Evolutionary algorithm

In artificial intelligence, an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators. Artificial evolution (AE) describes a process involving individual evolutionary algorithms; EAs are individual components that participate in an AE..

Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape; this generality is shown by successes in fields as diverse as engineering, art, biology, economics, marketing, genetics, operations research, robotics, social sciences, physics, politics and chemistry.

Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics.

In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems; therefore, there may be no direct link between algorithm complexity and problem complexity.

A possible limitation of many evolutionary algorithms is their lack of a clear genotype-phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature phenotype. This indirect encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the evolvability of the organism.^[1]^[2] Such indirect (aka generative or developmental) encodings also enable evolution to exploit the regularity in the environment.^[3] Recent work in the field of artificial embryogeny, or artificial developmental systems, seeks to address these concerns. And gene expression programming successfully explores a genotype-phenotype system, where the genotype consists of linear multigenic chromosomes of fixed length and the phenotype consists of multiple expression trees or computer programs of different sizes and shapes.^[4]

Implementation of biological processes

Generate the initial population of individuals randomly – (first generation)
Evaluate the fitness of each individual in that population.
Repeat on this generation until termination (time limit, sufficient fitness achieved, etc.):
1. Select the best-fit individuals for reproduction – (parents)
2. Breed new individuals through crossover and mutation operations to give birth to offspring.
3. Evaluate the individual fitness of new individuals.
4. Replace least-fit population with new individuals.

Evolutionary algorithm types

Similar techniques differ in the implementation details and the nature of the particular applied problem.

Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems.
Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem.
Evolutionary programming – Similar to genetic programming, but the structure of the program is fixed and its numerical parameters are allowed to evolve.
Gene expression programming – Like genetic programming, GEP also evolves computer programs but it explores a genotype-phenotype system, where computer programs of different sizes are encoded in linear chromosomes of fixed length.
Evolution strategy – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates.
Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems.
Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect.
Learning classifier system – Here the solutions are classifiers (rules or conditions). A Michigan-LCS works with individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is determined with either a strength or accuracy based reinforcement learning approach.

Related techniques

Swarm algorithms, including:

Ant colony optimization – Based on the ideas of ant foraging by pheromone communication to form paths. Primarily suited for combinatorial optimization and graph problems.
The runner-root algorithm (RRA) is inspired by the function of runners and roots of plants in nature ^[5]
Artificial Bee Colony Algorithm – Based on the honey bee foraging behaviour. Primarily proposed for numerical optimization and extended to solve combinatorial, constrained and multi-objective optimization problems.
Bees algorithm is based on the foraging behaviour of honey bees. It has been applied in many applications such as routing and scheduling.
Cuckoo search is inspired by the brooding parasitism of the cuckoo species. It also uses Lévy flights, and thus it suits for global optimization problems.
Particle swarm optimization – Based on the ideas of animal flocking behaviour. Also primarily suited for numerical optimization problems.

Other population-based metaheuristic methods

Adaptive dimensional search – Adaptive dimensional search algorithm differs from nature-inspired metaheuristic techniques in the sense that it does not use any metaphor as an underlying principle for its implementation. Rather it utilizes a simple performance-oriented methodology based on the update of the search dimensionality ratio (SDR) parameter at each iterationm.^[6]
Firefly algorithm is inspired by the behavior of fireflies, attracting each other by flashing light. This is especially useful for multimodal optimization.
Harmony search – Based on the ideas of musicians' behavior in searching for better harmonies. This algorithm is suitable for combinatorial optimization as well as parameter optimization.
Gaussian adaptation – Based on information theory. Used for maximization of manufacturing yield, mean fitness or average information. See for instance Entropy in thermodynamics and information theory.
Memetic algorithm – It is the hybrid form of population based methods. Inspired by Dawkins’ notion of a meme, it commonly takes the form of a population-based algorithm coupled with individual learning procedures capable of performing local refinements. Emphasizes the exploitation of problem-specific knowledge, and tries to orchestrate local and global search in a synergic way.

Gallery^[7]

A two-population EA search of a bounded optima in 2D
A two-population EA search over a constrained Rosenbrock function with bounded global optimum.
A two-population EA search over a constrained Rosenbrock function. Global optimum is not bounded.
Estimation of Distribution Algorithm over Keane's function

References

↑ G.S. Hornby and J.B. Pollack. Creating high-level components with a generative representation for body-brain evolution. Artificial Life, 8(3):223–246, 2002.
↑ Jeff Clune, Benjamin Beckmann, Charles Ofria, and Robert Pennock. "Evolving Coordinated Quadruped Gaits with the HyperNEAT Generative Encoding". Proceedings of the IEEE Congress on Evolutionary Computing Special Section on Evolutionary Robotics, 2009. Trondheim, Norway.
↑ J. Clune, C. Ofria, and R. T. Pennock, "How a generative encoding fares as problem-regularity decreases," in PPSN (G. Rudolph, T. Jansen, S. M. Lucas, C. Poloni, and N. Beume, eds.), vol. 5199 of Lecture Notes in Computer Science, pp. 358–367, Springer, 2008.
↑ Ferreira, C., 2001. Gene Expression Programming: A New Adaptive Algorithm for Solving Problems. Complex Systems, Vol. 13, issue 2: 87-129.
↑ F. Merrikh-Bayat, The runner-root algorithm: A metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature, Applied Soft Computing, Vol. 33, pp. 292–303, 2015
↑ Hasançebi, O., Kazemzadeh Azad, S. (2015), Adaptive Dimensional Search: A New Metaheuristic Algorithm for Discrete Truss Sizing Optimization, Computers and Structures, 154, 1-16.
↑ Simionescu, P.A. (2014). Computer Aided Graphing and Simulation Tools for AutoCAD Users (1st ed.). Boca Raton, FL: CRC Press. ISBN 9-781-48225290-3.

Bibliography

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Evolutionary computation

Main Topics	Convergence (evolutionary computing) Evolutionary algorithm Evolutionary data mining Evolutionary multimodal optimization Human-based evolutionary computation Interactive evolutionary computation

Algorithms	Cellular evolutionary algorithm Covariance Matrix Adaptation Evolution Strategy (CMA-ES) Differential evolution Evolutionary programming Genetic algorithm Genetic programming Gene expression programming Evolution strategy Natural evolution strategy Neuroevolution Learning classifier system

Related topics	Artificial development Artificial intelligence Developmental biology Digital organism Evolutionary robotics Fitness function Fitness landscape Fitness approximation Genetic operators Interactive evolutionary computation List of digital organism simulators No free lunch in search and optimization Machine learning Program synthesis

Journals	Evolutionary Computation (journal)

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