A
genetic algorithm is a
searchIn computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items. The items may be stored individually as records in a database; or may be elements of a search space defined by a mathematical formula or procedure, such as the roots...
heuristicHeuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...
that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to
optimizationIn mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
and
searchIn computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items. The items may be stored individually as records in a database; or may be elements of a search space defined by a mathematical formula or procedure, such as the roots...
problemA problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal...
s. Genetic algorithms belong to the larger class of
evolutionary algorithmIn artificial intelligence, an evolutionary algorithm is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses some mechanisms inspired by biological evolution: reproduction, mutation, recombination, and selection...
s (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as
inheritanceHeredity is the passing of traits to offspring . This is the process by which an offspring cell or organism acquires or becomes predisposed to the characteristics of its parent cell or organism. Through heredity, variations exhibited by individuals can accumulate and cause some species to evolve...
,
mutationIn genetic algorithms of computing, mutation is a genetic operator used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next...
,
selectionSelection is the stage of a genetic algorithm in which individual genomes are chosen from a population for later breeding .A generic selection procedure may be implemented as follows:...
, and
crossoverIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
.
Methodology
In a genetic algorithm, a
populationA population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...
of strings (called
chromosomesIn genetic algorithms, a chromosome is a set of parameters which define a proposed solution to the problem that the genetic algorithm is trying to solve...
or the
genotypeThe genotype is the genetic makeup of a cell, an organism, or an individual usually with reference to a specific character under consideration...
of the
genomeIn modern molecular biology and genetics, the genome is the entirety of an organism's hereditary information. It is encoded either in DNA or, for many types of virus, in RNA. The genome includes both the genes and the non-coding sequences of the DNA/RNA....
), which encode
candidate solutionIn optimization , a candidate solution is a member of a set of possible solutions to a given problem. A candidate solution does not have to be a likely or reasonable solution to the problem – it is simply in the set that satisfies all constraints.The space of all candidate solutions is called the...
s (called individuals, creatures, or
phenotypeA phenotype is an organism's observable characteristics or traits: such as its morphology, development, biochemical or physiological properties, behavior, and products of behavior...
s) 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 randomly mutated) to form a new population. The new population is then used in the next iteration of the
algorithmIn mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. If the algorithm has terminated due to a maximum number of generations, a satisfactory solution may or may not have been reached.
Genetic algorithms find application in
bioinformaticsBioinformatics is the application of computer science and information technology to the field of biology and medicine. Bioinformatics deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, software...
,
phylogeneticsIn biology, phylogenetics is the study of evolutionary relatedness among groups of organisms , which is discovered through molecular sequencing data and morphological data matrices...
,
computational scienceComputational science is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems...
,
engineeringEngineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
,
economicsEconomics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
,
chemistryChemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
,
manufacturingManufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...
,
mathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
,
physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and other fields.
A typical genetic algorithm requires:
- a genetic representation
Genetic representation is a way of representing solutions/individuals in evolutionary computation methods. Genetic representation can encode appearance, behavior, physical qualities of individuals. Designing a good genetic representation that is expressive and evolvable is a hard problem in...
of the solution domain,
- a fitness function
A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims....
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, which facilitates simple crossover operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in
genetic programmingIn artificial intelligence, genetic programming is an evolutionary algorithm-based methodology inspired by biological evolution to find computer programs that perform a user-defined task. It is a specialization of genetic algorithms where each individual is a computer program...
and graph-form representations are explored in
evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
.
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 problemThe knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the count of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as...
one wants to maximize the total value of objects that can be 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 algorithmsInteractive evolutionary computation or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation...
are used.
Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions (usually randomly) and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.
Initialization
Initially many individual solutions are (usually) 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, allowing 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 generation, a proportion of the existing population is
selectedSelection is the stage of a genetic algorithm in which individual genomes are chosen from a population for later breeding .A generic selection procedure may be implemented as follows:...
to breed a new generation. Individual solutions are selected through a
fitness-based process, where
fitterFitness is a central idea in evolutionary theory. It can be defined either with respect to a genotype or to a phenotype in a given environment...
solutions (as measured by a
fitness functionA fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims....
) 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 the latter process may be very time-consuming.
Reproduction
The next step is to generate a second generation population of solutions from those selected through
genetic operatorA genetic operator is an operator used in genetic algorithms to maintain genetic diversity, known as Mutation and to combine existing solutions into others, Crossover...
s:
crossoverIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
(also called recombination), and/or
mutationIn genetic algorithms of computing, mutation is a genetic operator used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next...
.
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 new child, and the process continues until a new population of solutions of appropriate size is generated.
Although reproduction methods that are based on the use of two parents are more "biology inspired", some research suggests more than two "parents" are better to be used to reproduce a good quality chromosome.
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.
Although Crossover and Mutation are known as the main genetic operators, it is possible to use other operators such as regrouping, colonization-extinction, or migration in genetic algorithms.
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
Simple generational genetic algorithm procedure:
- Choose the initial population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...
of individualAn individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...
s
- Evaluate the fitness
Fitness is a central idea in evolutionary theory. It can be defined either with respect to a genotype or to a phenotype in a given environment...
of each individual in that population
- Repeat on this generation
Generation , also known as procreation in biological sciences, is the act of producing offspring....
until termination (time limit, sufficient fitness achieved, etc.):
- Select the best-fit individuals for reproduction
- Breed
A breed is a group of domestic animals or plants with a homogeneous appearance, behavior, and other characteristics that distinguish it from other animals or plants of the same species. Despite the centrality of the idea of "breeds" to animal husbandry, there is no scientifically accepted...
new individuals through crossoverIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
and mutationIn genetic algorithms of computing, mutation is a genetic operator used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next...
operations to give birth to offspringIn biology, offspring is the product of reproduction, of a new organism produced by one or more parents.Collective offspring may be known as a brood or progeny in a more general way...
- Evaluate the individual fitness of new individuals
- Replace least-fit population with new individuals
The building block hypothesis
Genetic algorithms are simple to implement, but their behavior is difficult to understand. In particular it is difficult to understand why these algorithms frequently succeed at generating solutions of high fitness when applied to practical problems. The building block hypothesis (BBH) consists of:
- A description of a heuristic that performs adaptation by identifying and recombining "building blocks", i.e. low order, low defining-length schemata
A schema is a template in computer science used in the field of genetic algorithms that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets; and so form a topological space.- Description :...
with above average fitness.
- A hypothesis that a genetic algorithm performs adaptation by implicitly and efficiently implementing this heuristic.
Goldberg describes the heuristic as follows:
- "Short, low order, and highly fit schemata
A schema is a template in computer science used in the field of genetic algorithms that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets; and so form a topological space.- Description :...
are sampled, recombinedIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
[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.
- "Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks. Just as a child creates magnificent fortresses through the arrangement of simple blocks of wood, so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks."
Observations
There are several general observations about the generation of solutions specifically via a genetic algorithm:
- 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). There are many references in Fogel
Dr. David B. Fogel , is a pioneer in evolutionary computation. Dr. Fogel received his Ph.D. in engineering from the University of California, San Diego in 1992. He is currently CEO of Natural Selection, Inc. He is probably best known for his research project, Blondie24, in which a machine evolved...
(2006) that support the importance of mutation-based search.
- As with all current machine learning problems it is worth tuning the parameters such as mutation
In genetic algorithms of computing, mutation is a genetic operator used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next...
probability, crossoverIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
probability and population size to find reasonable settings for the problem class being worked on. A very small mutation rate may lead to genetic driftGenetic drift or allelic drift is the change in the frequency of a gene variant in a population due to random sampling.The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces...
(which is non-ergodic in nature). A recombination rate that is too high may lead to premature convergence of the genetic algorithm. A mutation rate that is too high may lead to loss of good solutions unless there is elitist selection. There are theoretical but not yet practical upper and lower bounds for these parameters that can help guide selection.
- Often, GAs can rapidly locate good solutions, even for large search spaces. The same is of course also true for evolution strategies
In computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
and evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
.
Criticisms
There are several criticisms of the use of a genetic algorithm compared to alternative optimization algorithms:
- Repeated fitness function
A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims....
evaluation for complex problems is often the most prohibitive and limiting segment of artificial evolutionary algorithms. Finding the optimal solution to complex high dimensional, multimodal problems often requires very expensive fitness functionA fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims....
evaluations. In real world problems such as structural optimization problems, one single function evaluation may require several hours to several days of complete simulation. Typical optimization methods can not deal with such types of problem. In this case, it may be necessary to forgo an exact evaluation and use an approximated fitnessIn function optimization, fitness approximation is a method for decreasing the number of fitness function evaluations to reach a target solution...
that is computationally efficient. It is apparent that amalgamation of approximate modelsIn function optimization, fitness approximation is a method for decreasing the number of fitness function evaluations to reach a target solution...
may be one of the most promising approaches to convincingly use GA to solve complex real life problems.
- The "better" solution is only in comparison to other solutions. As a result, the stop criterion is not clear in every problem.
- In many problems, GAs may have a tendency to converge towards local optima
Local optimum is a term in applied mathematics and computer science.A local optimum of a combinatorial optimization problem is a solution that is optimal within a neighboring set of solutions...
or even arbitrary points rather than the global optimumIn mathematics, a global optimum is a selection from a given domain which yields either the highest value or lowest value , when a specific function is applied. For example, for the function...
of the problem. This means that it does not "know how" to sacrifice short-term fitness to gain longer-term fitness. The likelihood of this occurring depends on the shape of the fitness landscapeIn evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate . This fitness is the "height" of the 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, although the No Free Lunch theorem proves that there is no general solution to this problem. A common technique to maintain diversity is to impose a "niche penalty", wherein, any group of individuals of sufficient similarity (niche radius) have a penalty added, which will reduce the representation of that group in subsequent generations, permitting other (less similar) individuals to be maintained in the population. This trick, however, may not be effective, depending on the landscape of the problem. Another possible technique would be to simply replace part of the population with randomly generated individuals, when most of the population is too similar to each other. Diversity is important in genetic algorithms (and genetic programmingIn artificial intelligence, genetic programming is an evolutionary algorithm-based methodology inspired by biological evolution to find computer programs that perform a user-defined task. It is a specialization of genetic algorithms where each individual is a computer program...
) because crossing over a homogeneous population does not yield new solutions. In evolution strategiesIn computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
and evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
, diversity is not essential because of a greater reliance on mutation.
- 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). Again, evolution strategies
In computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
and evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
can be implemented with a so-called "comma strategy" in which parents are not maintained and new parents are selected only from offspring. This can be more effective on dynamic problems.
- GAs cannot effectively solve problems in which the only fitness measure is a single right/wrong measure (like decision problem
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem...
s), 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. However, if the situation allows the success/failure trial to be repeated giving (possibly) different results, then the ratio of successes to failures provides a suitable fitness measure.
- For specific optimization problems and problem instances, other optimization algorithms may find better solutions than genetic algorithms (given the same amount of computation time). Alternative and complementary algorithms include evolution strategies
In computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
, evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
, simulated annealingSimulated annealing is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete...
, Gaussian adaptationGaussian adaptation is an evolutionary algorithm designed for the maximization of manufacturing yield due to statistical deviation of component values of signal processing systems...
, hill climbingIn computer science, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution...
, and swarm intelligenceSwarm intelligence is the collective behaviour of decentralized, self-organized systems, natural or artificial. The concept is employed in work on artificial intelligence...
(e.g.: ant colony optimizationIn computer science and operations research, the ant colony optimization algorithm ' is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs....
, particle swarm optimizationIn computer science, particle swarm optimization is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality...
) and methods based on integer linear programming. The question of which, if any, problems are suited to genetic algorithms (in the sense that such algorithms are better than others) is open and controversial.
Variants
The simplest algorithm represents each chromosome as a
bit string. Typically, numeric parameters can be represented by
integerThe integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s, though it is possible to use
floating pointIn computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
representations. The floating point representation is natural to
evolution strategiesIn computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
and
evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by
John Henry HollandJohn Henry Holland is an American scientist and Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. He is a pioneer in complex systems and nonlinear science. He is known as the father of genetic algorithms. He was awarded...
in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). 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 listIn computer science, a linked list is a data structure consisting of a group of nodes which together represent a sequence. Under the simplest form, each node is composed of a datum and a reference to the next node in the sequence; more complex variants add additional links...
,
hashesIn computer science, an associative array is an abstract data type composed of a collection of pairs, such that each possible key appears at most once in the collection....
,
objectsIn computer science, an object is any entity that can be manipulated by the commands of a programming language, such as a value, variable, function, or data structure...
, or any other imaginable
data structureIn computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks...
. 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-string 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 very successful (slight) 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.
Genetic algorithms with adaptive parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation (pm) greatly determine the degree of solution accuracy and the convergence speed that genetic algorithms can obtain. Instead of using fixed values of pc and pm, AGAs utilize the population information in each generation and adaptively adjust the pc and pm in order to maintain the population diversity as well as to sustain the convergence capacity. In AGA (adaptive genetic algorithm), the adjustment of pc and pm depends on the fitness values of the solutions. In
CAGA (clustering-based adaptive genetic algorithm), through the use of clustering analysis to judge the optimization states of the population, the adjustment of pc and pm depends on these optimization states. The
GEGA program is an
ab initio gradient embedded GA, a program for finding the global minima of clusters developed by Anastassia Alexandrova at
Utah State UniversityUtah State University is a public university located in Logan, Utah. It is a land-grant and space-grant institution and is accredited by the Northwest Commission on Colleges and Universities....
. GEGA employs geometry-cuts for the GA,
ab initio level of
computationComputation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
for
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
optimization and vibrational frequency analysis, with local minima only, and a specific mutational procedure based on the so called "kick technique".
It can be quite effective to combine GA with other optimization methods. GA tends to be quite good at finding generally good global solutions, but quite inefficient at finding the last few mutations to find the absolute optimum. Other techniques (such as simple hill climbing) are quite efficient at finding absolute optimum in a limited region. Alternating GA and hill climbing can improve the efficiency of GA while overcoming the lack of robustness of hill climbing.
This means that the rules of genetic variation may have a different meaning in the natural case. For instance – provided that steps are stored in consecutive order – crossing over may sum a number of steps from maternal DNA adding a number of steps from paternal DNA and so on. This is like adding vectors that more probably may follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be increased by many orders of magnitude. Moreover, the
inversion operatorIn the mathematics, inversion operator can refer to:* the operator which assigns the inverse element to an element of a group* Inversion in a point* Chromosomal inversion, reordering of genes in a DNA-sequence....
has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency. (See for instance or example in
travelling salesman problemThe travelling salesman problem is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find the shortest possible tour that visits each city exactly once...
, in particular the use of an
edge recombination operatorThe edge recombination operator is an operator that creates a path that is similar to a set of existing paths by looking at the edges rather than the vertices...
.)
A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination.
Linkage-learning
A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i.e. where the fitness of a solution consists of interacting subsets of its variables. Such algorithms aim to learn (before exploiting) these beneficial phenotypic interactions. As such, they are aligned with the Building Block Hypothesis in adaptively reducing disruptive recombination. Prominent examples of this approach include the mGA, GEMGA and LLGA.
Problem domains
Problems which appear to be particularly appropriate for solution by genetic algorithms include
timetablingA timeline is a way of displaying a list of events in chronological order, sometimes described as a project artifact . It is typically a graphic design showing a long bar labeled with dates alongside itself and events labeled on points where they would have happened.-Uses of timelines:Timelines...
and scheduling problems, and many scheduling software packages are based on GAs. GAs have also been applied to
engineeringEngineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
. Genetic algorithms are often applied as an approach to solve
global optimizationGlobal optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria.- General :The most common form is the minimization of one real-valued function...
problems.
As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex
fitness landscapeIn evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate . This fitness is the "height" of the landscape...
as mixing, i.e.,
mutationIn genetic algorithms of computing, mutation is a genetic operator used to maintain genetic diversity from one generation of a population of algorithm chromosomes to the next...
in combination with
crossoverIn genetic algorithms, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based...
, is designed to move the population away from local optima that a traditional
hill climbingIn computer science, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution...
algorithm might get stuck in. Observe that commonly used crossover operators cannot change any uniform population. Mutation alone can provide ergodicity of the overall genetic algorithm process (seen as a Markov chain).
Examples of problems solved by genetic algorithms include: mirrors designed to funnel sunlight to a solar collector, antennae designed to pick up radio signals in space, and walking methods for computer figures. Many of their solutions have been highly effective, unlike anything a human engineer would have produced, and inscrutable as to how they arrived at that solution.
History
Computer simulations of evolution started as early as in 1954 with the work of
Nils Aall BarricelliNils Aall Barricelli was a Norwegian-Italian mathematician.Barricelli's early computer-assisted experiments in symbiogenesis and evolution are considered pioneering in artificial life research. Barricelli, who was independently wealthy, held an unpaid residency at the Institute for Advanced Study...
, who was using the computer at the
Institute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in
Princeton, New JerseyPrinceton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. His 1954 publication was not widely noticed. Starting in 1957, the Australian quantitative geneticist
Alex FraserAlex Fraser was a major innovator in the development of the computer modeling of population genetics and his work has stimulated many advances in genetic research over the past decades....
published a series of papers on simulation of
artificial selectionArtificial selection describes intentional breeding for certain traits, or combination of traits. The term was utilized by Charles Darwin in contrast to natural selection, in which the differential reproduction of organisms with certain traits is attributed to improved survival or reproductive...
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). Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition,
Hans-Joachim BremermannHans-Joachim Bremermann was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations...
published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms. Other noteworthy early pioneers include Richard Friedberg, George Friedman, and Michael Conrad. Many early papers are reprinted by
FogelDr. David B. Fogel , is a pioneer in evolutionary computation. Dr. Fogel received his Ph.D. in engineering from the University of California, San Diego in 1992. He is currently CEO of Natural Selection, Inc. He is probably best known for his research project, Blondie24, in which a machine evolved...
(1998).
Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game, artificial evolution became a widely recognized optimization method as a result of the work of
Ingo RechenbergIngo Rechenberg is a German computer scientist and professor. Rechenberg is a pioneer of the fields of evolutionary computation and artificial evolution. In the 1960s and 1970s he invented a highly influential set of optimization methods known as evolution strategies...
and
Hans-Paul SchwefelHans-Paul Schwefel is a German computer scientist and professor emeritus at University of Dortmund , where he held the chair of systems analysis from 1985 until 2006. He is one of the pioneers in evolutionary computation and one of the authors responsible for the evolution strategies...
in the 1960s and early 1970s – Rechenberg's group was able to solve complex engineering problems through
evolution strategiesIn computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
. Another approach was the evolutionary programming technique of
Lawrence J. FogelDr. Lawrence J. Fogel , was a pioneer in evolutionary computation and human factors analysis. He is known as the father of evolutionary programming. Born in Brooklyn, New York, he earned his B.E.E. from New York University in 1948, M.S. from Rutgers University in 1952 and Ph.D...
, which was proposed for generating artificial intelligence.
Evolutionary programmingEvolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
originally used finite state machines for predicting environments, and used variation and selection to optimize the predictive logics. Genetic algorithms in particular became popular through the work of
John HollandJohn Henry Holland is an American scientist and Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. He is a pioneer in complex systems and nonlinear science. He is known as the father of genetic algorithms. He was awarded...
in the early 1970s, and particularly his book
Adaptation in Natural and Artificial Systems (1975). His work originated with studies of cellular automata, conducted by
HollandJohn Henry Holland is an American scientist and Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. He is a pioneer in complex systems and nonlinear science. He is known as the father of genetic algorithms. He was awarded...
and his students at the
University of MichiganThe University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
. Holland introduced a formalized framework for predicting the quality of the next generation, known as
Holland's Schema TheoremHolland's schema theorem is widely taken to be the foundation for explanations of the power of genetic algorithms. It was proposed by John Holland in the 1970s....
. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held in
Pittsburgh, PennsylvaniaPittsburgh is the second-largest city in the US Commonwealth of Pennsylvania and the county seat of Allegheny County. Regionally, it anchors the largest urban area of Appalachia and the Ohio River Valley, and nationally, it is the 22nd-largest urban area in the United States...
.
As academic interest grew, the dramatic increase in desktop computational power allowed for practical application of the new technique. In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes. In 1989, Axcelis, Inc. released
EvolverEvolver is a software package that allows users to solve a wide variety of optimization problems using a genetic algorithm. Launched in 1990, it was the first commercially available genetic algorithm package for personal computers. The program was originally developed by Axcelis, Inc. and is now...
, the world's first commercial GA product for desktop computers.
The New York TimesThe New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
technology writer
John MarkoffJohn Markoff is a journalist best known for his work at The New York Times, and a book and series of articles about the 1990s pursuit and capture of hacker Kevin Mitnick.- Biography :...
wrote about Evolver in 1990.
Parent fields
Genetic algorithms are a sub-field of:
- Evolutionary algorithms
- Evolutionary computing
- Metaheuristic
In computer science, metaheuristic designates a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Metaheuristics make few or no assumptions about the problem being optimized and can search very large spaces...
s
- Stochastic optimization
Stochastic optimization methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involve random objective functions or random constraints, for example. Stochastic...
- Optimization
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
Evolutionary algorithms
Evolutionary algorithms is a sub-field of
evolutionary computingIn computer science, evolutionary computation is a subfield of artificial intelligence that involves combinatorial optimization problems....
.
- Evolution strategies
In computer science, evolution strategy is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.-History:...
(ES, see Rechenberg, 1994) evolve individuals by means of mutation and intermediate or discrete recombination. ES algorithms are designed particularly to solve problems in the real-value domain. They use self-adaptation to adjust control parameters of the search. De-randomization of self-adaptation has led to the contemporary Covariance Matrix Adaptation Evolution Strategy (CMA-ESCMA-ES stands for Covariance Matrix Adaptation Evolution Strategy. Evolution strategies are stochastic, derivative-free methods for numerical optimization of non-linear or non-convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation...
).
- Evolutionary programming
Evolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve....
(EP) involves populations of solutions with primarily mutation and selection and arbitrary representations. They use self-adaptation to adjust parameters, and can include other variation operations such as combining information from multiple parents.
- Genetic programming
In artificial intelligence, genetic programming is an evolutionary algorithm-based methodology inspired by biological evolution to find computer programs that perform a user-defined task. It is a specialization of genetic algorithms where each individual is a computer program...
(GP) is a related technique popularized by John KozaJohn R. Koza is a computer scientist and a former consulting professor at Stanford University, most notable for his work in pioneering the use of genetic programming for the optimization of complex problems. He was a cofounder of Scientific Games Corporation, a company which built computer systems...
in which computer programs, rather than function parameters, are optimized. Genetic programming often uses tree-basedIn computer science, a tree is a widely-used data structure that emulates a hierarchical tree structure with a set of linked nodes.Mathematically, it is an ordered directed tree, more specifically an arborescence: an acyclic connected graph where each node has zero or more children nodes and at...
internal data structureIn computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks...
s to represent the computer programs for adaptation instead of the list structures typical of genetic algorithms.
- Grouping genetic algorithm (GGA) is an evolution of the GA where the focus is shifted from individual items, like in classical GAs, to groups or subset of items. The idea behind this GA evolution proposed by Emanuel Falkenauer is that solving some complex problems, a.k.a. clustering or partitioning problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes. These kind of problems include bin packing
In computational complexity theory, the bin packing problem is a combinatorial NP-hard problem. In it, objects of different volumes must be packed into a finite number of bins of capacity V in a way that minimizes the number of bins used....
, line balancing, clustering with respect to a distance measure, equal piles, etc., on which classic GAs proved to perform poorly. Making genes equivalent to groups implies chromosomes that are in general of variable length, and special genetic operators that manipulate whole groups of items. For bin packing in particular, a GGA hybridized with the Dominance Criterion of Martello and Toth, is arguably the best technique to date.
- Interactive evolutionary algorithms are evolutionary 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.
Swarm intelligence
Swarm intelligence is a sub-field of
evolutionary computingIn computer science, evolutionary computation is a subfield of artificial intelligence that involves combinatorial optimization problems....
.
- Ant colony optimization
In computer science and operations research, the ant colony optimization algorithm ' is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs....
(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.
- Particle swarm optimization
In computer science, particle swarm optimization is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality...
(PSO) is a computational method for multi-parameter optimization which also uses population-based approach. A population (swarm) of candidate solutions (particles) moves in the search space, and the movement of the particles is influenced both by their own best known position and swarm's global best known position. Like genetic algorithms, the PSO method depends on information sharing among population members. In some problems the PSO is often more computationally efficient than the GAs, especially in unconstrained problems with continuous variables.
- Intelligent Water Drops or the IWD algorithm is a nature-inspired optimization algorithm inspired from natural water drops which change their environment to find the near optimal or optimal path to their destination. The memory is the river's bed and what is modified by the water drops is the amount of soil on the river's bed.
Other evolutionary computing algorithms
Evolutionary computation is a sub-field of the
metaheuristicIn computer science, metaheuristic designates a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Metaheuristics make few or no assumptions about the problem being optimized and can search very large spaces...
methods.
- Harmony search
In computer science and operations research, harmony search is a phenomenon-mimicking algorithm inspired by the improvisation process of musicians...
(HS) is an algorithm mimicking musicians behaviors in improvisation process.
- Memetic algorithm
Memetic algorithms represent one of the recent growing areas of research in evolutionary computation. The term MA is now widely used as a synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search...
(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 memeA meme is "an idea, behaviour or style that spreads from person to person within a culture."A meme acts as a unit for carrying cultural ideas, symbols or practices, which can be transmitted from one mind to another through writing, speech, gestures, rituals or other imitable phenomena...
s, which unlike genes, can adapt themselves. In some problem areas they are shown to be more efficient than traditional evolutionary algorithms.
- Bacteriologic algorithms (BA) inspired by evolutionary ecology
Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can be seen as an approach to the study of evolution that...
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. It is also believed BAs could be successfully applied to complex positioning problems (antennas for cell phones, urban planning, and so on) or data mining.
- Cultural algorithm
Cultural algorithms are a branch of evolutionary computation where there is a knowledge component that is called the belief space in addition to the population component. In this sense, cultural algorithms can be seen as an extension to a conventional genetic algorithm. Cultural algorithms were...
(CA) consists of the population component almost identical to that of the genetic algorithm and, in addition, a knowledge component called the belief space.
- Gaussian adaptation
Gaussian adaptation is an evolutionary algorithm designed for the maximization of manufacturing yield due to statistical deviation of component values of signal processing systems...
(normal or natural adaptation, abbreviated NA to avoid confusion with GA) is intended for the maximisation of manufacturing yield of signal processing systems. It may also be used for ordinary parametric optimisation. It relies on a certain theorem valid for all regions of acceptability and all Gaussian distributions. The efficiency of NA relies on information theory and a certain theorem of efficiency. Its efficiency is defined as information divided by the work needed to get the information. Because NA maximises mean fitness rather than the fitness of the individual, the landscape is smoothed such that valleys between peaks may disappear. Therefore it has a certain “ambition” to avoid local peaks in the fitness landscape. NA is also good at climbing sharp crests by adaptation of the moment matrix, because NA may maximise the disorder (average information) of the Gaussian simultaneously keeping the mean fitness constant.
Other metaheuristic methods
Metaheuristic methods broadly fall within
stochasticStochastic optimization methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involve random objective functions or random constraints, for example. Stochastic...
optimisation methods.
- Simulated annealing
Simulated annealing is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete...
(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.
- Tabu search
Tabu search is a mathematical optimization method, belonging to the class of trajectory based techniques. Tabu search enhances the performance of a local search method by using memory structures that describe the visited solutions: once a potential solution has been determined, it is marked as...
(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.
- Extremal optimization
Extremal Optimization is an optimization heuristic inspired by the Bak-Sneppen model of self-organized criticality from the field of statistical physics...
(EO) Unlike GAs, which work with a population of candidate solutions, EO evolves a single solution and makes localIn computer science, local search is a metaheuristic method for solving computationally hard optimization problems. Local search can be used on problems that can be formulated as finding a solution maximizing a criterion among a number of candidate solutions...
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.
Other stochastic optimisation methods
- The cross-entropy (CE) method
The cross-entropy method attributed to Reuven Rubinstein is a general Monte Carlo approach tocombinatorial and continuous multi-extremal optimization and importance sampling.The method originated from the field of rare event simulation, where...
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.
- Reactive search optimization
Reactive search optimization defines local-search heuristics based on machine learning, a family of optimization algorithms based on the local search techniques...
(RSO) advocates the integration of sub-symbolic machine learning techniques into search heuristics for solving complex optimization problems. The word reactive hints at a ready response to events during the search through an internal online feedback loop for the self-tuning of critical parameters. Methodologies of interest for Reactive Search include machine learning and statistics, in particular reinforcement learning, active or query learning, neural networks, and meta-heuristics.
Resources
Tutorials
Examples