Evolutionary algorithm

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Evolutionary algorithm
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In

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.

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. 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. In most real applications of EAs, computational complexity is a prohibiting factor.[2] 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;[3][4][5] therefore, there may be no direct link between algorithm complexity and problem complexity.

Evolutionary algorithms can be seen as a kind of

Monte-Carlo method.[6]

Implementation

The following is an example of a generic single-objective genetic algorithm.

Step One: Generate the initial population of individuals randomly. (First generation)

Step Two: Repeat the following regenerational steps until termination:

  1. Evaluate the fitness of each individual in the population (time limit, sufficient fitness achieved, etc.)
  2. Select the fittest individuals for
    reproduction
    . (Parents)
  3. Breed new individuals through crossover and mutation operations to give birth to offspring.
  4. Replace the least-fit individuals of the population with new individuals.

Types

Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem.

  • 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. There are many variants of Genetic Programming, including Cartesian genetic programming, gene expression programming, grammatical evolution, linear genetic programming, multi expression programming etc.
  • Evolutionary programming – Similar to genetic programming, but the structure of the program is fixed and its numerical parameters are allowed to evolve.
  • Evolution strategy – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks.[7][8]
  • numerical optimization
    problems.
  • Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions.[9][10]
  • 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 solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of 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 typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach.
  • Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique.[11][12][13]

Theoretical background

The following theoretical principles apply to all or almost all EAs.

No free lunch theorem

The no free lunch theorem of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a problem-adapted coding). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through heuristics or other procedures.[14][15] Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, local search procedures or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a memetic algorithm. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust.[14][16]

Convergence

Further information: Convergence (evolutionary computing)
See also: Convergent evolution

For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of

optimum exists. Without loss of generality
, a maximum search is assumed for the proof:

From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation an improvement of the fitness of the respective best individual will occur with a probability . Thus:

I.e., the fitness values represent a monotonically non-decreasing sequence, which is bounded due to the existence of the optimum. From this follows the convergence of the sequence against the optimum.

Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual panmictic population model, elitist EAs tend to converge prematurely more than non-elitist ones.[17] In a panmictic population model, mate selection (step 2 of the section about implementation) is such that every individual in the entire population is eligible as a mate. In non-panmictic populations, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection.[18][19]

Virtual alphabets

With the theory of virtual alphabets, David E. Goldberg showed in 1990 that by using a representation with real numbers, an EA that uses classical recombination operators (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers.[20] This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion.[21][22]

Comparison to biological processes

A possible limitation[

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.[23][24] Such indirect (also known as generative or developmental) encodings also enable evolution to exploit the regularity in the environment.[25] 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.[26][improper synthesis?
]

Applications

The areas in which evolutionary algorithms are practically used are almost unlimited[5] and range from industry,[27][28] engineering,[2][3][29] complex scheduling,[4][30][31] agriculture,[32] robot movement planning[33] and finance[34][35] to research[36][37] and art. The application of an evolutionary algorithm requires some rethinking from the inexperienced user, as the approach to a task using an EA is different from conventional exact methods and this is usually not part of the curriculum of engineers or other disciplines. For example, the fitness calculation must not only formulate the goal but also support the evolutionary search process towards it, e.g. by rewarding improvements that do not yet lead to a better evaluation of the original quality criteria. For example, if peak utilisation of resources such as personnel deployment or energy consumption is to be avoided in a scheduling task, it is not sufficient to assess the maximum utilisation. Rather, the number and duration of exceedances of a still acceptable level should also be recorded in order to reward reductions below the actual maximum peak value.[38] There are therefore some publications that are aimed at the beginner and want to help avoiding beginner's mistakes as well as leading an application project to success.[38][39][40] This includes clarifying the fundamental question of when an EA should be used to solve a problem and when it is better not to.

Related techniques

Swarm algorithms[clarification needed] include:

Other population-based metaheuristic methods

  • Hunting search – A method inspired by the group hunting of some animals, such as wolves, that organize their position to surround the prey, each of them relative to the position of the others and especially that of their leader. It is a continuous optimization method[43] adapted as a combinatorial optimization method.[44]
  • Adaptive dimensional search – Unlike nature-inspired metaheuristic techniques, an adaptive dimensional search algorithm does not implement any metaphor as an underlying principle. Rather it uses a simple performance-oriented method, based on the update of the search dimensionality ratio (SDR) parameter at each iteration.[45]
  • 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.
  • average information. See for instance Entropy in thermodynamics and information theory
    .
  • Memetic algorithm – A hybrid method, inspired by Richard Dawkins's 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 synergistic way.

Examples

In 2020, Google stated that their AutoML-Zero can successfully rediscover classic algorithms such as the concept of neural networks.[46]

The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics.

Gallery

[47][48][49]

References

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External links

Bibliography

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