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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 a methodology to overcome these difficulties. It is based on standard ideas from statistics: analysis of variance and its extension to mixed models. This paper combines essential ideas from two approaches: problem generation and statistical analysis of computer experiments.
This paper proposes an experimental methodology for on-line machine learning algorithms, i.e., for algorithms that work on data that are available in a sequential order.
It is demonstrated how established tools from experimental algorithmics (EA) can be applied in the on-line or streaming data setting.
The massive on-line analysis (MOA) framework is used to perform the experiments.
Benefits of a well-defined report structure are discussed.
The application of methods from the EA community to on-line or streaming data is referred to as experimental algorithmics for streaming data (EADS).
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.
The performance of optimization algorithms relies crucially on their parameterizations. Finding good parameter settings is called algorithm tuning. Using
a simple simulated annealing algorithm, we will demonstrate how optimization algorithms can be tuned using the Sequential Parameter Optimization Toolbox (SPOT). SPOT provides several tools for automated and interactive tuning. The underlying concepts of the SPOT approach are explained. This includes key techniques such as exploratory fitness landscape analysis and response surface methodology. Many examples illustrate
how SPOT can be used for understanding the performance of algorithms and gaining insight into algorithm behavior. Furthermore, we demonstrate how SPOT can be used as an optimizer and how a sophisticated ensemble approach is able to combine several meta models via stacking.
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.
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.
EventDetectR: An efficient Event Detection System (EDS) capable of detecting unexpected water quality conditions. This approach uses multiple algorithms to model the relationship between various multivariate water quality signals. Then the residuals of the models were utilized in constructing the event detection algorithm, which provides a continuous measure of the probability of an event at every time step. The proposed framework was tested for water contamination events with industrial data from automated water quality sensors. The results showed that the framework is reliable with better performance and is highly suitable for event detection.
We propose to apply typed Genetic Programming (GP) to the problem of finding surrogate-model ensembles for global optimization on compute-intensive target functions. In a model ensemble, base-models such as linear models, random forest models, or Kriging models, as well as pre- and post-processing methods, are combined. In theory, an optimal ensemble will join the strengths of its comprising base-models while avoiding their weaknesses, offering higher prediction accuracy and robustness. This study defines a grammar of model ensemble expressions and searches the set for optimal ensembles via GP. We performed an extensive experimental study based on 10 different objective functions and 2 sets of base-models. We arrive at promising results, as on unseen test data, our ensembles perform not significantly worse than the best base-model.
When using machine learning techniques for learning a function approximation from given data it is often a difficult task to select the right modeling technique.
In many real-world settings is no preliminary knowledge about the objective function available. Then it might be beneficial if the algorithm could learn all models by itself and select the model that suits best to the problem.
This approach is known as automated model selection. In this work we propose a
generalization of this approach.
It combines the predictions of several into one more accurate ensemble surrogate model. This approach is studied in a fundamental way, by first evaluating minimalistic ensembles of only two surrogate models in detail and then proceeding to ensembles with three and more surrogate models.
The results show to what extent combinations of models can perform better than single surrogate models and provides insights into the scalability and robustness of the approach. The study focuses on multi-modal functions topologies, which are important in surrogate-assisted global optimization.
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.
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.
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.
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.
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.
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.