The aim of this paper is to provide an introduction to the rapidly developing field of genetic programming (GP). Particular emphasis is placed on the application of GP to engineering problem solving. First, the basic methodology is introduced. This is followed by a review of applications in the areas of systems modelling, control, optimisation and scheduling, design and signal processing. The paper concludes by suggesting potential avenues of research.

This paper describes an approach for data-driven generation of structured models of complex and unknown processes by means of genetic programming. The basic approach which is used to generate and to modify symbolic model descriptions represented as block diagrams is introduced and an application for modelling of an industrial biotechnological fed-batch fermentation process is presented.

The article at hand describes an approach for the self-organizing generation of models of complex and unknown processes by means of genetic programming and its application on a biotechnological fed-batch production.

Modeling of bioprocesses for engineering applications is a very dif®cult and time consuming task, due to their complex nonlinear dynamic behavior. In the last years several propositions for hybrid models, and especially serial approaches, were published and discussed, in order to combine analytical prior knowledge with the learning capabilities of Arti®cial Neural Networks (ANN). These approaches often require synchronous and equidistant sampled training data. However, in practice concentrations are mostly off-line measured, rare, and asynchronous. In this paper a new training method especially suited for very few asynchronously sampled data is presented and applied for modeling animal cell cultures. The achieved model is able to predict the concentrations of the reaction components inside a stirred tank bioreactor. IntroductionBiotechnology is among the most modern technologies. Its fundamentals are the subject of scienti®c research and its various applications are explored in engineering science. One problem in process engineering is the lack of accurate process models at the macroscopic level. Those are not only necessary for the design of control, but also for the development and understanding of a process. Computer simulations based on a process model are useful to reduce the number of experiments with the real bioprocesses, which are expensive, and particularly time consuming.ANN is one of the most commonly used approach from a large variety of data driven modeling techniques [1]. The disadvantage of neural modeling is the lack of transparency. In ANN models process knowledge is represented in an unstructured``black box''. Therefore, it is extremely dif®cult to make use of existing process knowledge.Numerous authors have shown that so called hybrid approaches offer certain advantages compared to pure ANN approaches. Prior knowledge, which is usually available in form of balance equations, is used as basis for the model and only the unknown parts are learned by an ANN. Thompson and Kramer [2] distinguish between two types of hybrid models. In the ®rst type of approach, the weights of classical ANNs are trained with respect to certain constraints which limit the search space. These constraints are de®ned using the existing knowledge, e.g. in order to insure the stability of the model [3]. In the second type classical``white box'' models are combined with neural``black box'' components. Among several possible architectures the parallel and serial structures, as shown in Fig. 1, are the most common ones.In the parallel structure (Fig. 1, left) a complete classical model is connected in parallel with a neural network. The classical model provides an estimation of the output, while the neural network is trained to compensate remaining errors between the model and the observed process behaviour. In the serial structure (Fig. 1, right) an incomplete classical model is used. The unknown or hardly known terms ± e.g. the process kinetics ± are represented by an ANN. The latter approach is used in the present work.In ...

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