Nonlinear model structure identification using genetic programming

Genetic programming can be used for structural optimisation. Combined with a hybrid simplex/simulated annealing algorithm, it is applied to the identification of nonlinear dynamic models from simulated experimental data. Nonlinear models similar to the original test model of the system are identified, yielding both correct structures and accurate parameters.

Structural system identification using genetic programming and a block diagram oriented simulation tool

Systems modelling using genetic programming

Evolutionary self-organising modelling of a municipal wastewater treatment plant.

Symbolic regression methods generate expression trees that simultaneously define the functional form of a regression model and the regression parameter values. As a result, the regression problem can search many nonlinear functional forms using only the specification of simple mathematical operators such as addition, subtraction, multiplication, and division, among others. Currently, state-of-the-art symbolic regression methods leverage genetic algorithms and adaptive programming techniques. Genetic algorithms lack optimality certifications and are typically stochastic in nature. In contrast, we propose an optimization formulation for the rigorous deterministic optimization of the symbolic regression problem. We present a mixed-integer nonlinear programming (MINLP) formulation to solve the symbolic regression problem as well as several alternative models to eliminate redundancies and symmetries. We demonstrate this symbolic regression technique using an array of experiments based upon literature instances. We then use a set of 24 MINLPs from symbolic regression to compare the performance of five local and five global MINLP solvers. Finally, we use larger instances to demonstrate that a portfolio of models provides an effective solution mechanism for problems of the size typically addressed in the symbolic regression literature.

A global MINLP approach to symbolic regression

The article describes an approach for the self organizing generation of models of complex and unknown processes by means of genetic programming and its application in a biotechnological fed batch production. The approach described combines novel results of computer science-genetic programming-with well known and proven techniques of control and system theory-block diagrams and Z transformation. The synthesis of these approaches is a powerful tool for data driven modelling that offers a large number of possibilities to integrate existing knowledge e.g. on submodels or expected elements. The models received by the use of this tool provide a transparent insight into the structure of the process and a basis for long term prediction of the process behaviour and therefore for the determination of optimal setpoint profiles. That means that this approach may overcome the specific difficulties that are bound to the use of adaptive or learning-in the sense of neural networks-methods.

H. Rettenmaier

Papers

Self-organizing structured modelling of a biotechnological fed-batch fermentation by means of genetic programming