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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.
There is a strong need for sound statistical analysis of simulation and optimization algorithms. Based on this analysis, improved parameter settings can be determined. This will be referred to as tuning. Model-based investigations are common approaches in simulation and optimization. The sequential parameter optimization toolbox (SPOT), which is implemented as a package for the statistical programming language R, provides sophisticated means for tuning and understanding simulation and optimization algorithms. The toolbox includes methods for tuning based on classical regression and analysis of variance techniques; tree-based models such as classification and regressions trees (CART) and random forest; Gaussian process models (Kriging), and combinations of different meta-modeling approaches. This article exemplifies how an existing optimization algorithm, namely simulated annealing, can be tuned using the SPOT framework.
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.
Dieser Schlussbericht beschreibt die im Projekt „CI-basierte mehrkriterielle Optimierungsverfahren für Anwendungen in der Industrie“ (CIMO) im Zeitraum von November 2011 bis einschließlich Oktober 2014 erzielten Ergebnisse. Für aufwändige Optimierungsprobleme aus der Industrie wurden geeignete Lösungsverfahren entwickelt. Der Schwerpunkt lag hierbei auf Methoden aus den Bereichen Computational Intelligence (CI) und Surrogatmodellierung. Diese bieten die Möglichkeit, wichtige Herausforderung von aufwändigen, komplexen Optimierungsproblemen zu lösen. Die entwickelten Methoden können verschiedene konfliktäre Zielgrößen berücksichtigen, verschiedene Hierarchieebenen des Problems in die Optimierung integrieren, Nebenbedingungen beachten, vektorielle aber auch strukturierte Daten verarbeiten (kombinatorische Optimierung) sowie die Notwendigkeit teurer/zeitaufwändiger Zielfunktionsberechnungen reduzieren. Die entwickelten Methoden wurden schwerpunktmäßig auf einer Problemstellung aus der Kraftwerkstechnik angewendet, nämlich der Optimierung der Geometrie eines Fliehkraftabscheiders (auch: Zyklon), der Staubanteile aus Abgasen filtert. Das Optimierungsproblem, das diese FIiehkraftabscheider aufwerfen, führt zu konfliktären Zielsetzungen (z.B. Druckverlust, Abscheidegrad). Zyklone können unter anderem über aufwändige Computational Fluid Dynamics (CFD) Simulationen berechnet werden, es stehen aber auch einfache analytische Gleichungen als Schätzung zu Verfügung. Die Verknüpfung von beidem zeigt hier beispielhaft wie Hierarchieebenen eines Optimierungsproblems mit den Methoden des Projektes verbunden werden können. Neben dieser Schwerpunktanwendung konnte auch gezeigt werden, dass die Methoden in vielen weiteren Bereichen Erfolgreich zur Anwendung kommen können: Biogaserzeugung, Wasserwirtschaft, Stahlindustrie. Die besondere Herausforderung der behandelten Probleme und Methoden bietet viele wichtige Forschungsmöglichkeiten für zukünftige Projekte, die derzeit durch die Projektpartner vorbereitet werden.
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.
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.
Ziel des Forschungsprojektes "Mehrkriterielle CI-basierte Optimierungsverfahren für den industriellen Einsatz" (MCIOP) war die Verringerung von Schadstoffemissionen in Kohlekraftwerken. Der wissenschaftliche Fokus lag auf der Entwicklung von Methoden, die in der Lage sind, interpretierbare Modelle für die Schadstoffemissionen automatisch zu generieren. Hierzu wurden mehrkriterielle Optimierungsverfahren entwickelt und eingesetzt. Zur Zeit- und Kostenreduktion wurde die Optimierung durch Surrogat-Modelle erfolgen, die abgestuft mit aufwändigeren Simulationen zum Einsatz kamen („optimization via simulation“). Bei der Untersuchung von Staubabscheidern konnten durch eine mehrkriterielle Optimierung unterschiedliche Zielgrößen, wie z.B. Abscheidegrad und Druckverlust, gleichzeitig berücksichtigt werden.
Dieser Bericht beschreibt die im Projekt MCIOP im Zeitraum von August 2011 bis einschließlich Juni 2015 erzielten Ergebnisse.
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.
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.