The impact of operator disruption and genetic drift on the extinction of EA subpopulations on multimodal landscapes is estimated by means of idealized two-peak landscape models. To establish upper and lower bounds for extinction times the behavior of an EA that employs (µ + , λ) selection and recombination mechanisms is studied, assuming disruptive recombination. Markov chain and statistical simulation studies reveal that panmictic selection mechanisms as used in evolution strategies (ES) do not allow for maintaining several populations of similar fitness at the same time. Moreover, when using comma selection, good individuals might easily get lost if forming the minority of a population, an effect seemingly amplified by recombination. Niching techniques are suggested to facilitate coexistence of populations on distant attractors; conducted studies confirm their aptitude.
In time-dependent optimization problems the main task for a problem solver is not to find a good solution, but to track the moving best solution. It is well-knownthat evolutionary algorithms (EA) can cope with this requirement. A main attribute of many EA is the self-adaptability. The functioning of this feature depends on the setting of several EA parameters. In case of evolution strategies it is still unknown under which conditions the algorithm is able to converge against the optimum. Our investigations concern different population sizes and X as well as the correlation between the best function value and the diversity of the population on some selected test functions.
Summary. Numerical parameter optimization is an often needed task. In many times, it is not necessary to find the exact optimum but a good solution in an appropriate time. Especially in dynamic environments the main task is not to find one nearly optimal solution but to track the moving optimum as narrow as possible. For this type of problems it is necessary for an optimization algorithm to own mechanisms for adaptation to the problem at hand. Evolutionary algorithms with self-adaptive features are state-of-the-art and known as good problem solvers for this type of optimization tasks. In this chapter, we present a detailed description of one main variant of this class of problem solvers, namely evolution strategies.
IntroductionEvolutionary algorithms (EA) are a class of nature inspired problem solvers. They use mechanisms known from natural evolution and have in common the transfer of their biological background into optimization. EA have proven their potentials in many real world applications. It is known that in static environments evolutionary algorithms find good or nearly optimal solutions even for difficult problems in a short time. In addition, they own a high robustness against changes of the problem instance over a certain range. Moreover, state-of-the-art EA like evolution strategies (ES) can adapt to different situations during the run. Such a feature makes them interesting for application in dynamic environments . These types of problems seem to be the more interesting ones since most real world problems are of non-stationary type.In dynamic optimization we can divide two distinct phases. At first, the algorithm needs some time to search for the optimum. The period needed for this task is called the searching phase. Once the algorithm has found the optimum within a certain accuracy the algorithm must follow the moving optimum with a distance as small as possible. This phase is called the tracking phase and lasts potentially eternally.Dynamic optimization problems are harder to optimize than static problems. The more difficulty of optimization in non-stationary environments is L. Schönemann: Evolution Strategies in Dynamic Environments, Studies in Computational Intelligence (SCI) 51, 51-77 (2007) www.springerlink.com
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