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- David E. Goldberg
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- Genetic algorithms in search, optimization, and machine learning
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## David E. Goldberg

In computer science and operations research , a genetic algorithm GA is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms EA. Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation , crossover and selection. In a genetic algorithm, a population of candidate solutions called individuals, creatures, or phenotypes to an optimization problem is evolved toward better solutions.

Each candidate solution has a set of properties its chromosomes or genotype which can be mutated and altered; 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 is an iterative process , with the population in each iteration called a generation. In each generation, the fitness of every individual in the population is evaluated; the fitness is usually the value of the objective function in the optimization problem being solved.

The more fit individuals are stochastically selected from the current population, and each individual's genome is modified recombined and possibly randomly mutated to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm. 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.

A standard representation of each candidate solution is as an array of bits. 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 programming and graph-form representations are explored in evolutionary programming ; a mix of both linear chromosomes and trees is explored in gene expression programming.

Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.

The population size depends on the nature of the problem, but typically contains several hundreds or thousands of possible solutions. Often, the initial 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. During each successive generation, a portion 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 the former process may be very time-consuming.

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 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, a simulation may be used to determine the fitness function value of a phenotype e. The next step is to generate a second generation population of solutions from those selected through a combination of genetic operators : crossover also called recombination , and 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 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 [3] [4] suggests that more than two "parents" generate higher quality chromosomes.

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.

These less fit solutions ensure genetic diversity within the genetic pool of the parents and therefore ensure the genetic diversity of the subsequent generation of children. Opinion is divided over the importance of crossover versus mutation. There are many references in Fogel that support the importance of mutation-based search.

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. It is worth tuning parameters such as the mutation probability, crossover 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. 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 elitist selection is employed. An adequate population size ensures sufficient genetic diversity for the problem at hand, but can lead to a waste of computational resources if set to a value larger than required.

In addition to the main operators above, other heuristics may be employed to make the calculation faster or more robust. The speciation heuristic penalizes crossover between candidate solutions that are too similar; this encourages population diversity and helps prevent premature convergence to a less optimal solution.

This generational process is repeated until a termination condition has been reached. Common terminating conditions are:. 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:. Despite the lack of consensus regarding the validity of the building-block hypothesis, it has been consistently evaluated and used as reference throughout the years.

Many estimation of distribution algorithms , for example, have been proposed in an attempt to provide an environment in which the hypothesis would hold. Indeed, there is a reasonable amount of work that attempts to understand its limitations from the perspective of estimation of distribution algorithms.

There are limitations of the use of a genetic algorithm compared to alternative optimization algorithms:. 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 floating point representation is natural to evolution strategies and evolutionary programming. 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 Holland in the s. 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 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-string representations of integers are used, Gray coding is often employed. In this way, small changes in the integer can be readily affected 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. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a virtual alphabet when selection and recombination are dominant with a much lower cardinality than would be expected from a floating point representation.

An expansion of the Genetic Algorithm accessible problem domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller such as a fuzzy system which has an inherently different description.

This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes. A practical variant of the general process of constructing a new population is to allow the best organism s from the current generation to carry over to the next, unaltered.

This strategy is known as elitist selection and guarantees that the solution quality obtained by the GA will not decrease from one generation to the next. Parallel implementations of genetic algorithms come in two flavors. 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 , [19] the adjustment of pc and pm depends on the fitness values of the solutions.

In CAGA clustering-based adaptive genetic algorithm , [20] 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.

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 [ citation needed ] 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 operator has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency.

A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination.

A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i. 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.

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 [ citation needed ].

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David Edward Goldberg born September 26, is an American computer scientist , civil engineer, and former professor. He is the author of Genetic Algorithms in Search, Optimization and Machine Learning , one of the most cited books in computer science. David E. Goldberg received a PhD in civil engineering in from the University of Michigan. His advisors were E.

## Genetic algorithms in search, optimization, and machine learning

What Are Genetic Algorithms? Open navigation menu. Close suggestions Search Search.

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*In computer science and operations research , a genetic algorithm GA is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms EA. Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation , crossover and selection.*

### In this section:

View larger cover. This book describes the theory, operation, and application of genetic algorithms-search algorithms based on the mechanics of natural selection and genetics. This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.

My favorite GA technique is still the micro-GA. At this point, I recommend using the micro-GA with uniform crossover and a small population size. The following inputs gave me excellent performance:. If you decide to use the micro-GA, you will not need to worry about the population sizing or creep mutation tips below. I've had a lot of people ask me about population sizing, especially people who are attempting large problems where individuals is probably not enough. The true authority on the subject is David E.

#### micro-GA Technique

Download to read the full article text. Bateson, G. Steps to an ecology of mind. New York: Ballantine. Google Scholar. Davis, L. Genetic algorithms and communication link speed design: Theoretical considerations.

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