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Benchmark experiments are required to test, compare, tune, and understand optimization algorithms. Ideally, benchmark problems closely reflect real-world problem behavior. Yet, real-world problems are not always readily available for benchmarking. For example, evaluation costs may be too high, or resources are unavailable (e.g., software or equipment). As a solution, data from previous evaluations can be used to train surrogate models which are then used for benchmarking. The goal is to generate test functions on which the performance of an algorithm is similar to that on the real-world objective function. However, predictions from data-driven models tend to be smoother than the ground-truth from which the training data is derived. This is especially problematic when the training data becomes sparse. The resulting benchmarks may not reflect the landscape features of the ground-truth, are too easy, and may lead to biased conclusions.
To resolve this, we use simulation of Gaussian processes instead of estimation (or prediction). This retains the covariance properties estimated during model training. While previous research suggested a decomposition-based approach for a small-scale, discrete problem, we show that the spectral simulation method enables simulation for continuous optimization problems. In a set of experiments with an artificial ground-truth, we demonstrate that this yields more accurate benchmarks than simply predicting with the Gaussian process model.

Multi-criteria optimization has gained increasing attention during the last decades. This article exemplifies multi-criteria features, which are implemented in the statistical software package SPOT. It describes related software packages such as mco and emoa and gives a comprehensive introduction to simple multi criteria optimization tasks. Several hands-on examples are used for illustration. The article is well-suited as a starting point for performing multi-criteria optimization tasks with SPOT.

An essential task for operation and planning of biogas plants is the optimization of substrate feed mixtures. Optimizing the monetary gain requires the determination of the exact amounts of maize, manure, grass silage, and other substrates. Accurate simulation models are mandatory for this optimization, because the underlying chemical processes are very slow. The simulation models themselves may be time-consuming to evaluate, hence we show how to use surrogate-model-based approaches to optimize biogas plants efficiently. In detail, a Kriging surrogate is employed. To improve model quality of this surrogate, we integrate cheaply available data into the optimization process. Doing so, Multi-fidelity modeling methods like Co-Kriging are employed. Furthermore, a two-layered modeling approach is employed to avoid deterioration of model quality due to discontinuities in the search space. At the same time, the cheaply available data is shown to be very useful for initialization of the employed optimization algorithms. Overall, we show how biogas plants can be efficiently modeled using data-driven methods, avoiding discontinuities as well as including cheaply available data. The application of the derived surrogate models to an optimization process is shown to be very difficult, yet successful for a lower problem dimension.

When designing or developing optimization algorithms, test functions are crucial to evaluate
performance. Often, test functions are not sufficiently difficult, diverse, flexible or relevant to real-world
applications. Previously,
test functions with real-world relevance were generated by training a machine learning model based on
real-world data. The model estimation is used as a test function.
We propose a more principled approach using simulation instead of estimation.
Thus, relevant and varied test functions
are created which represent the behavior of real-world fitness landscapes.
Importantly, estimation can lead to excessively smooth test functions
while simulation may avoid this pitfall. Moreover, the simulation
can be conditioned by the data, so that the simulation reproduces the training data
but features diverse behavior in unobserved regions of the search space.
The proposed test function generator is illustrated with an intuitive, one-dimensional
example. To demonstrate the utility of this approach it
is applied to a protein sequence optimization problem.
This application demonstrates the advantages as well as practical limits of simulation-based
test functions.

Formerly, multi-criteria optimization algorithms were often tested using tens of thousands function evaluations. In many real-world settings function evaluations are very costly or the available budget is very limited. Several methods were developed to solve these cost-extensive multi-criteria optimization problems by reducing the number of function evaluations by means of surrogate optimization. In this study, we apply different multi-criteria surrogate optimization methods to improve (tune) an event-detection software for water-quality monitoring. For tuning two important parameters of this software, four state-of-the-art methods are compared: S-Metric-Selection Efficient Global Optimization (SMS-EGO), S-Metric-Expected Improvement for Efficient Global Optimization SExI-EGO, Euclidean Distance based Expected Improvement Euclid-EI (here referred to as MEI-SPOT due to its implementation in the Sequential Parameter Optimization Toolbox SPOT) and a multi-criteria approach based on SPO (MSPOT). Analyzing the performance of the different methods provides insight into the working-mechanisms of cutting-edge multi-criteria solvers. As one of the approaches, namely MSPOT, does not consider the prediction variance of the surrogate model, it is of interest whether this can lead to premature convergence on the practical tuning problem. Furthermore, all four approaches will be compared to a simple SMS-EMOA to validate that the use of surrogate models is justified on this problem.

Surrogate-assisted optimization has proven to be very successful if applied to industrial problems. The use of a data-driven surrogate model of an objective function during an optimization cycle has many bene ts, such as being cheap to evaluate and further providing both information about the objective landscape and the parameter space. In preliminary work, it was researched how surrogate-assisted optimization can help to optimize the structure of a neural network (NN) controller. In this work, we will focus on how surrogates can help to improve the direct learning process of a transparent feed-forward neural network controller. As an initial case study we will consider a manageable real-world control task: the elevator supervisory group problem (ESGC) using a simplified simulation model. We use this model as a benchmark which should indicate the applicability and performance of surrogate-assisted optimization to this kind of tasks. While the optimization process itself is in this case not onsidered expensive, the results show that surrogate-assisted optimization is capable of outperforming metaheuristic optimization methods for a low number of evaluations. Further the surrogate can be used for signi cance analysis of the inputs and weighted connections to further exploit problem information.

The availability of several CPU cores on current computers enables
parallelization and increases the computational power significantly.
Optimization algorithms have to be adapted to exploit these highly
parallelized systems and evaluate multiple candidate solutions in
each iteration. This issue is especially challenging for expensive
optimization problems, where surrogate models are employed to
reduce the load of objective function evaluations.
This paper compares different approaches for surrogate modelbased
optimization in parallel environments. Additionally, an easy
to use method, which was developed for an industrial project, is
proposed. All described algorithms are tested with a variety of
standard benchmark functions. Furthermore, they are applied to
a real-world engineering problem, the electrostatic precipitator
problem. Expensive computational fluid dynamics simulations are
required to estimate the performance of the precipitator. The task
is to optimize a gas-distribution system so that a desired velocity
distribution is achieved for the gas flow throughout the precipitator.
The vast amount of possible configurations leads to a complex
discrete valued optimization problem. The experiments indicate
that a hybrid approach works best, which proposes candidate solutions
based on different surrogate model-based infill criteria and
evolutionary operators.

Surrogate-based optimization relies on so-called infill criteria (acquisition functions) to decide which point to evaluate next. When Kriging is used as the surrogate model of choice (also called Bayesian optimization), one of the most frequently chosen criteria is expected improvement. We argue that the popularity of expected improvement largely relies on its theoretical properties rather than empirically validated performance. Few results from the literature show evidence, that under certain conditions, expected improvement may perform worse than something as simple as the predicted value of the surrogate model. We benchmark both infill criteria in an extensive empirical study on the ‘BBOB’ function set. This investigation includes a detailed study of the impact of problem dimensionality on algorithm performance. The results support the hypothesis that exploration loses importance with increasing problem dimensionality. A statistical analysis reveals that the purely exploitative search with the predicted value criterion performs better on most problems of five or higher dimensions. Possible reasons for these results are discussed. In addition, we give an in-depth guide for choosing the infill criteria based on prior knowledge about the problem at hand, its dimensionality, and the available budget.

To maximize the throughput of a hot rolling mill,
the number of passes has to be reduced. This can be achieved by maximizing the thickness reduction in each pass. For this purpose, exact predictions of roll force and torque are required. Hence, the predictive models that describe the physical behavior of the product have to be accurate and cover a wide range of different materials.
Due to market requirements a lot of new materials are tested and rolled. If these materials are chosen to be rolled more often, a suitable flow curve has to be established. It is not reasonable to determine those flow curves in laboratory, because of costs and time. A strong demand for quick parameter determination and the optimization of flow curve parameter with minimum costs is the logical consequence. Therefore parameter estimation and the optimization with real data, which were collected during previous runs, is a promising idea. Producers benefit from this data-driven approach and receive a huge gain in flexibility when rolling new
materials, optimizing current production, and increasing quality. This concept would also allow to optimize flow curve parameters, which have already been treated by standard methods. In this article, a new data-driven approach for predicting the physical behavior of the product and setting important parameters is presented.
We demonstrate how the prediction quality of the roll force and roll torque can be optimized sustainably. This offers the opportunity to continuously increase the workload in each pass to the theoretical maximum while product quality and process stability can also be improved.

This paper introduces UniFIeD, a new data preprocessing method for time series. UniFIeD can cope with large intervals of missing data. A scalable test function generator, which allows the simulation of time series with different gap sizes, is presented additionally. An experimental study demonstrates that (i) UniFIeD shows a significant better performance than simple imputation methods and (ii) UniFIeD is able to handle situations, where advanced imputation methods fail. The results are independent from the underlying error measurements.