# Evolutionary algorithm

an evolutionary algorithm (I/O) is an optimization procedure, which has the biological evolution as model.

## procedures

the evolution is in the situation, by manipulation of the hereditary property complex ways of lifeto adapt and organisms to their environmental and living conditions. It solves thereby a very difficult optimization problem. The most amazing characteristic of the evolution is the relative simplicity of their proceeding and cooperating the different control mechanisms. In a simple model the accomplished search process on three simple principles leaves itselflead back: Mutation, selection and recombination.

• The mutation of the hereditary property is a nondirectional process, whose sense only lies in the production of alternatives and variants. From view to the mutation the task comes to the optimization theory to overcome local optima. It ensures for the fact that the population notpromptly against a local optimum converges. The probabilities of mutation per gene are appropriate generally between [itex] 10^ {- for 4}< /math> and [itex] 10^ {- 7}< /math>.
• The recombination (Crossover) of the heiress formation lies regarding its contribution for Zielfindung in the context of the evolution between mutation and selection. The places, at those a Crossover between homologous Chromosomentakes place, are coincidentally determined. Actual recombination takes place however no longer coincidentally. Close adjoining and functionally connected genes are separated more rarely than groups of genes lying apart further. An evolutionary algorithm can get along without recombination (i.e. there is a asexuelle reproduction of the individual individuals with only one parentsper child), in certain cases the use of recombination is however more efficient.
• The selection is responsible for the actual controlling of the search direction of the evolution. It determines the direction, in which changed, by specifying, which phenotypes increase the hereditary property more strongly. The selection would beso, if there were no disturbances, a deterministic component within the evolution. In nature the selection is disturbed again and again however by usually fortuitous events. Also best the individuals adapted to their environment can die by a misfortune, before they witness to descendants. Thusbecame if the genetic information, which represents an optimum, lost to go. Two further influences make the selection a indeterministischen factor. On the one hand it is not constant size, since the environment and the living conditions of the individuals can change, on the other hand gives it a feedback betweenthe individual individuals and their environment. These can affect their own selection by interferences into the environment.

## at the beginning

of the sixties different groups of researchers the principles of the evolution already began to copy history, in order to develop efficient optimization algorithms. So Holland and gold mountain have those Genetic algorithms (GA), Fogel evolutionary programming (EP), sulfur and computing mountain the evolution-strategic algorithms (IT) develops. These developments developed independently, which are summarized under the comprehensive term evolutionary algorithms (I/O), to have the common characteristic to copy consciously principles of the evolution around it in the sense of optimization rulesto begin.

## areas of application

the most important areas of application of the evolutionary algorithms are optimization problems, for which traditional optimization procedures fail due to Nichtlinearitäten , these continuities and multi-modality. The characteristic of their robustness lies in the fact justified that on the one hand no acceptance are met over the problem posed, and toothers always with a quantity of permissible solutions (population of solutions) one works. Thus several ways to the optimum, whereby also still information about the different ways are tried out at the same time (by transmission and/or. Recombination) to be exchanged. In this way the knowledge becomes over the underlying problemin the entire population it distributes whereby an early convergence can be prevented during the optimization.

## characteristics

recapitulatory one can describe the pro and cons of the evolutionary algorithms as follows:

• They offer a parallel search in a population of possible solutions, so that alwaysseveral potential solutions to be found.
• They need no gradient information, can thus also with nonlinear or intermittent problems be used.
• They belong to no more to the class of the stochastic search methods, make possible thus also the treatment of complicated problems, those due to a too high cost of computation with traditional optimization methodsare manageable.
• Evolutionary algorithms offer generally no warranty to find the global optimum. However there is a proof for the procedure of the simulated cooling (simulated annealing) under further conditions that this finds the global optimum in finite time.
• Large disadvantagethe EAs is the often very large computing time need: Evolutionary algorithms should not for the solution by problems are used, for which there are already traditional optimization procedures, since this are usually more efficient. So e.g. are.Newton Raphson methods, which use gradients during the optimization, with thatSearch local minima around a multiple faster than evolutionary algorithms.

Among the evolutionary algorithms one ranks: