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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 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.
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.
This survey compiles ideas and recommendations from more than a dozen researchers with different backgrounds and from different institutes around the world. Promoting best practice in benchmarking is its main goal. The article discusses eight essential topics in benchmarking: clearly stated goals, well- specified problems, suitable algorithms, adequate performance measures, thoughtful analysis, effective and efficient designs, comprehensible presentations, and guaranteed reproducibility. The final goal is to provide well-accepted guidelines (rules) that might be useful for authors and reviewers. As benchmarking in optimization is an active and evolving field of research this manuscript is meant to co-evolve over time by means of periodic updates.
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.
When researchers and practitioners in the field of
computational intelligence are confronted with real-world
problems, the question arises which method is the best to
apply. Nowadays, there are several, well established test
suites and well known artificial benchmark functions
available.
However, relevance and applicability of these methods to
real-world problems remains an open question in many
situations. Furthermore, the generalizability of these
methods cannot be taken for granted.
This paper describes a data-driven approach for the
generation of test instances, which is based on
real-world data. The test instance generation uses
data-preprocessing, feature extraction, modeling, and
parameterization. We apply this methodology on a classical
design of experiment real-world project and generate test
instances for benchmarking, e.g. design methods, surrogate
techniques, and optimization algorithms. While most
available results of methods applied on real-world
problems lack availability of the data for comparison,
our future goal is to create a toolbox covering multiple
data sets of real-world projects to provide a test
function generator to the research community.
RGP is genetic programming system based on, as well as fully integrated into, the R environment. The system implements classical tree-based genetic programming as well as other variants including, for example, strongly typed genetic programming and Pareto genetic programming. It strives for high modularity through a consistent architecture that allows the customization and replacement of every algorithm component, while maintaining accessibility for new users by adhering to the "convention over configuration" principle.
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.
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.
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.
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.
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.
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.