 187-201
- Michalewicz, Zbigniew (1999), Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag.
- Mitchell, Melanie, (1996), An Introduction to Genetic Algorithms, MIT Press, Cambridge, MA.
- Schmitt, Lothar M, Nehaniv Chrystopher N, Fujii Robert H (1998), Linear analysis of genetic algorithms, Theoretical Computer Science (208), pp. 111-148
- Schmitt, Lothar M (2001), Theory of Genetic Algorithms, Theoretical Computer Science (259), pp. 1-61
- Schmitt, Lothar M (2004), Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling, Theoretical Computer Science (310), pp. 181-231
- Vose, Michael D (1999), The Simple Genetic Algorithm: Foundations and Theory, MIT Press, Cambridge, MA.
- Whitley, D. (1994). A genetic algorithm tutorial. Statistics and Computing 4, 65–85.
External links
- A Fast TSP Solver using a genetic algorithm Very fast TSP solver that uses aditional heuristics for faster operation.
- C# implementation of a genetic algorithm to route network traffic, Lawrence Botley.
- Follow-the-wall Robot - An interactive applet that allows you to experiment with genetic algorithms.
- Introduction to Genetic Algorithms Using RPL2
- Genetic algorithm in search and optimization, by Richard Baker
- Differential Evolution using Genetic Algorithm
- Genetic Algorithm Solves the Toads and Frogs Puzzle at cut-the-knot
- MIT OpenCourseWare | Health Sciences and Technology | HST.508 Genomics and Computational Biology, Fall 2002 | Lecture Notes
- A Genetic Algorithm Tutorial by Darrell Whitley Computer Science Department Colorado State University An excellent tutorial with lots of theory
- Evolutionary computing in search-based software engineering. Leo Rela. How evolutionary computing (specifically GA) is used in software engineering.
- Genetic Algorithm Applet A Java Applet that allows you to experiment with genetic algorithms. Source code included.
- Trainable Mechanical Arm Physical simulation of a mechanical arm and a ball. Using genetic algorithms it learns how to perform a given exercise (e.g. throw the ball as far as possible).
- A video showing a 20 generation evolution of a natural walking legs model
- VisualBots - Freeware multi-agent simulator in Microsoft Excel. Sample programs include genetic algorithm, ACO, and simulated annealing solutions to TSP.
- Genetics Studio - Freeware numeric genetic algorithm utility for the novice to advanced user.
- PIKAIA- a free genetic algorithm subroutine developed in Fortran. PIKAIA is also available in an Excel/VBA version and a parallel processing version.