This book is devoted to the application of genetic algorithms in continuous global optimization. Some of their properties and behavior are highlighted and formally justified. Various optimization techniques and their taxonomy are the background for detailed discussion. The nature of continuous genetic search is explained by studying the dynamics of probabilistic measure, which is utilized to create subsequent populations. This approach shows that genetic algorithms can be used to extract some areas of the search domain more effectively than to find isolated local minima. The biological metaphor of such behavior is the whole population surviving by rapid exploration of new regions of feeding rather than caring for a single individual. One group of strategies that can make use of this property are two-phase global optimization methods. In the first phase the central parts of the basins of attraction are distinguished by genetic population analysis. Afterwards, the minimizers are found by convex optimization methods executed in parallel.

Klappentext

Genetic algorithms today constitute a family of e?ective global optimization methods used to solve di?cult real-life problems which arise in science and technology. Despite their computational complexity, they have the ability to explore huge data sets and allow us to study exceptionally problematic cases in which the objective functions are irregular and multimodal, and where information about the extrema location is unobtainable in other ways. Theybelongtotheclassofiterativestochasticoptimizationstrategiesthat, during each step, produce and evaluate the set of admissible points from the search domain, called the random sample or population. As opposed to the Monte Carlo strategies, in which the population is sampled according to the uniform probability distribution over the search domain, genetic algorithms modify the probability distribution at each step. Mechanisms which adopt sampling probability distribution are transposed from biology. They are based mainly on genetic code mutation and crossover, as well as on selection among living individuals. Such mechanisms have been testedbysolvingmultimodalproblemsinnature,whichiscon?rmedinpart- ular by the many species of animals and plants that are well ?tted to di?erent ecological niches. They direct the search process, making it more e?ective than a completely random one (search with a uniform sampling distribution). Moreover,well-tunedgenetic-basedoperationsdonotdecreasetheexploration ability of the whole admissible set, which is vital in the global optimization process. The features described above allow us to regard genetic algorithms as a new class of arti?cial intelligence methods which introduce heuristics, well tested in other ?elds, to the classical scheme of stochastic global search.

Inhalt

Global optimization problems.- Basic models of genetic computations.- Asymptotic behavior of the artificial genetic systems.- Adaptation in genetic search.- Two-phase stochastic global optimization strategies.- Summary and perspectives of genetic algorithms in continuous global optimization.