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Real-world problems such as computational fluid dynamics simulations and finite element analyses are computationally expensive. A standard approach to mitigating the high computational expense is Surrogate-Based Optimization (SBO). Yet, due to the high-dimensionality of many simulation problems, SBO is not directly applicable or not efficient. Reducing the dimensionality of the search space is one method to overcome this limitation. In addition to the applicability of SBO, dimensionality reduction enables easier data handling and improved data and model interpretability. Regularization is considered as one state-of-the-art technique for dimensionality reduction. We propose a hybridization approach called Regularized-Surrogate-Optimization (RSO) aimed at overcoming difficulties related to high-dimensionality. It couples standard Kriging-based SBO with regularization techniques. The employed regularization methods are based on three adaptations of the least absolute shrinkage and selection operator (LASSO). In addition, tree-based methods are analyzed as an alternative variable selection method. An extensive study is performed on a set of artificial test functions and two real-world applications: the electrostatic precipitator problem and a multilayered composite design problem. Experiments reveal that RSO requires significantly less time than standard SBO to obtain comparable results. The pros and cons of the RSO approach are discussed, and recommendations for practitioners are presented.
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.
Drinking water supply and distribution systems are critical infrastructure that has to be well maintained for the safety of the public. One important tool in the maintenance of water distribution systems (WDS) is flushing. Flushing is a process carried out in a periodic fashion to clean sediments and other contaminants in the water pipes. Given the different topographies, water composition and supply demand between WDS no single flushing strategy is suitable for all of them. In this report a non-exhaustive overview of optimization methods for flushing in WDS is given. Implementation of optimization methods for the flushing procedure and the flushing planing are presented. Suggestions are given as a possible option to optimise existing flushing planing frameworks.
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.
This report presents a practical approach to stacked generalization in surrogate model based optimization. It exemplifies the integration of stacking methods into the surrogate model building process. First, a brief overview of the current state in surrogate model based opti- mization is presented. Stacked generalization is introduced as a promising ensemble surrogate modeling approach. Then two examples (the first is based on a real world application and the second on a set of artificial test functions) are presented. These examples clearly illustrate two properties of stacked generalization: (i) combining information from two poor performing models can result in a good performing model and (ii) even if the ensemble contains a good performing model, combining its information with information from poor performing models results in a relatively small performance decrease only.
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.
Cyclone Dust Separators are devices often used to filter solid particles from flue gas. Such cyclones are supposed to filter as much solid particles from the carrying gas as possible. At the same time, they should only introduce a minimal pressure loss to the system. Hence, collection efficiency has to be maximized and pressure loss minimized. Both the collection efficiency and pressure loss are heavily influenced by the cyclones geometry. In this paper, we optimize seven geometrical parameters of an analytical cyclone model. Furthermore, noise variables are introduced to the model, representing the non-deterministic structure of the real-world problem. This is used to investigate robustness and sensitivity of solutions. Both the deterministic as well as the stochastic model are optimized with an SMS-EMOA. The SMS-EMOA is compared to a single objective optimization algorithm. For the harder, stochastic optimization problem, a surrogate-model-supported SMS-EMOA is compared against the model-free SMS-EMOA. The model supported approach yields better solutions with the same run-time budget.
Sequential Parameter Optimization is a model-based optimization methodology, which includes several techniques for handling uncertainty. Simple approaches such as sharp- ening and more sophisticated approaches such as optimal computing budget allocation are available. For many real world engineering problems, the objective function can be evaluated at different levels of fidelity. For instance, a CFD simulation might provide a very time consuming but accurate way to estimate the quality of a solution.The same solution could be evaluated based on simplified mathematical equations, leading to a cheaper but less accurate estimate. Combining these different levels of fidelity in a model-based optimization process is referred to as multi-fidelity optimization. This chapter describes uncertainty-handling techniques for meta-model based search heuristics in combination with multi-fidelity optimization. Co-Kriging is one power- ful method to correlate multiple sets of data from different levels of fidelity. For the first time, Sequential Parameter Optimization with co-Kriging is applied to noisy test functions. This study will introduce these techniques and discuss how they can be applied to real-world examples.
Sensor placement for contaminant detection in water distribution systems (WDS) has become a topic of great interest aiming to secure a population's water supply. Several approaches can be found in the literature with differences ranging from the objective selected to optimize to the methods implemented to solve the optimization problem. In this work we aim to give an overview of the current work in sensor placement with focus on contaminant detection for WDS. We present some of the objectives for which the sensor placement problem is defined along with common optimization algorithms and Toolkits available to help with algorithm testing and comparison.
Many black-box optimization problems rely on simulations to evaluate the quality of candidate solutions. These evaluations can be computationally expensive and very time-consuming. We present and approach to mitigate this problem by taking into consideration two factors: The number of evaluations and the execution time. We aim to keep the number of evaluations low by using Bayesian optimization (BO) – known to be sample efficient– and to reduce wall-clock times by executing parallel evaluations. Four parallelization methods using BO as optimizer are compared against the inherently parallel CMA-ES. Each method is evaluated on all the 24 objective functions of the Black-Box-Optimization-Benchmarking test suite in their 20-dimensional versions. The results show that parallelized BO outperforms the state-of-the-art CMA-ES on most of the test functions, also on higher dimensions.
An important class of black-box optimization problems relies on using simulations to assess the quality of a given candidate solution. Solving such problems can be computationally expensive because each simulation is very time-consuming. We present an approach to mitigate this problem by distinguishing two factors of computational cost: the number of trials and the time needed to execute the trials. Our approach tries to keep down the number of trials by using Bayesian optimization (BO) –known to be sample efficient– and reducing wall-clock times by parallel execution of trials. We compare the performance of four parallelization methods and two model-free alternatives. Each method is evaluated on all 24 objective functions of the Black-Box-Optimization- Benchmarking (BBOB) test suite in their five, ten, and 20-dimensional versions. Additionally, their performance is investigated on six test cases in robot learning. The results show that parallelized BO outperforms the state-of-the-art CMA-ES on the BBOB test functions, especially for higher dimensions. On the robot learning tasks, the differences are less clear, but the data do support parallelized BO as the ‘best guess’, winning on some cases and never losing.
Increasing computational power and the availability of 3D printers provide new tools for the combination of modeling and experimentation. Several simulation tools can be run independently and in parallel, e.g., long running computational fluid dynamics simulations can be accompanied by experiments with 3D printers. Furthermore, results from analytical and data-driven models can be incorporated. However, there are fundamental differences between these modeling approaches: some models, e.g., analytical models, use domain knowledge, whereas data-driven models do not require any information about the underlying processes.
At the same time, data-driven models require input and output data, but analytical models do not. Combining results from models with different input-output structures might improve and accelerate the optimization process. The optimization via multimodel simulation (OMMS) approach, which is able to combine results from these different models, is introduced in this paper.
Using cyclonic dust separators as a real-world simulation problem, the feasibility of this approach is demonstrated and a proof-of-concept is presented. Cyclones are popular devices used to filter dust from the emitted flue gases. They are applied as pre-filters in many industrial processes including energy production and grain processing facilities. Pros and cons of this multimodel optimization approach are discussed and experiences from experiments are presented.
Cyclone separators are popular devices used to filter dust from the emitted flue gases. They are applied as pre-filters in many industrial processes including energy production and grain processing facilities.
Increasing computational power and the availability of 3D printers provide new tools for the combination of modeling and experimentation, which necessary for constructing efficient cyclones. Several simulation tools can be run in parallel, e.g., long running CFD simulations can be accompanied by experiments with 3D printers. Furthermore, results from analytical and data-driven models can be incorporated. There are fundamental differences between these modeling approaches: some models, e.g., analytical models, use domain knowledge, whereas data-driven models do not require any information about the underlying processes.
At the same time, data-driven models require input and output data, whereas analytical models do not. Combining results from models with different input-output structure is of great interest. This combination inspired the development of a new methodology. An optimization via multimodel simulation approach, which combines results from different models, is introduced.
Using cyclonic dust separators (cyclones) as a real-world simulation problem, the feasibility of this approach is demonstrated. Pros and cons of this approach are discussed and experiences from the experiments are presented.
Furthermore, technical problems, which are related to 3D-printing approaches, are discussed.
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.
Modelling Zero-inflated Rainfall Data through the Use of Gaussian Process and Bayesian Regression
(2018)
Rainfall is a key parameter for understanding the water cycle. An accurate rainfall measurement is vital in the development of hydrological models. By means of indirect measurement, satellites can nowadays estimate the rainfall around the world. However, these measurements are not always accurate. As a first approach to generate a bias-corrected rainfall estimate using satellite data, the performance of Gaussian process and Bayesian regression is studied. The results show Gaussian process as the better option for this dataset but leave place to improvements on both modelling strategies.
In this paper we present a comparison of different data driven modeling methods. The first instance of a data driven linear Bayesian model is compared with several linear regression models, a Kriging model and a genetic programming model.
The models are build on industrial data for the development of a robust gas sensor.
The data contain limited amount of samples and a high variance.
The mean square error of the models implemented in a test dataset is used as the comparison strategy.
The results indicate that standard linear regression approaches as well as Kriging and GP show good results,
whereas the Bayesian approach, despite the fact that it requires additional resources, does not lead to improved results.
The use of surrogate models is a standard method to deal with complex, realworld
optimization problems. The first surrogate models were applied to continuous
optimization problems. In recent years, surrogate models gained importance
for discrete optimization problems. This article, which consists of three
parts, takes care of this development. The first part presents a survey of modelbased
methods, focusing on continuous optimization. It introduces a taxonomy,
which is useful as a guideline for selecting adequate model-based optimization
tools. The second part provides details for the case of discrete optimization
problems. Here, six strategies for dealing with discrete data structures are introduced.
A new approach for combining surrogate information via stacking
is proposed in the third part. The implementation of this approach will be
available in the open source R package SPOT2. The article concludes with a
discussion of recent developments and challenges in both application domains.
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.
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.
Computational intelligence methods have gained importance in several real-world domains such as process optimization, system identification, data mining, or statistical quality control. Tools are missing, which determine the applicability of computational intelligence methods in these application domains in an objective manner. Statistics provide methods for comparing algorithms on certain data sets. In the past, several test suites were presented and considered as state of the art. However, there are several drawbacks of these test suites, namely: (i) problem instances are somehow artificial and have no direct link to real-world settings; (ii) since there is a fixed number of test instances, algorithms can be fitted or tuned to this specific and very limited set of test functions; (iii) statistical tools for comparisons of several algorithms on several test problem instances are relatively complex and not easily to analyze. We propose amethodology to overcome these dificulties. It is based on standard ideas from statistics: analysis of variance and its extension to mixed models. This work combines essential ideas from two approaches: problem generation and statistical analysis of computer experiments.