Meta-Modeling by Symbolic Regression and Pareto Simulated Annealing

The subject of this paper is a new approach to Symbolic Regression.Other publications on Symbolic Regression use Genetic Programming.This paper describes an alternative method based on Pareto Simulated Annealing.Our method is based on linear regression for the estimation of constants.Interval arithmetic is applied to ensure the consistency of a model.In order to prevent over-fitting, we merit a model not only on predictions in the data points, but also on the complexity of a model.For the complexity we introduce a new measure.We compare our new method with the Kriging meta-model and against a Symbolic Regression meta-model based on Genetic Programming.We conclude that Pareto Simulated Annealing based Symbolic Regression is very competitive compared to the other meta-model approachesapproximation;meta-modeling;pareto simulated annealing;symbolic regression

The Meta-Model Approach for Simulation-based Design Optimization.

The design of products and processes makes increasing use of computer simulations for the prediction of its performance. These computer simulations are considerably cheaper than their physical equivalent. Finding the optimal design has therefore become a possibility. One approach for finding the optimal design using computer simulations is the meta-model approach, which approximates the behaviour of the computer simulation outcome using a limited number of time-consuming computer simulations. This thesis contains four main contributions, which are illustrated by industrial cases. First, a method is presented for the construction of an experimental design for computer simulations when the design space is restricted by many (nonlinear) constraints. The second contribution is a new approach for the approximation of the simulation outcome. This approximation method is particularly useful when the simulation model outcome reacts highly nonlinear to its inputs. Third, the meta-model based approach is extended to a robust optimization framework. Using this framework, many uncertainties can be taken into account, including uncertainty on the simulation model outcome. The fourth main contribution is the extension of the approach for use in integral design of many parts of complex systems.

Robust Optimization Using Computer Experiments

During metamodel-based optimization three types of implicit errors are typically made.The first error is the simulation-model error, which is defined by the difference between reality and the computer model.The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel.The third is the implementation error.This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors.We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models.The methods proposed are applied to the design of two parts of the TV tube.The simulationmodel errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors

Meta-Modeling by Symbolic Regression and Pareto Simulated Annealing

The subject of this paper is a new approach to Symbolic Regression.Other publications on Symbolic Regression use Genetic Programming.This paper describes an alternative method based on Pareto Simulated Annealing.Our method is based on linear regression for the estimation of constants.Interval arithmetic is applied to ensure the consistency of a model.In order to prevent over-fitting, we merit a model not only on predictions in the data points, but also on the complexity of a model.For the complexity we introduce a new measure.We compare our new method with the Kriging meta-model and against a Symbolic Regression meta-model based on Genetic Programming.We conclude that Pareto Simulated Annealing based Symbolic Regression is very competitive compared to the other meta-model approaches

Coordination of Coupled Black Box Simulations in the Construction of Metamodels

This paper introduces methods to coordinate black box simulations in the construction of metamodels for situations in which we have to deal with coupled black boxes.We de.ne three coordination methods: parallel simulation, sequential simulation and sequential modeling.To compare these three methods we focus on .ve aspects: throughput time, .exibility, simulated product designs, coordination complexityand the use of prior information.Special attention is given to the throughput time aspect.For this aspect we derive mathematical formulas and we give relations between the throughput times of the three coordination methods.At the end of this paper we summarize the results and give recommendations on the choice of a suitable coordination method.simulation;simulation models;coordination;black box;metamodels

Multi-stage metal forming: Variation and transformation

During precision forming of metal parts made of metastable austenitic stainless steels, the relationship between the scatter on the initial parameters like the strip thickness, yield stress, etc. on the product accuracy need to be known. This becomes complex if the material is instable, i.e. martensite forms very easily. The transformation rate depends on the stress state, which is related to friction. It also depends on the temperature, which is related to deformation heat. A greater understanding of these phenomena is obtained by doing a process window study, using design and analysis of computer experiments (DACE). This paper demonstrates how to perform a DACE study on a three-stage metal forming process, using distributed computing. The study focuses on:\ud \ud •Hardening due to strain-induced and stress-assisted transformation.\ud •The influence of metal forming parameters on the product accuracy