@inproceedings{46397, abstract = {{In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the R2 indicator exist. In this paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented.}}, author = {{Brockhoff, Dimo and Wagner, Tobias and Trautmann, Heike}}, booktitle = {{Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation}}, isbn = {{9781450311779}}, keywords = {{hypervolume indicator, multiobjective optimization, performance assessment, r2 indicator}}, pages = {{465–472}}, publisher = {{Association for Computing Machinery}}, title = {{{On the Properties of the R2 Indicator}}}, doi = {{10.1145/2330163.2330230}}, year = {{2012}}, } @inproceedings{46396, abstract = {{The steady supply of new optimization methods makes the algorithm selection problem (ASP) an increasingly pressing and challenging task, specially for real-world black-box optimization problems. The introduced approach considers the ASP as a cost-sensitive classification task which is based on Exploratory Landscape Analysis. Low-level features gathered by systematic sampling of the function on the feasible set are used to predict a well-performing algorithm out of a given portfolio. Example-specific label costs are defined by the expected runtime of each candidate algorithm. We use one-sided support vector regression to solve this learning problem. The approach is illustrated by means of the optimization problems and algorithms of the BBOB’09/10 workshop.}}, author = {{Bischl, Bernd and Mersmann, Olaf and Trautmann, Heike and Preuß, Mike}}, booktitle = {{Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation}}, isbn = {{9781450311779}}, keywords = {{machine learning, exploratory landscape analysis, fitness landscape, benchmarking, evolutionary optimization, bbob test set, algorithm selection}}, pages = {{313–320}}, publisher = {{Association for Computing Machinery}}, title = {{{Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning}}}, doi = {{10.1145/2330163.2330209}}, year = {{2012}}, } @article{46399, abstract = {{Meta-modeling has become a crucial tool in solving expensive optimization problems. Much of the work in the past has focused on finding a good regression method to model the fitness function. Examples include classical linear regression, splines, neural networks, Kriging and support vector regression. This paper specifically draws attention to the fact that assessing model accuracy is a crucial aspect in the meta-modeling framework. Resampling strategies such as cross-validation, subsampling, bootstrapping, and nested resampling are prominent methods for model validation and are systematically discussed with respect to possible pitfalls, shortcomings, and specific features. A survey of meta-modeling techniques within evolutionary optimization is provided. In addition, practical examples illustrating some of the pitfalls associated with model selection and performance assessment are presented. Finally, recommendations are given for choosing a model validation technique for a particular setting.}}, author = {{Bischl, B and Mersmann, O and Trautmann, Heike and Weihs, C}}, journal = {{Evolutionary Computation Journal}}, number = {{2}}, pages = {{249–275}}, title = {{{Resampling Methods in Model Validation}}}, doi = {{10.1162/EVCO_a_00069}}, volume = {{20}}, year = {{2012}}, } @article{46400, abstract = {{Es werden mehrkriterielle evolutio-näre Algorithmen (EMOA) für zwei- und höherdimensio-nale Probleme vorgestellt, die gleichmäßig verteilte Lö-sungen entlang der wahren Paretofront generieren. Diesist insbesondere wichtig im Kontext mehrkriterieller Kon-trollprobleme. Die Methodik beruht auf der Minimierungdes gemittelten Hausdorff-Abstandes in Bezug aufdie Paretofront. Die EMOA-Varianten werden vergleichendzu aktuellen Verfahren auf Benchmarkproblemen getestet.}}, author = {{Rudolph, G and Trautmann, Heike and Schütze, O}}, journal = {{at-Automatisierungstechnik}}, pages = {{610–621}}, title = {{{Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen}}}, doi = {{10.1524/auto.2012.1033}}, volume = {{60}}, year = {{2012}}, } @inproceedings{48890, abstract = {{With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem TSP. Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.}}, author = {{Mersmann, Olaf and Bischl, Bernd and Bossek, Jakob and Trautmann, Heike and Wagner, Markus and Neumann, Frank}}, booktitle = {{Revised Selected Papers of the 6th International Conference on Learning and Intelligent Optimization - Volume 7219}}, isbn = {{978-3-642-34412-1}}, keywords = {{2-opt, Classification, Feature Selection, MARS, TSP}}, pages = {{115–129}}, publisher = {{Springer-Verlag}}, title = {{{Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness}}}, year = {{2012}}, } @inbook{48888, abstract = {{With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.}}, author = {{Mersmann, Olaf and Bischl, Bernd and Bossek, Jakob and Trautmann, Heike and Wagner, Markus and Neumann, Frank}}, booktitle = {{Learning and Intelligent Optimization}}, isbn = {{978-3-642-34412-1 978-3-642-34413-8}}, pages = {{115–129}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness}}}, doi = {{10.1007/978-3-642-34413-8_9}}, volume = {{7219}}, year = {{2012}}, } @inproceedings{46398, abstract = {{With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.}}, author = {{Mersmann, Olaf and Bischl, Bernd and Bossek, Jakob and Trautmann, Heike and Wagner, Markus and Neumann, Frank}}, booktitle = {{Learning and Intelligent Optimization}}, editor = {{Hamadi, Youssef and Schoenauer, Marc}}, isbn = {{978-3-642-34413-8}}, pages = {{115–129}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness}}}, doi = {{https://doi.org/10.1007/978-3-642-34413-8_9}}, year = {{2012}}, } @inproceedings{46401, abstract = {{Exploratory Landscape Analysis subsumes a number of techniques employed to obtain knowledge about the properties of an unknown optimization problem, especially insofar as these properties are important for the performance of optimization algorithms. Where in a first attempt, one could rely on high-level features designed by experts, we approach the problem from a different angle here, namely by using relatively cheap low-level computer generated features. Interestingly, very few features are needed to separate the BBOB problem groups and also for relating a problem to high-level, expert designed features, paving the way for automatic algorithm selection.}}, author = {{Mersmann, Olaf and Bischl, Bernd and Trautmann, Heike and Preuss, Mike and Weihs, Claus and Rudolph, Günter}}, booktitle = {{Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation}}, isbn = {{9781450305570}}, keywords = {{exploratory landscape analysis, evolutionary optimization, fitness landscape, benchmarking, BBOB test set}}, pages = {{829–836}}, publisher = {{Association for Computing Machinery}}, title = {{{Exploratory Landscape Analysis}}}, doi = {{10.1145/2001576.2001690}}, year = {{2011}}, } @inproceedings{46402, abstract = {{The use of multi-objective evolutionary algorithms for solving black-box problems with multiple conflicting objectives has become an important research area. However, when no gradient information is available, the examination of formal convergence or optimality criteria is often impossible. Thus, sophisticated heuristic online stopping criteria (OSC) have recently become subject of intensive research. In order to establish formal guidelines for a systematic research, we present a taxonomy of OSC in this paper. We integrate the known approaches within the taxonomy and discuss them by extracting their building blocks. The formal structure of the taxonomy is used as a basis for the implementation of a comprehensive MATLAB toolbox. Both contributions, the formal taxonomy and the MATLAB implementation, provide a framework for the analysis and evaluation of existing and new OSC approaches.}}, author = {{Wagner, Tobias and Trautmann, Heike and Martí, Luis}}, booktitle = {{Evolutionary Multi-Criterion Optimization}}, editor = {{Takahashi, Ricardo H. C. and Deb, Kalyanmoy and Wanner, Elizabeth F. and Greco, Salvatore}}, isbn = {{978-3-642-19893-9}}, pages = {{16–30}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms}}}, doi = {{https://doi.org/10.1007/978-3-642-19893-9_2}}, year = {{2011}}, } @article{46403, abstract = {{ Evolutionary (multi-objective optimization) algorithms (EMOAs) are widely accepted to be competitive optimization methods in industry today. However, normally only standard techniques are employed by the engineering experts. Here, it is shown how these standard techniques can be completed and improved with respect to interactivity to other tools, runtime, and parameterization. The coupling with metamodels serves as an example for the interactivity to other tools, while the online convergence detection relates to runtime, i.e. stopping criteria. Finally, sequential parameter optimization improves results focussing on parameter tuning. We show that invoking all these methods on their own already enhances EMOAs for aerodynamic applications. It is concluded with an outlook on how these methods might come together to foster aerospace applications and, at a time, widen the application area to multi-disciplinary optimization tasks. }}, author = {{Naujoks, B and Trautmann, Heike and Wessing, S and Weihs, C}}, journal = {{Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering}}, number = {{10}}, pages = {{1081--1096}}, title = {{{Advanced concepts for multi-objective evolutionary optimization in aircraft industry}}}, doi = {{10.1177/0954410011414120}}, volume = {{225}}, year = {{2011}}, } @inproceedings{46408, abstract = {{The integration of experts’ preferences is an important aspect in multi-objective optimization. Usually, one out of a set of Pareto optimal solutions has to be chosen based on expert knowledge. A combination of multi-objective particle swarm optimization (MOPSO) with the desirability concept is introduced to efficiently focus on desired and relevant regions of the true Pareto front of the optimization problem which facilitates the solution selection process. Desirability functions of the objectives are optimized, and the desirability index is used for selecting the global best particle in each iteration. The resulting MOPSO variant DF-MOPSO in most cases exclusively generates solutions in the desired area of the Pareto front. Approximations of the whole Pareto front result in cases of misspecified desired regions.}}, author = {{Mostaghim, Sanaz and Trautmann, Heike and Mersmann, Olaf}}, booktitle = {{Parallel Problem Solving from Nature, PPSN XI}}, editor = {{Schaefer, Robert and Cotta, Carlos and Kołodziej, Joanna and Rudolph, Günter}}, isbn = {{978-3-642-15871-1}}, pages = {{101–110}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Preference-Based Multi-Objective Particle Swarm Optimization Using Desirabilities}}}, doi = {{https://doi.org/10.1007/978-3-642-15871-1_11}}, year = {{2010}}, } @inproceedings{46405, abstract = {{We present methods to answer two basic questions that arise when benchmarking optimization algorithms. The first one is: which algorithm is the ’best’ one? and the second one: which algorithm should I use for my real world problem? Both are connected and neither is easy to answer. We present methods which can be used to analyse the raw data of a benchmark experiment and derive some insight regarding the answers to these questions. We employ the presented methods to analyse the BBOB’09 benchmark results and present some initial findings.}}, author = {{Mersmann, Olaf and Preuss, Mike and Trautmann, Heike}}, booktitle = {{Proceedings of the 11th International Conference on Parallel Problem Solving from Nature: Part I}}, isbn = {{3642158439}}, keywords = {{benchmarking, multidimensional scaling, consensus ranking, evolutionary optimization, BBOB test set}}, pages = {{73–82}}, publisher = {{Springer-Verlag}}, title = {{{Benchmarking Evolutionary Algorithms: Towards Exploratory Landscape Analysis}}}, year = {{2010}}, } @inproceedings{46406, abstract = {{We present methods to answer two basic questions that arise when benchmarking optimization algorithms. The first one is: which algorithm is the 'best' one? and the second one: which algorithm should I use for my real world problem? Both are connected and neither is easy to answer. We present methods which can be used to analyse the raw data of a benchmark experiment and derive some insight regarding the answers to these questions. We employ the presented methods to analyse the BBOB'09 benchmark results and present some initial findings.}}, author = {{Mersmann, O and Trautmann, Heike and Naujoks, B and Weihs, C}}, booktitle = {{Learning and Intelligent Optimization, 4$^th$ International Conference, LION 4, Venice, Italy}}, editor = {{Blum, C and Battiti, R}}, pages = {{333–337}}, publisher = {{Springer}}, title = {{{On the Distribution of EMOA Hypervolumes}}}, volume = {{6073}}, year = {{2010}}, } @inproceedings{46407, abstract = {{Choosing and tuning an optimization procedure for a given class of nonlinear optimization problems is not an easy task. One way to proceed is to consider this as a tournament, where each procedure will compete in different ‘disciplines’. Here, disciplines could either be different functions, which we want to optimize, or specific performance measures of the optimization procedure. We would then be interested in the algorithm that performs best in a majority of cases or whose average performance is maximal. We will focus on evolutionary multiobjective optimization algorithms (EMOA), and will present a novel approach to the design and analysis of evolutionary multiobjective benchmark experiments based on similar work from the context of machine learning. We focus on deriving a consensus among several benchmarks over different test problems and illustrate the methodology by reanalyzing the results of the CEC 2007 EMOA competition.}}, author = {{Mersmann, Olaf and Trautmann, Heike and Naujoks, Boris and Weihs, Claus}}, booktitle = {{IEEE Congress on Evolutionary Computation}}, issn = {{1941-0026}}, pages = {{1--8}}, title = {{{Benchmarking evolutionary multiobjective optimization algorithms}}}, doi = {{10.1109/CEC.2010.5586241}}, year = {{2010}}, } @inproceedings{46404, author = {{Ding, J and Wessing, S and Trautmann, Heike and Mehnen, J and Naujoks, B}}, booktitle = {{Proceedings of the 7$^th$ CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (CIRP ICME ’10)}}, editor = {{Teti, R}}, publisher = {{Copyright C.O.C. Com. org. Conv.}}, title = {{{Sequential Parameter Optimisation for Multi-Objective Evolutionary Optimisation of Additive Layer Manufacturing}}}, year = {{2010}}, } @inproceedings{46409, abstract = {{Since many real-world optimization problems are noisy, vector optimization algorithms that can cope with noise and uncertainty are required. We propose new, robust selection strategies for evolutionary multi-objective optimization in the presence of noise. We apply new measures of uncertainty for estimating the recently introduced Pareto-dominance for uncertain and noisy environments (PDU). The first measure is the inter-quartile range of the outcomes of repeated function evaluations. The second is based on axis-aligned bounding boxes around the upper and lower quantiles of the sampled fitness values in objective space. Experiments on real and artificial problems show promising results.}}, author = {{Voß, Thomas and Trautmann, Heike and Igel, Christian}}, booktitle = {{Parallel Problem Solving from Nature, PPSN XI}}, editor = {{Schaefer, Robert and Cotta, Carlos and Kołodziej, Joanna and Rudolph, Günter}}, isbn = {{978-3-642-15871-1}}, pages = {{260–269}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{New Uncertainty Handling Strategies in Multi-objective Evolutionary Optimization}}}, doi = {{https://doi.org/10.1007/978-3-642-15871-1_27}}, year = {{2010}}, } @article{46412, abstract = {{In this paper, a concept for efficiently approximating the practically relevant regions of the Pareto front (PF) is introduced. Instead of the original objectives, desirability functions (DFs) of the objectives are optimized, which express the preferences of the decision maker. The original problem formulation and the optimization algorithm do not have to be modified. DFs map an objective to the domain [0, 1] and nonlinearly increase with better objective quality. By means of this mapping, values of different objectives and units become comparable. A biased distribution of the solutions in the PF approximation based on different scalings of the objectives is prevented. Thus, we propose the integration of DFs into the S-metric selection evolutionary multiobjective algorithm. The transformation ensures the meaning of the hypervolumes internally computed. Furthermore, it is shown that the reference point for the hypervolume calculation can be set intuitively. The approach is analyzed using standard test problems. Moreover, a practical validation by means of the optimization of a turning process is performed.}}, author = {{Wagner, Tobias and Trautmann, Heike}}, issn = {{1941-0026}}, journal = {{IEEE Transactions on Evolutionary Computation}}, number = {{5}}, pages = {{688--701}}, title = {{{Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary Algorithms by Means of Desirability Functions}}}, doi = {{10.1109/TEVC.2010.2058119}}, volume = {{14}}, year = {{2010}}, } @article{46411, abstract = {{The paper presents a framework to optimise the design of work roll based on the cooling performance. The framework develops meta-models from a set of finite element analyses (FEA) of the roll cooling. A design of experiment technique is used to identify the FEA runs. The research also identifies sources of uncertainties in the design process. A robust evolutionary multi-objective evaluation technique is applied to the design optimisation in constrained problems with real life uncertainty. The approach handles uncertainties associated both with design variables and fitness functions. Constraints violation within the neighbourhood of a design is considered as part of a measurement for degree of feasibility and robustness of a solution.}}, author = {{Azene, Y.T. and Roy, R. and Farrugia, D. and Onisa, C. and Mehnen, J. and Trautmann, Heike}}, issn = {{1755-5817}}, journal = {{CIRP Journal of Manufacturing Science and Technology}}, keywords = {{Roll cooling design, Uncertainty, Design optimisation, Multi-objective optimisation, Constraint in design}}, number = {{4}}, pages = {{290--298}}, title = {{{Work roll cooling system design optimisation in presence of uncertainty and constrains}}}, doi = {{https://doi.org/10.1016/j.cirpj.2010.06.001}}, volume = {{2}}, year = {{2010}}, } @inproceedings{46410, abstract = {{The design and application of termination criteria has become an important aspect in evolutionary multi-objective optimization. Online convergence detection (OCD) determines when further generations are no longer promising based on statistical tests on a set of performance indicators. The behavior of OCD mainly depends on two parameters, the number of preceding generations considered in the statistical tests and the desired variance limit. In this paper, guidelines for selecting appropriate combinations of these parameters are empirically derived based on design-of-experiment methods. Furthermore, a variant of OCD is introduced which directly operates on the hypervolume indicator - the internal measure of the SMS-EMOA. This allows a separated analysis of the variance criterion and reduces the complexity of OCD. Based on the experimental design, a systematic comparison with the classical OCD approach is performed and differences between the appropriate parameterizations of both variants are highlighted.}}, author = {{Wagner, Tobias and Trautmann, Heike}}, booktitle = {{IEEE Congress on Evolutionary Computation}}, issn = {{1941-0026}}, pages = {{1--8}}, title = {{{Online convergence detection for evolutionary multi-objective algorithms revisited}}}, doi = {{10.1109/CEC.2010.5586474}}, year = {{2010}}, } @inproceedings{46414, abstract = {{Over the last decades, evolutionary algorithms (EA) have proven their applicability to hard and complex industrial optimization problems in many cases. However, especially in cases with high computational demands for fitness evaluations (FE), the number of required FE is often seen as a drawback of these techniques. This is partly due to lacking robust and reliable methods to determine convergence, which would stop the algorithm before useless evaluations are carried out. To overcome this drawback, we define a method for online convergence detection (OCD) based on statistical tests, which invokes a number of performance indicators and which can be applied on a stand-alone basis (no predefined Pareto fronts, ideal and reference points). Our experiments show the general applicability of OCD by analyzing its performance for different algorithmic setups and on different classes of test functions. Furthermore, we show that the number of FE can be reduced considerably – compared to common suggestions from literature – without significantly deteriorating approximation accuracy.}}, author = {{Wagner, Tobias and Trautmann, Heike and Naujoks, Boris}}, booktitle = {{Evolutionary Multi-Criterion Optimization}}, editor = {{Ehrgott, Matthias and Fonseca, Carlos M. and Gandibleux, Xavier and Hao, Jin-Kao and Sevaux, Marc}}, isbn = {{978-3-642-01020-0}}, pages = {{198–215}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{OCD: Online Convergence Detection for Evolutionary Multi-Objective Algorithms Based on Statistical Testing}}}, doi = {{https://doi.org/10.1007/978-3-642-01020-0_19}}, year = {{2009}}, }