The problem of finding optimal values in complex parameter optimization problems has often been solved with success by evolutionary algorithms (EAs). In many cases, these algorithms are employed as black-box methods over imprecisely known domains. Such problems arise frequently in engineering design. The principal barrier to the general use of EAs for those problems is the huge number of function evaluations that is often required. This makes EAs an impractical approach when the function evaluation depends on numerically heavy design analysis tools, for example, finite elements methods. This paper presents the use of kriging interpolation as a function approximation method for the construction of an internal model of the fitness landscape. This model is intended to guide the search process with a reduced number of fitness function evaluations.

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The application of Genetic Programming to the discovery of empirical laws is often impaired by the huge size of the search space, and consequently by the computer resources needed. In many cases, the extreme demand for memory and CPU is due to the massive growth of non-coding segments, the introns. The paper presents a new program evolution framework which combines distribution-based evolution in the PBIL spirit, with grammar-based genetic programming; the information is stored as a probability distribution on the grammar rules, rather than in a population. Experiments on a real-world like problem show that this approach gives a practical solution to the problem of intron growth.